Digital signal processing (DSP) Books

Book SynopsisThe focus of this book is on providing students with insights into geometry that can help them understand deep learning from a unified perspective. Rather than describing deep learning as an implementation technique, as is usually the case in many existing deep learning books, here, deep learning is explained as an ultimate form of signal processing techniques that can be imagined. To support this claim, an overview of classical kernel machine learning approaches is presented, and their advantages and limitations are explained. Following a detailed explanation of the basic building blocks of deep neural networks from a biological and algorithmic point of view, the latest tools such as attention, normalization, Transformer, BERT, GPT-3, and others are described. Here, too, the focus is on the fact that in these heuristic approaches, there is an important, beautiful geometric structure behind the intuition that enables a systematic understanding. A unified geometric analysis to understand the working mechanism of deep learning from high-dimensional geometry is offered. Then, different forms of generative models like GAN, VAE, normalizing flows, optimal transport, and so on are described from a unified geometric perspective, showing that they actually come from statistical distance-minimization problems.Because this book contains up-to-date information from both a practical and theoretical point of view, it can be used as an advanced deep learning textbook in universities or as a reference source for researchers interested in acquiring the latest deep learning algorithms and their underlying principles. In addition, the book has been prepared for a codeshare course for both engineering and mathematics students, thus much of the content is interdisciplinary and will appeal to students from both disciplines.Trade Review“This book is based on material that has been prepared for senior-level undergraduate classes, this book can be used for one-semester senior-level undergraduate and graduate-level classes.” (Arzu Ahmadova, zbMATH 1493.68003, 2022)Table of ContentsPart I Basic Tools for Machine Learning: 1. Mathematical Preliminaries.- 2. Linear and Kernel Classifiers.- 3. Linear, Logistic, and Kernel Regression.- 4. Reproducing Kernel Hilbert Space, Representer Theorem.- Part II Building Blocks of Deep Learning: 5. Biological Neural Networks.- 6. Artificial Neural Networks and Backpropagation.- 7. Convolutional Neural Networks.- 8. Graph Neural Networks.- 9. Normalization and Attention.- Part III Advanced Topics in Deep Learning.- 10. Geometry of Deep Neural Networks.- 11. Deep Learning Optimization.- 12. Generalization Capability of Deep Learning.- 13. Generative Models and Unsupervised Learning.- Summary and Outlook.- Bibliography.- Index.

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Book SynopsisTable of Contents1. Introduction to Signal Processing and Machine Learning Theory 2. Continuous-Time Signals and Systems 3. Discrete-Time Signals and Systems 4. Random Signals and Stochastic Processes 5. Sampling and Quantization 6. Digital Filter Structures and Their Implementation 7. Multi-rate Signal Processing for Software Radio Architectures 8. Modern Transform Design for Practical Audio/Image/Video Coding Applications 9. Discrete Multi-Scale Transforms in Signal Processing 10. Frames in Signal Processing 11. Parametric Estimation 12. Adaptive Filters 13. Signal Processing over Graphs 14. Tensors for Signal Processing and Machine Learning 15. Non-convex Optimization for Machine Learning 16. Dictionary Learning and Sparse Representation

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Book SynopsisFoundations.- to Music Transcription.- An Introduction to Statistical Signal Processing and Spectrum Estimation.- Sparse Adaptive Representations for Musical Signals.- Rhythm and Timbre Analysis.- Beat Tracking and Musical Metre Analysis.- Unpitched Percussion Transcription.- Automatic Classification of Pitched Musical Instrument Sounds.- Multiple Fundamental Frequency Analysis.- Multiple Fundamental Frequency Estimation Based on Generative Models.- Auditory Model-Based Methods for Multiple Fundamental Frequency Estimation.- Unsupervised Learning Methods for Source Separation in Monaural Music Signals.- Entire Systems, Acoustic and Musicological Modelling.- Auditory Scene Analysis in Music Signals.- Music Scene Description.- Singing Transcription.Table of ContentsFoundations.- to Music Transcription.- An Introduction to Statistical Signal Processing and Spectrum Estimation.- Sparse Adaptive Representations for Musical Signals.- Rhythm and Timbre Analysis.- Beat Tracking and Musical Metre Analysis.- Unpitched Percussion Transcription.- Automatic Classification of Pitched Musical Instrument Sounds.- Multiple Fundamental Frequency Analysis.- Multiple Fundamental Frequency Estimation Based on Generative Models.- Auditory Model-Based Methods for Multiple Fundamental Frequency Estimation.- Unsupervised Learning Methods for Source Separation in Monaural Music Signals.- Entire Systems, Acoustic and Musicological Modelling.- Auditory Scene Analysis in Music Signals.- Music Scene Description.- Singing Transcription.

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Book SynopsisThis book discusses non-conventional digital signal processing based on direct processing of delta-sigma modulated bit-stream. The main attributes of low-pass delta-sigma analog-to-digital converters are: simple and inexpensive design, robustness of design to component tolerances, low-power consumption, high input impedance, high resolution (more than 20 bits) and possibility of direct arithmetic operation on its bit-stream. The author presents a number of theoretical and simulation results related to newly proposed linear and non-linear circuits such as delta-sigma adders, delta-sigma rectifiers, delta-sigma RMS and AGC circuits, delta-sigma frequency deviation meters, etc. The proposed circuits are not application limited and can be used in instrumentation, sensor application, bio-medical application, communications, etc. Presents novel linear and nonlinear circuits for direct processing of delta-sigma modulated bit-stream; The proposed circuits are supported by theoretical and simulation results; Recommends potential applications of the proposed circuits, and proposes ideas for further investigation. Table of ContentsChapter 1. Basics of Low-Pass Modulation.- Chapter 2. Linear Processing of Delta-Modulated Bit-Stream.- Chapter 3. Rectification of a Delta-Sigma Modulated Signal.- Chapter 4. Multiplication of Two Δ-Σ Bit-Streams.- Chapter 5. Digital Architecture for Δ-Σ RMS-to-DC Converter.- Chapter 6. Companding Circuits and Systems Based on Δ-Σ Modulation.- Chapter 7. A Δ-Σ Digital Stereo Multiplexing-Demultiplexing System.- Chapter 8. Δ-Σ Digital Amplitude Modulation System.- Chapter 9. Δ-Σ Methods for Frequency Deviation Measurement of a Known Nominal Frequency.- Chapter 10. Δ-Σ Automatic Gain Controller.- Chapter 11. Δ-Σ Integrator and Differentiator Circuits.

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Book SynopsisAcoustic Signals and Systems.- Signals and Systems.- Acoustic Data Acquisition.- Spectral Analysis and Correlation.- The FFT and Tone Identification.- Measuring Transfer-Functions and Impulse Responses.- Digital Sequences.- Filters.- Adaptive Processing.- Beamforming and Wavenumber Processing.- Auditory System and Hearing.- Anatomy, Physiology and Function of the Auditory System.- Physiological Measures of Auditory Function.- Auditory Processing Models.- Speech Intelligibility.- Signal Processing in Hearing Aids.- Psychoacoustics.- Methods for Psychoacoustics in Relation to Long-Term Sounds.- Masking and Critical Bands.- Aspects of Modeling Pitch Perception.- Calculation of Loudness for Normal and Hearing-Impaired Listeners.- Psychoacoustical Roughness.- Musical Acoustics.- Automatic Music Transcription.- Music Structure Analysis from Acoustic Signals.- Computer Music Synthesis and Composition.- Singing Voice Analysis, Synthesis, and Modeling.- Instrument Modeling and Synthesis.- DigitTrade ReviewFrom the reviews:“The ‘Handbook of Signal Processing in Acoustics’ provides an excellent reference for practicing acousticians and engineers. … encompasses essential background material, technical details, standards, and practical tips. It is aimed to a public with some knowledge of signal processing, and it is meant to be used as a reference. … Signal processing techniques which find major application in different areas of acoustics are well presented from different perspectives … . this compendium is an excellent reference for engineers and professionals working in acoustics.” (Joaquin E. Moran, Noise Control Engineering Journal, Vol. 58 (6), November-December, 2010)Table of Contents1. Acoustical oceanography Models for Propagation Codes Transducer Arrays: structure, data acquisition, signal generation, calibration Sonar MFP Tomography Other Inverse Techniques Signal and Noise Characteristics 2. Active Noise Control Principles of adaptive techniques Plant modeling Sound/vibration field sensing Actuator characteristics and requirements Performance limitations Multi-channel systems Performance and complexity 3. Animal bioacoustics Recording and monitoring systems Models of echolocation Hearing performance and modelling Characteristics of calls Stimuli generation Locating and tracking Archives and Databases of signals 4. Architectural acoustics Room models Measurement of transmissions, absorption, reverberation, etc. Sound fields (definitions, criteria, measurement, typical values) MLS and other coded signals Auralization: Modelling techniques, listening modes, processing requirements, existing systems, performace Artificial reverberation Sound reinforcement Acoustic privacy 5. Audio engineering Transducer modeling Loudspeaker performance characteristics Audio recording and playback formats Audio-visual interaction ADC, DAC, and Codec technologies Multi-channel sound and Virtual audio Restoration Digital audio editing Effects generation 6. Auditory System, Hearing Modeling of hearing Thresholds and Masking Frequency and level discrimination Binaural hearing and spatialization HRTF HATS and other physical models Hearing aids Auditory illusions 7. Education in acoustics 8. Electroacoustics Microphone types and their characteristics Vibration sensors and their characteristics Acoustic actuators and their characteristics Smart sensors and actuators 9. Engineering acoustics 10. Infrasonics Background noise and source signals Sensors and their characteristics Propagation models Event detection Data archiving Source identification 11. Musical Acoustics Computer music synthesis and composition Computer music recognition and analysis Singing voice analysis, synthesis, and processing Instrument measurement, modeling and synthesis Coding and compression of music 12. Noise Noise source modeling Acoustic holography Atmospheric sound propagation Source localization Noise evaluation and Annoyance thresholds 13. Non-linear acoustics Propagation equations and codes Example non-linear systems Parametric array Measurement methods Detection of non-linearities 14. Psychoacoustics Perceptual models Cochlear implants Auditory alarms 15. Seismology Seismic Coda Acoustic Profiling Propagation modes and properties for modeling Seismo-acoustic coupling 16. Speech Characteristics of speech as signals Synthesis Recognition Intelligibility and quality metrics Corpus for tests Coding and compression Display and analysis 17. Strutural acoustics and vibration BEM, FEM, EA, etc. Actuator design and deployment Propagation and radiation Machine diagnostics and prognosis Modeling, measuring and analyzing shock Materials testing 18. Telecomm POTS Wideband Echo supression Hearing aids Handset, Headset, and Wireless standards Systems for handicapped users 19. Ultrasonics

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Book SynopsisMultimedia Signal Processing is a comprehensive and accessible text to the theory and applications of digital signal processing (DSP). The applications of DSP are pervasive and include multimedia systems, cellular communication, adaptive network management, radar, pattern recognition, medical signal processing, financial data forecasting, artificial intelligence, decision making, control systems and search engines. This book is organised in to three major parts making it a coherent and structured presentation of the theory and applications of digital signal processing. A range of important topics are covered in basic signal processing, model-based statistical signal processing and their applications. Part 1: Basic Digital Signal Processing gives an introduction to the topic, discussing sampling and quantization, Fourier analysis and synthesis, Z-transform, and digital filters. Part 2: Model-based Signal Processing covers probability and infoTrade Review"A valuable and accessible text … .Suited not only for senior undergraduates and postgraduates but also for researchers and engineers." (Zentralblatt Math, 2008/17)Table of ContentsPreface. Acknowledgement. Symbols. Abbreviations. Part I Basic Digital Signal Processing. 1 Introduction. 1.1 Signals and Information. 1.2 Signal Processing Methods. 1.3 Applications of Digital Signal Processing. 1.4 Summary. 2 Fourier Analysis and Synthesis. 2.1 Introduction. 2.2 Fourier Series: Representation of Periodic Signals. 2.3 Fourier Transform: Representation of Nonperiodic Signals. 2.4 Discrete Fourier Transform. 2.5 Short-Time Fourier Transform. 2.6 Fast Fourier Transform (FFT). 2.7 2-D Discrete Fourier Transform (2-D DFT). 2.8 Discrete Cosine Transform (DCT). 2.9 Some Applications of the Fourier Transform. 2.10 Summary. 3 z-Transform. 3.1 Introduction. 3.2 Derivation of the z-Transform. 3.3 The z-Plane and the Unit Circle. 3.4 Properties of z-Transform. 3.5 z-Transfer Function, Poles (Resonance) and Zeros (Anti-resonance). 3.6 z-Transform of Analysis of Exponential Transient Signals. 3.7 Inverse z-Transform. 3.8 Summary. 4 Digital Filters. 4.1 Introduction. 4.2 Linear Time-Invariant Digital Filters. 4.3 Recursive and Non-Recursive Filters. 4.4 Filtering Operation: Sum of Vector Products, A Comparison of Convolution and Correlation. 4.5 Filter Structures: Direct, Cascade and Parallel Forms. 4.6 Linear Phase FIR Filters. 4.7 Design of Digital FIR Filter-banks. 4.8 Quadrature Mirror Sub-band Filters. 4.9 Design of Infinite Impulse Response (IIR) Filters by Pole–zero Placements. 4.10 Issues in the Design and Implementation of a Digital Filter. 4.11 Summary. 5 Sampling and Quantisation. 5.1 Introduction. 5.2 Sampling a Continuous-Time Signal. 5.3 Quantisation. 5.4 Sampling Rate Conversion: Interpolation and Decimation. 5.5 Summary. Part II Model-Based Signal Processing. 6 Information Theory and Probability Models. 6.1 Introduction: Probability and Information Models. 6.2 Random Processes. 6.3 Probability Models of Random Signals. 6.4 Information Models. 6.5 Stationary and Non-Stationary Random Processes. 6.6 Statistics (Expected Values) of a Random Process. 6.7 Some Useful Practical Classes of Random Processes. 6.8 Transformation of a Random Process. 6.9 Search Engines: Citation Ranking. 6.10 Summary. 7 Bayesian Inference. 7.1 Bayesian Estimation Theory: Basic Definitions. 7.2 Bayesian Estimation. 7.3 Expectation Maximisation Method. 7.4 Cramer–Rao Bound on the Minimum Estimator Variance. 7.5 Design of Gaussian Mixture Models (GMM). 7.6 Bayesian Classification. 7.7 Modelling the Space of a Random Process. 7.8 Summary. 8 Least Square Error, Wiener–Kolmogorov Filters. 8.1 Least Square Error Estimation: Wiener–Kolmogorov Filter. 8.2 Block-Data Formulation of the Wiener Filter. 8.3 Interpretation of Wiener Filter as Projection in Vector Space. 8.4 Analysis of the Least Mean Square Error Signal. 8.5 Formulation of Wiener Filters in the Frequency Domain. 8.6 Some Applications of Wiener Filters. 8.7 Implementation of Wiener Filters. 8.8 Summary. 9 Adaptive Filters: Kalman, RLS, LMS. 9.1 Introduction. 9.2 State-Space Kalman Filters. 9.3 Sample Adaptive Filters. 9.4 Recursive Least Square (RLS) Adaptive Filters. 9.5 The Steepest-Descent Method. 9.6 LMS Filter. 9.7 Summary. 10 Linear Prediction Models. 10.1 Linear Prediction Coding. 10.2 Forward, Backward and Lattice Predictors. 10.3 Short-Term and Long-Term Predictors. 10.4 MAP Estimation of Predictor Coefficients. 10.5 Formant-Tracking LP Models. 10.6 Sub-Band Linear Prediction Model. 10.7 Signal Restoration Using Linear Prediction Models. 10.8 Summary. 11 Hidden Markov Models. 11.1 Statistical Models for Non-Stationary Processes. 11.2 Hidden Markov Models. 11.3 Training Hidden Markov Models. 11.4 Decoding Signals Using Hidden Markov Models. 11.5 HMM in DNA and Protein Sequences. 11.6 HMMs for Modelling Speech and Noise. 11.7 Summary. 12 Eigenvector Analysis, Principal Component Analysis and Independent Component Analysis. 12.1 Introduction – Linear Systems and Eigenanalysis. 12.2 Eigenvectors and Eigenvalues. 12.3 Principal Component Analysis (PCA). 12.4 Independent Component Analysis. 12.5 Summary. Part III Applications of Digital Signal Processing to Speech, Music and Telecommunications. 13 Music Signal Processing and Auditory Perception. 13.1 Introduction. 13.2 Musical Notes, Intervals and Scales. 13.3 Musical Instruments. 13.4 Review of Basic Physics of Sounds. 13.5 Music Signal Features and Models. 13.6 Anatomy of the Ear and the Hearing Process. 13.7 Psychoacoustics of Hearing. 13.8 Music Coding (Compression). 13.9 High Quality Audio Coding: MPEG Audio Layer-3 (MP3). 13.10 Stereo Music Coding. 13.11 Summary. 14 Speech Processing. 14.1 Speech Communication. 14.2 Acoustic Theory of Speech: The Source–filter Model. 14.3 Speech Models and Features. 14.4 Linear Prediction Models of Speech. 14.5 Harmonic Plus Noise Model of Speech. 14.6 Fundamental Frequency (Pitch) Information. 14.7 Speech Coding. 14.8 Speech Recognition. 14.9 Summary. 15 Speech Enhancement. 15.1 Introduction. 15.2 Single-Input Speech Enhancement Methods. 15.3 Speech Bandwidth Extension – Spectral Extrapolation. 15.4 Interpolation of Lost Speech Segments – Packet Loss Concealment. 15.5 Multi-Input Speech Enhancement Methods. 15.6 Speech Distortion Measurements. 15.7 Summary. 16 Echo Cancellation. 16.1 Introduction: Acoustic and Hybrid Echo. 16.2 Telephone Line Hybrid Echo. 16.3 Hybrid (Telephone Line) Echo Suppression. 16.4 Adaptive Echo Cancellation. 16.5 Acoustic Echo. 16.6 Sub-Band Acoustic Echo Cancellation. 16.7 Echo Cancellation with Linear Prediction Pre-whitening. 16.8 Multi-Input Multi-Output Echo Cancellation. 16.9 Summary. 17 Channel Equalisation and Blind Deconvolution. 17.1 Introduction. 17.2 Blind Equalisation Using Channel Input Power Spectrum. 17.3 Equalisation Based on Linear Prediction Models. 17.4 Bayesian Blind Deconvolution and Equalisation. 17.5 Blind Equalisation for Digital Communication Channels. 17.6 Equalisation Based on Higher-Order Statistics. 17.7 Summary. 18 Signal Processing in Mobile Communication. 18.1 Introduction to Cellular Communication. 18.2 Communication Signal Processing in Mobile Systems. 18.3 Capacity, Noise, and Spectral Efficiency. 18.4 Multi-path and Fading in Mobile Communication. 18.5 Smart Antennas – Space–Time Signal Processing. 18.6 Summary. Index.

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Book SynopsisThe filtering of real world signals requires an adaptive mode of operation to deal with the statistically nonstationary nature of the data. Feedback and nonlinearity within filtering architectures are needed to cater for long time dependencies and possibly nonlinear signal generating mechanisms.Table of ContentsPreface xiii Acknowledgements xvii 1 The Magic of Complex Numbers 1 1.1 History of Complex Numbers 2 1.2 History of Mathematical Notation 8 1.3 Development of Complex Valued Adaptive Signal Processing 9 2 Why Signal Processing in the Complex Domain? 13 2.1 Some Examples of Complex Valued Signal Processing 13 2.2 Modelling in C is Not Only Convenient But Also Natural 19 2.3 Why Complex Modelling of Real Valued Processes? 20 2.4 Exploiting the Phase Information 23 2.5 Other Applications of Complex Domain Processing of Real Valued Signals 26 2.6 Additional Benefits of Complex Domain Processing 29 3 Adaptive Filtering Architectures 33 3.1 Linear and Nonlinear Stochastic Models 34 3.2 Linear and Nonlinear Adaptive Filtering Architectures 35 3.3 State Space Representation and Canonical Forms 39 4 Complex Nonlinear Activation Functions 43 4.1 Properties of Complex Functions 43 4.2 Universal Function Approximation 46 4.3 Nonlinear Activation Functions for Complex Neural Networks 48 4.4 Generalised Splitting Activation Functions (GSAF) 53 4.5 Summary: Choice of the Complex Activation Function 54 5 Elements of CR Calculus 55 5.1 Continuous Complex Functions 56 5.2 The Cauchy–Riemann Equations 56 5.3 Generalised Derivatives of Functions of Complex Variable 57 5.4 CR-derivatives of Cost Functions 62 6 Complex Valued Adaptive Filters 69 6.1 Adaptive Filtering Configurations 70 6.2 The Complex Least Mean Square Algorithm 73 6.3 Nonlinear Feedforward Complex Adaptive Filters 80 6.4 Normalisation of Learning Algorithms 85 6.5 Performance of Feedforward Nonlinear Adaptive Filters 87 6.6 Summary: Choice of a Nonlinear Adaptive Filter 89 7 Adaptive Filters with Feedback 91 7.1 Training of IIR Adaptive Filters 92 7.2 Nonlinear Adaptive IIR Filters: Recurrent Perceptron 97 7.3 Training of Recurrent Neural Networks 99 7.4 Simulation Examples 102 8 Filters with an Adaptive Stepsize 107 8.1 Benveniste Type Variable Stepsize Algorithms 108 8.2 Complex Valued GNGD Algorithms 110 8.3 Simulation Examples 113 9 Filters with an Adaptive Amplitude of Nonlinearity 119 9.1 Dynamical Range Reduction 119 9.2 FIR Adaptive Filters with an Adaptive Nonlinearity 121 9.3 Recurrent Neural Networks with Trainable Amplitude of Activation Functions 122 9.4 Simulation Results 124 10 Data-reusing Algorithms for Complex Valued Adaptive Filters 129 10.1 The Data-reusing Complex Valued Least Mean Square (DRCLMS) Algorithm 129 10.2 Data-reusing Complex Nonlinear Adaptive Filters 131 10.3 Data-reusing Algorithms for Complex RNNs 134 11 Complex Mappings and M¨obius Transformations 137 11.1 Matrix Representation of a Complex Number 137 11.2 The M¨obius Transformation 140 11.3 Activation Functions and M¨obius Transformations 142 11.4 All-pass Systems as M¨obius Transformations 146 11.5 Fractional Delay Filters 147 12 Augmented Complex Statistics 151 12.1 Complex Random Variables (CRV) 152 12.2 Complex Circular Random Variables 158 12.3 Complex Signals 159 12.4 Second-order Characterisation of Complex Signals 161 13 Widely Linear Estimation and Augmented CLMS (ACLMS) 169 13.1 Minimum Mean Square Error (MMSE) Estimation in C 169 13.2 Complex White Noise 172 13.3 Autoregressive Modelling in C 173 13.4 The Augmented Complex LMS (ACLMS) Algorithm 175 13.5 Adaptive Prediction Based on ACLMS 178 14 Duality Between Complex Valued and Real Valued Filters 183 14.1 A Dual Channel Real Valued Adaptive Filter 184 14.2 Duality Between Real and Complex Valued Filters 186 14.3 Simulations 188 15 Widely Linear Filters with Feedback 191 15.1 The Widely Linear ARMA (WL-ARMA) Model 192 15.2 Widely Linear Adaptive Filters with Feedback 192 15.4 The Augmented Kalman Filter Algorithm for RNNs 198 15.5 Augmented Complex Unscented Kalman Filter (ACUKF) 200 15.6 Simulation Examples 203 16 Collaborative Adaptive Filtering 207 16.1 Parametric Signal Modality Characterisation 207 16.2 Standard Hybrid Filtering in R 209 16.3 Tracking the Linear/Nonlinear Nature of Complex Valued Signals 210 16.4 Split vs Fully Complex Signal Natures 214 16.5 Online Assessment of the Nature of Wind Signal 216 16.6 Collaborative Filters for General Complex Signals 217 17 Adaptive Filtering Based on EMD 221 17.1 The Empirical Mode Decomposition Algorithm 222 17.2 Complex Extensions of Empirical Mode Decomposition 226 17.3 Addressing the Problem of Uniqueness 230 17.4 Applications of Complex Extensions of EMD 230 18 Validation of Complex Representations – Is This Worthwhile? 233 18.1 Signal Modality Characterisation in R 234 18.2 Testing for the Validity of Complex Representation 239 18.3 Quantifying Benefits of Complex Valued Representation 243 Appendix A: Some Distinctive Properties of Calculus in C 245 Appendix B: Liouville's Theorem 251 Appendix C: Hypercomplex and Clifford Algebras 253 Appendix D: Real Valued Activation Functions 257 Appendix E: Elementary Transcendental Functions (ETF) 259 Appendix F: The O Notation and Standard Vector and Matrix Differentiation 263 Appendix G: Notions From Learning Theory 265 Appendix H: Notions from Approximation Theory 269 Appendix I: Terminology Used in the Field of Neural Networks 273 Appendix J: Complex Valued Pipelined Recurrent Neural Network (CPRNN) 275 Appendix K: Gradient Adaptive Step Size (GASS) Algorithms in R 279 Appendix L: Derivation of Partial Derivatives from Chapter 8 283 Appendix M: A Posteriori Learning 287 Appendix N: Notions from Stability Theory 291 Appendix O: Linear Relaxation 293 Appendix P: Contraction Mappings, Fixed Point Iteration and Fractals 299 References 309 Index 321

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Book SynopsisThe first book to present a systematic and coherent picture of MIMO radars Due to its potential to improve target detection and discrimination capability, Multiple-Input and Multiple-Output (MIMO) radar has generated significant attention and widespread interest in academia, industry, government labs, and funding agencies.Table of ContentsPREFACE. CONTRIBUTORS. 1 MIMO Radar — Diversity Means Superiority (Jian Li and Petre Stoica). 1.1 Introduction. 1.2 Problem Formulation. 1.3 Parameter Identifiability. 1.4 Nonparametric Adaptive Techniques for Parameter Estimation. 1.5 Parametric Techniques for Parameter Estimation. 1.6 Transmit Beampattern Designs. 1.7 Conclusions. Appendix IA Generalized Likelihood Ratio Test. Appendix 1B Lemma and Proof. Acknowledgments. References. 2 MIMO Radar: Concepts, Performance Enhancements, and Applications (Keith W. Forsythe and Daniel W. Bliss). 2.1 Introduction. 2.2 Notation. 2.3 MIMO Radar Virtual Aperture. 2.4 MIMO Radar in Clutter-Free Environments. 2.5 Optimality of MIMO Radar for Detection. 2.6 MIMO Radar with Moving Targets in Clutter: GMTI Radars. 2.7 Summary. Appendix 2A A Localization Principle. Appendix 2B Bounds on R(N). Appendix 2C An Operator Norm Inequality. Appendix 2D Negligible Terms. Appendix 2E Bound on Eigenvalues. Appendix 2F Some Inner Products. Appendix 2G An Invariant Inner Product. Appendix 2H Kro¨necker and Tensor Products. Acknowledgments. References. 3 Generalized MIMO Radar Ambiguity Functions (Geoffrey San Antonio, Daniel R. Fuhrmann, and Frank C. Robey). 3.1 Introduction. 3.2 Background. 3.3 MIMO Signal Model. 3.4 MIMO Parametric Channel Model. 3.5 MIMO Ambiguity Function. 3.6 Results and Examples. 3.7 Conclusion. References. 4 Performance Bounds and Techniques for Target Localization Using MIMO Radars (Joseph Tabrikian). 4.1 Introduction. 4.2 Problem Formulation. 4.3 Properties. 4.4 Target Localization. 4.5 Performance Lower Bound for Target Localization. 4.6 Simulation Results. 4.7 Discussion and Conclusions. Appendix 4A Log-Likelihood Derivation. Appendix 4B Transmit–Receive Pattern Derivation. Appendix 4C Fisher Information Matrix Derivation. References. 5 Adaptive Signal Design For MIMO Radars (Benjamin Friedlander). 5.1 Introduction. 5.2 Problem Formulation. 5.3 Estimation. 5.4 Detection. 5.5 MIMO Radar and Phased Arrays. Appendix 5A Theoretical SINR Calculation. References. 6 MIMO Radar Spacetime Adaptive Processing and Signal Design (Chun-Yang Chen and P. P. Vaidyanathan). 6.1 Introduction. 6.2 The Virtual Array Concept. 6.3 Spacetime Adaptive Processing in MIMO Radar. 6.4 Clutter Subspace in MIMO Radar. 6.5 New STAP Method for MIMO Radar. 6.6 Numerical Examples. 6.7 Signal Design of the STAP Radar System. 6.8 Conclusions. Acknowledgments. References. 7 Slow-Time MIMO SpaceTime Adaptive Processing (Vito F. Mecca, Dinesh Ramakrishnan, Frank C. Robey, and Jeffrey L. Krolik). 7.1 Introduction. 7.2 SIMO Radar Modeling and Processing. 7.3 Slow-Time MIMO Radar Modeling. 7.4 Slow-Time MIMO Radar Processing. 7.5 OTHr Propagation and Clutter Model. 7.6 Simulations Examples. 7.7 Conclusion. Acknowledgment. References. 8 MIMO as a Distributed Radar System (H. D. Griffiths, C. J. Baker, P. F. Sammartino, and M. Rangaswamy). 8.1 Introduction. 8.2 Systems. 8.3 Performance. 8.4 Conclusions. Acknowledgment. References. 9 Concepts and Applications of A MIMO Radar System with Widely Separated Antennas (Hana Godrich, Alexander M. Haimovich, and Rick S. Blum). 9.1 Background. 9.2 MIMO Radar Concept. 9.3 NonCoherent MIMO Radar Applications. 9.4 Coherent MIMO Radar Applications. 9.5 Chapter Summary. Appendix 9A Deriving the FIM. Appendix 9B Deriving the CRLB on the Location Estimate Error. Appendix 9C MLE of Time Delays — Error Statistics. Appendix 9D Deriving the Lowest GDOP for Special Cases. Acknowledgments. References. 10 SpaceTime Coding for MIMO Radar (Antonio De Maio and Marco Lops). 10.1 Introduction. 10.2 System Model. 10.3 Detection In MIMO Radars. 10.4 Spacetime Code Design. 10.5 The Interplay Between STC and Detection Performance. 10.6 Numerical Results. 10.7 Adaptive Implementation. 10.8 Conclusions. Acknowledgment. References. INDEX.

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Book SynopsisFundamentals of Signal Processing for Sound and Vibration Engineers is based on Joe Hammond's many years of teaching experience at the Institute of Sound and Vibration Research, University of Southampton.Table of ContentsPreface. 1. Introduction to Signal Processing. 1.1 Descriptions of Physical Data (Signals). 1.2 Classification of Data. PART I: DETERMINISTIC SIGNALS. 2. Classification of Deterministic Data. 2.1 Periodic Signals. 2.2 Almost Periodic Signals. 2.3 Transient Signals. 2.4 Brief Summary and Concluding Remarks. 2.5 MATLAB Examples. 3. Fourier Series. 3.1 Periodic Signals and Fourier Series. 3.2 The Delta Function. 3.3 Fourier Series and the Delta Function. 3.4 The Complex Form of the Fourier Series. 3.5 Spectra. 3.6 Some Computational Considerations. 3.7 Brief Summary. 3.8 MATLAB Examples. 4. Fourier Integrals (Fourier Transform) and Continuous-Time Linear Systems. 4.1 The Fourier Integral. 4.2 Energy Spectra. 4.3 Some Examples of Fourier Transforms. 4.4 Properties of Fourier Transforms. 4.5 The Importance of Phase. 4.6 Echoes. 4.7 Continuous-Time Linear Time-Invariant Systems and Convolution. 4.8 Group Delay (Dispersion). 4.9 Minimum and Non-Minimum Phase Systems. 4.10 The Hilbert Transform. 4.11 The Effect of Data Truncation (Windowing). 4.12 Brief Summary. 4.13 MATLAB Examples. 5. Time Sampling and Aliasing. 5.1 The Fourier Transform of An Ideal Sampled Signal. 5.2 Aliasing and Anti-Aliasing Filters. 5.3 Analogue-to-Digital Conversion and Dynamic Range. 5.4 Some Other Considerations in Signal Acquisition. 5.5 Shannon’s Sampling Theorem (Signal Reconstruction). 5.6 Brief Summary. 5.7 MATLAB Examples. 6. The Discrete Fourier Transform. 6.1 Sequences and Linear Filters. 6.2 Frequency Domain Representation of Discrete Systems and Signals. 6.3 The Discrete Fourier Transform. 6.4 Properties of the DFT. 6.5 Convolution of Periodic Sequences. 6.6 The Fast Fourier Transform. 6.7 Brief Summary. 6.8 MATLAB Examples. PART II: INTRODUCTION TO RANDOM PROCESSES. 7. Random Processes. 7.1 Basic Probability Theory. 7.2 Random Variables and Probability Distributions. 7.3 Expectations of Functions of a Random Variable. 7.4 Brief Summary. 7.5 MATLAB Examples. 8. Stochastic Processes; Correlation Functions and Spectra. 8.1 Probability Distribution Associated with a Stochastic Process. 8.2 Moments of a Stochastic Process. 8.3 Stationarity. 8.4 The Second Moments of a Stochastic Process; Covariance. (Correlation) Functions. 8.5 Ergodicity and Time Averages. 8.6 Examples. 8.7 Spectra. 8.8 Brief Summary. 8.9 MATLAB Examples. 9. Linear System Response to Random Inputs: System Identification. 9.1 Single-Input, Single-Output Systems. 9.2 The Ordinary Coherence Function. 9.3 System Identification. 9.4 Brief Summary. 9.5 MATLAB Examples. 10. Estimation Methods and Statistical Considerations. 10.1 Estimator Errors and Accuracy. 10.2 Mean Value and Mean Square Value. 10.3 Correlation and Covariance Functions. 10.4 Power Spectral Density Function. 10.5 Cross-spectral Density Function. 10.6 Coherence Function. 10.7 Frequency Response Function. 10.8 Brief Summary. 10.9 MATLAB Examples. 11. Multiple-Input/Response Systems. 11.1 Description of Multiple-Input, Multiple-Output (MIMO) Systems. 11.2 Residual Random Variables, Partial and Multiple Coherence Functions. 11.3 Principal Component Analysis. Appendices. References. Index.

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Book SynopsisSemiconductor-based Ultra-Fast All-Optical Signal Processing Devices a key technology for the next generation of ultrahigh bandwidth optical communication systems! The introduction of ultra-fast communication systems based on all-optical signal processing is considered to be one of the most promising ways to handle the rapidly increasing global communication traffic. Such systems will enable real time super-high definition moving pictures such as high reality TV-conference, remote diagnosis and surgery, cinema entertainment and many other applications with small power consumption. The key issue to realize such systems is to develop ultra-fast optical devices such as light sources, all-optical gates and wavelength converters. Ultra-Fast All-Optical Signal Processing Devices discusses the state of the art development of semiconductor-based ultrafast all-optical devices, and their various signal processing applications for bit-rates 100Gb/s to 1Tb/s. UltTable of ContentsContributors ix Preface xi 1 Introduction 1Hiroshi Ishikawa 1.1 Evolution of Optical Communication Systems and Device Technologies 1 1.2 Increasing Communication Traffic and Power Consumption 2 1.3 Future Networks and Technologies 4 1.3.1 Future Networks 4 1.3.2 Schemes for Huge Capacity Transmission 5 1.4 Ultrafast All-Optical Signal Processing Devices 6 1.4.1 Challenges 6 1.4.2 Basics of the Nonlinear Optical Process 7 1.5 Overview of the Devices and Their Concepts 11 1.6 Summary 13 References 13 2 Light Sources 15Yoh Ogawa and Hitoshi Murai 2.1 Requirement for Light Sources 15 2.1.1 Optical Short Pulse Source 16 2.1.2 Optical Time Division Multiplexer 19 2.2 Mode-locked Laser Diodes 20 2.2.1 Active Mode Locking 20 2.2.2 Passive Mode Locking 23 2.2.3 Hybrid Mode Locking 25 2.2.4 Optical Synchronous Mode Locking 27 2.2.5 Application for Clock Extraction 29 2.3 Electro-absorption Modulator Based Signal Source 30 2.3.1 Overview of Electro-absorption Modulator 30 2.3.2 Optical Short Pulse Generation Using EAM 33 2.3.3 Optical Time Division Multiplexer Based on EAMs 38 2.3.4 160-Gb/s Optical Signal Generation 41 2.3.5 Detection of a 160-Gb/s OTDM Signal 43 2.3.6 Transmission Issues 46 2.4 Summary 47 References 47 3 Semiconductor Optical Amplifier Based Ultrafast Signal Processing Devices 53Hidemi Tsuchida and Shigeru Nakamura 3.1 Introduction 53 3.2 Fundamentals of SOA 53 3.3 SOA as an Ultrafast Nonlinear Medium 56 3.4 Use of Ultrafast Response Component by Filtering 57 3.4.1 Theoretical Background 57 3.4.2 Signal Processing Using the Fast Response Component of SOA 60 3.5 Symmetric Mach–Zehnder (SMZ) All-Optical Gate 64 3.5.1 Fundamentals of the SMZ All-Optical Gate 64 3.5.2 Technology of Integrating Optical Circuits for an SMZ All-Optical Gate 67 3.5.3 Optical Demultiplexing 68 3.5.4 Wavelength Conversion and Signal Regeneration 73 3.6 Summary 83 References 83 4 Uni-traveling-carrier Photodiode (UTC-PD) and PD-EAM Optical Gate Integrating a UTC-PD and a TravelingWave Electro-absorption Modulator 89Hiroshi Ito and Satoshi Kodama 4.1 Introduction 89 4.2 Uni-traveling-carrier Photodiode (UTC-PD) 91 4.2.1 Operation 91 4.2.2 Fabrication and Characterization 96 4.2.3 Characteristics of the UTC-PD 98 4.2.4 Photo Receivers 114 4.3 Concept of a New Opto-electronic Integrated Device 117 4.3.1 Importance of High-output PDs 117 4.3.2 Monolithic Digital OEIC 118 4.3.3 Monolithic PD-EAM Optical Gate 118 4.4 PD-EAM Optical Gate Integrating UTC-PD and TW-EAM 119 4.4.1 Basic Structure 119 4.4.2 Design 120 4.4.3 Optical Gating Characteristics of PD-EAM 123 4.4.4 Fabrication 125 4.4.5 Gating Characteristics 127 4.4.6 Applications for Ultrafast All-Optical Signal Processing 131 4.4.7 Future Work 143 4.5 Summary and Prospects 147 References 148 5 Intersub-band Transition All-Optical Gate Switches 155Nobuo Suzuki, Ryoichi Akimoto, Hiroshi Ishikawa and Hidemi Tsuchida 5.1 Operation Principle 155 5.1.1 Transition Wavelength 156 5.1.2 Matrix Element 157 5.1.3 Saturable Absorption 157 5.1.4 Absorption Recovery Time 158 5.1.5 Dephasing Time and Spectral Linewidth 160 5.1.6 Gate Operation in Waveguide Structure 162 5.2 GaN/AlN ISBT Gate 164 5.2.1 Absorption Spectra 165 5.2.2 Saturation of Absorption in Waveguides 168 5.2.3 Ultrafast Optical Gate 170 5.3 (CdS/ZnSe)/BeTe ISBT Gate 172 5.3.1 Growth of CdS/ ZnSe/ BeTe QWs and ISBT Absorption Spectra 173 5.3.2 Waveguide Structure for a CdS/ ZnSe/ BeTe Gate 177 5.3.3 Characteristics of a CdS/ ZnSe/ BeTe Gate 181 5.4 InGaAs/AlAs/AlAsSb ISBT Gate 183 5.4.1 Device Structure and its Fabrication 183 5.4.2 Saturation Characteristics and Time Response 184 5.5 Cross-phase Modulation in an InGaAs/AlAs/AlAsSb-based ISBT Gate 186 5.5.1 Cross-phase Modulation Effect and its Mechanisms 187 5.5.2 Application to Wavelength Conversion 192 5.6 Summary 195 References 196 6 Wavelength Conversion Devices 201Haruhiko Kuwatsuka 6.1 Introduction 201 6.2 Wavelength Conversion Schemes 202 6.2.1 Optical Gate Switch Type 202 6.2.2 Coherent Type Conversion 204 6.3 Physics of Four-wave Mixing in LDs or SOAs 205 6.3.1 Model 205 6.3.2 Asymmetric χ(3) for Positive and Negative Detuning 210 6.3.3 Symmetric χ(3) in Quantum Dot SOAs 212 6.4 Wavelength Conversion of Short Pulses Using FWM in Semiconductor Devices 214 6.4.1 Model 214 6.4.2 The Effect of the Stop Band in DFB-LDs 217 6.4.3 The Effect of the Depletion of Gain 218 6.4.4 The Pulse Width Broadening in FWM Wavelength Conversion 219 6.5 Experimental Results ofWavelength Conversion Using FWM in SOAs or LDs 220 6.5.1 Wavelength Conversion of Short Pulses Using a DFB-LD 220 6.5.2 Wavelength Conversion of 160-Gb/s OTDM Signal Using a Quantum Dot SOAs 221 6.5.3 Format-free Wavelength Conversion 222 6.5.4 Chromatic Dispersion Compensation of Optical Fibers Using FWM in DFB-LDs 224 6.6 The Future View ofWavelength Conversion Using FWM 225 6.7 Summary 226 References 226 7 Summary and Future Prospects 231Hiroshi Ishikawa 7.1 Introduction 231 7.2 Transmission Experiments 231 7.2.1 FESTA Experiments 231 7.2.2 Test Bed Field Experiment 235 7.2.3 Recent Transmission Experiments above 160-Gb/s 236 7.3 Requirements on Devices and Prospects 238 7.3.1 Devices Described in this Book 238 7.3.2 Necessity for New Functionality Devices and Technology 240 7.4 Summary 241 References 242 Index 243

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Book SynopsisDigital Design of Signal Processing Systems discusses a spectrum of architectures and methods for effective implementation of algorithms in hardware (HW). Encompassing all facets of the subject this book includes conversion of algorithms from floating-point to fixed-point format, parallel architectures for basic computational blocks, Verilog Hardware Description Language (HDL), SystemVerilog and coding guidelines for synthesis. The book also covers system level design of Multi Processor System on Chip (MPSoC); a consideration of different design methodologies including Network on Chip (NoC) and Kahn Process Network (KPN) based connectivity among processing elements. A special emphasis is placed on implementing streaming applications like a digital communication system in HW. Several novel architectures for implementing commonly used algorithms in signal processing are also revealed. With a comprehensive coverage of topics the book provides an appropriate mix of examples to iTrade Review"It can be used in a course on advanced digital design and VLSI signal processing at the senior undergraduate or graduate level." (Booknews, 1 April 2011)Table of ContentsPreface. Acknowledgement. 1 Overview. 1.1 Introduction. 1.2 Fueling the Innovation: Moore’s Law. 1.3 Digital Systems. 1.4 Examples of Digital Systems. 1.5 Components of the Digital Design Process. 1.6 Competing Objectives in Digital Process. 1.7 Synchronous Digital Hardware Systems. 1.8 Design Strategies. References. 2. Using a Hardware Description Language. 2.1 Overview. 2.2 About Verilog. 2.3 System Design Flow. 2.4 Logic Synthesis. 2.5 Using the Verilog HDL. 2.6 Four Levels of Abstraction. 2.7 Verification in Hardware Design. 2.8 Example of a Verification Setup. 2.9 SystemVerilog. Exercises. References. 3. System Design Flow and Fixed-Point Arithmetic. 3.1 Overview. 3.2 System Design Flow. 3.3 Representations and Numbers. 3.4 Floating-point Format. 3.5 Qn.m Format for Fixed-point Arithmetic. 3.6 Floating-Point to Fixed-Point Conversion. 3.7 Block Floating-Point Format. 3.8 Forms of Digital Filter. Exercises. References. 4. Mapping on Fully Dedicated Architecture. 4.1 Introduction. 4.2 Discrete Real-Time Systems. 4.3 Synchronous Digital Hardware Systems. 4.4 Kahn Process Network. 4.5 Methods of Representing DSP Systems. 4.6 Performance Measures. 4.7 Fully Dedicated Architecture. 4.8 DFG to HW Synthesis. Exercises. References. 5. Design Options for Basic Building Blocks. 5.1 Introduction. 5.2 Embedded Processors and Arithmetic Units in FPGAs. 5.3 Instantiation of Embedded Blocks. 5.4 Basic Building Blocks: Introduction. 5.5 Adders. 5.6 Barrel Shifter. 5.7 Cary Save Adder and Compressors. 5.8 Parallel Multipliers. 5.9 Two’s Complement Signed Multiplier. 5.10 Compression Trees for Multi-operand Addition. 5.11 Algorithm Transformations for CSA. Exercises. References. 6. Multiplier-less Multiplication by Constants. 6.1 Introduction. 6.2 Canonic Sign Digit Representation. 6.3 Minimum Signed Digit Representation. 6.4 Multiplication by Constant in Signal Processing Algorithm. 6.5 Optimized DFG Transformation. 6.6 Fully Dedicated Architecture for Direct-form FIR Filter. 6.7 Complexity Reduction. 6.8 Distributed Arithmetic. 6.9 FFT Architecture using FIR Filter Structure. Exercises. References. 7. Pipelining, Retiming, Look-ahead Transformation and Polyphase Decomposition. 7.1 Introduction. 7.2 Pipelining and Retiming. 7.3 Digital Design of Feedback Systems. 7.4 C-slow Retiming. 7.5 Look-ahead Transformation for IIR filters. 7.6 Look-ahead Transformation for Generalized IIR Filters. 7.7 Polyphase Structure for Decimation and Interpolation Applications. 7.8 IIR Filter for Decimation and Interpolation. Exercises. References. 8. Unfolding and Folding Architectures. 8.1 Introduction. 8.2 Unfolding. 8.3 Sampling Rate Considerations. 8.4 Unfolding Techniques. 8.5 Folding Techniques. 8.6 Mathematical Transformation for Folding. 8.7 Algorithmic Transformation. Exercises. References. 9.Designs based on Finite State Machines. 9.1 Introduction. 9.2 Examples of Time-shared Architecture Design. 9.3 Sequencing and Control. 9.4 Algorithmic State Machine Representation. 9.5 FSM Optimization for Low Power and Area. 9.6 Designing for Testability. 9.7 Methods for Reducing Power Dissipation. Exercises. References. 10. Micro-programmed State Machines. 10.1 Introduction. 10.2 Micro-programmed Controller. 10.3 Counter-based State Machine. 10.4 Subroutine Support. 10.5 Nested Subroutine Support. 10.6 Nested Loop Support. 10.7 Examples. Exercises. References. 11. Micro-programmed Adaptive Filtering Applications. 11.1 Introduction. 11.2 Adaptive Filters Configurations. 11.3 Adaptive Algorithms. 11.4 Channel Equalizer using NLMS. 11.5 Echo Canceller. 11.6 Adaptive Algorithms with Micro-programmed State Machines. Exercises. References. 12 CORDIC-based DDFS Architectures. 12.1 Introduction. 12.2 Direct Digital Frequency Synthesizer. 12.3 Design of a Basic DDFS. 12.4 The CORDIC Algorithm. 12.5 Hardware Mapping of Modified CORDIC Algorithm. Exercises. References. 13. Digital Design of Communication Systems. 13.1 Introduction. 13.2 Top-level Design Options. 13.3 Typical Digital Communication System. Exercises. References. Index.

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Book SynopsisMaintenance and continuous health monitoring of air, land and sea structures is one of the most important concerns in a wide range of industries including transportation and civil engineering. Effective maintenance minimises not only the cost of ownership of structures but also improves safety and the perception of safety.Trade Review"...very relevant and timely...strongly recommend this multidisciplinary book...an integrated volume of real value..." (Measurement and Control, Vol 37(5), June 2004)Table of ContentsList of Contributors. Preface. 1. Introduction (G. Bartelds, J.H. Heida, J. McFeat and C. Boller). 1.1 Health and Usage Monitoring in Aircraft Structures – Why and How? 1.2 Smart Solution in Aircraft Monitoring. 1.3 End-User Requirements. 1.3.1 Damage Detection. 1.3.2 Load History Monitoring. 1.4 Assessment of Monitoring Technologies. 1.5 Background of Technology Qualification Process. 1.6 Technology Qualification. 1.6.1 Philosophy. 1.6.2 Performance and Operating Requirements. 1.6.3 Qualification Evidence – Requirements and Provision. 1.6.4 Risks. 1.7 Flight Vehicle Certification. 1.8 Summary. References. 2. Aircraft Structural Health and Usage Monitoring (C. Boller and W.J. Staszewski). 2.1 Introduction. 2.2 Aircraft Structural Damage. 2.3 Ageing Aircraft Problem. 2.4 LifeCycle Cost of Aerospace Structures. 2.4.1 Background. 2.4.2 Example. 2.5 Aircraft Structural Design. 2.5.1 Background. 2.5.2 Aircraft Design Process. 2.6 Damage Monitoring Systems in Aircraft. 2.6.1 Loads Monitoring. 2.6.2 Fatigue Monitoring. 2.6.3 Load Models. 2.6.4 Disadvantages of Current Loads Monitoring Systems. 2.6.5 Damage Monitoring and Inspections. 2.7 Non-Destructive Testing. 2.7.1 Visual Inspection. 2.7.2 Ultrasonic Inspection. 2.7.3 Eddy Current. 2.7.4 Acoustic Emission. 2.7.5 Radiography, Thermography and Shearography. 2.7.6 Summary. 2.8 Structural Health Monitoring. 2.8.1 Vibration and Modal Analysis. 2.8.2 Impact Damage Detection. 2.9 Emerging Monitoring Techniques and Sensor Technologies. 2.9.1 Smart Structures and Materials. 2.9.2 Damage Detection Techniques. 2.9.3 Sensor Technologies. 2.9.4 Intelligent Signal Processing. 2.10 Conclusions. References. 3. Operational Load Monitoring Using Optical Fibre Sensors (P. Foote, M. Breidne, K. Levin, P. Papadopolous, I. Read, M. Signorazzi, L.K. Nilsson, R. Stubbe and A. Claesson). 3.1 Introduction. 3.2 Fibre Optics. 3.2.1 Optical Fibres. 3.2.2 Optical Fibre Sensors. 3.2.3 Fibre Bragg Grating Sensors. 3.3 Sensor Target Specifications. 3.4 Reliability of Fibre Bragg Grating Sensors. 3.4.1 Fibre Strength Degradation. 3.4.2 Grating Decay. 3.4.3 Summary. 3.5 Fibre Coating Technology. 3.5.1 Polyimide Chemistry and Processing. 3.5.2 Polyimide Adhesion to Silica. 3.5.3 Silane Adhesion Promoters. 3.5.4 Experimental Example. 3.5.5 Summary. 3.6 Example of Surface Mounted Operational Load Monitoring Sensor System. 3.6.1 Sensors. 3.6.2 Optical Signal Processor. 3.6.3 Optical Interconnections. 3.7 Optical Fibre Strain Rosette. 3.8 Example of Embedded Optical Impact Detection System. 3.9 Summary. References. 4. Damage Detection Using Stress and Ultrasonic Waves (W.J. Staszewski, C. Boller, S. Grondel, C. Biemans, E. O’Brien, C. Delebarre and G.R. Tomlinson). 4.1 Introduction. 4.2 Acoustic Emission. 4.2.1 Background. 4.2.2 Transducers. 4.2.3 Signal Processing. 4.2.4 Testing and Calibration. 4.3 Ultrasonics. 4.3.1 Background. 4.3.2 Inspection Modes. 4.3.3 Transducers. 4.3.4 Display Modes. 4.4 Acousto-Ultrasonics. 4.5 Guided Wave Ultrasonics. 4.5.1 Background. 4.5.2 Guided Waves. 4.5.3 Lamb Waves. 4.5.4 Monitoring Strategy. 4.6 Piezoelectric Transducers. 4.6.1 Piezoelectricity and Piezoelectric Materials. 4.6.2 Constitutive Equations. 4.6.3 Properties. 4.7 Passive Damage Detection Examples. 4.7.1 Crack Monitoring Using Acoustic Emission. 4.7.2 Impact Damage Detection in Composite Materials. 4.8 Active Damage Detection Examples. 4.8.1 Crack Monitoring in Metallic Structures Using Broadband Acousto-Ultrasonics. 4.8.2 Impact Damage Detection in Composite Structures Using Lamb Waves. 4.9 Summary. References. 5. Signal Processing for Damage Detection (W.J. Staszewski and K. Worden). 5.1 Introduction. 5.2 Data Pre-Processing. 5.2.1 Signal Smoothing. 5.2.2 Signal Smoothing Filters. 5.3 Signal Features for Damage Identification. 5.3.1 Feature Extraction. 5.3.2 Feature Selection. 5.4 Time–Domain Analysis. 5.5 Spectral Analysis. 5.6 Instantaneous Phase and Frequency. 5.7 Time–Frequency Analysis. 5.8 Wavelet Analysis. 5.8.1 Continuous Wavelet Transform. 5.8.2 Discrete Wavelet Transform. 5.9 Dimensionality Reduction Using Linear and Nonlinear Transformation. 5.9.1 Principal Component Analysis. 5.9.2 Sammon Mapping. 5.10 Data Compression Using Wavelets. 5.11 Wavelet-Based Denoising. 5.12 Pattern Recognition for Damage Identification. 5.13 Artificial Neural Networks. 5.13.1 Parallel Processing Paradigm. 5.13.2 The Artificial Neuron. 5.13.3 Multi-Layer Networks. 5.13.4 Multi-Layer Perceptron Neural Networks and Others. 5.13.5 Applications. 5.14 Impact Detection in Structures Using Pattern Recognition. 5.14.1 Detection of Impact Positions. 5.14.2 Detection of Impact Energy. 5.15 Data Fusion. 5.16 Optimised Sensor Distributions. 5.16.1 Informativeness of Sensors. 5.16.2 Optimal Sensor Location. 5.17 Sensor Validation. 5.18 Conclusions. References. 6. Structural Health Monitoring Evaluation Tests (P.A. Lloyd, R. Pressland, J. McFeat, I. Read, P. Foote, J.P. Dupuis, E. O’Brien, L. Reithler, S. Grondel, C. Delebarre, K. Levin, C. Boller, C. Biemans and W.J. Staszewski). 6.1 Introduction. 6.2 Large-Scale Metallic Evaluator. 6.2.1 Lamb Wave Results from Riveted Metallic Specimens. 6.2.2 Acoustic Emission Results from a Full-Scale Fatigue Test. 6.3 Large-Scale Composite Evaluator. 6.3.1 Test Article. 6.3.2 Sensor and Specimen Integration. 6.3.3 Impact Tests. 6.3.4 Damage Detection Results – Distributed Optical Fibre Sensors. 6.3.5 Damage Detection Results – Bragg Grating Sensors. 6.3.6 Lamb Wave Damage Detection System. 6.4 Flight Tests. 6.4.1 Flying Test-Bed. 6.4.2 Acoustic Emission Optical Damage Detection System. 6.4.3 Bragg Grating Optical Load Measurement System. 6.4.4 Fibre Optic Load Measurement Rosette System. 6.5 Summary. References. Index.

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Book SynopsisQuickly Engages in Applying Algorithmic Techniques to Solve Practical Signal Processing Problems With its active, hands-on learning approach, this text enables readers to master the underlying principles of digital signal processing and its many applications in industries such as digital television, mobile and broadband communications, and medical/scientific devices. Carefully developed MATLAB examples throughout the text illustrate the mathematical concepts and use of digital signal processing algorithms. Readers will develop a deeper understanding of how to apply the algorithms by manipulating the codes in the examples to see their effect. Moreover, plenty of exercises help to put knowledge into practice solving real-world signal processing challenges. Following an introductory chapter, the text explores: Sampled signals and digital processing Random signals Representing signals and systems TemporTrade Review"Intended for undergraduate or graduate students in engineering or related disciplines, this introductory volume examines key theories in signal processing and presents this information optimized for use with MATLAB technical computing software." (Book News, 1 October 2011) Table of ContentsPreface xi Chapter 1. What Is Signal Processing? 1 1.1 Chapter Objectives 1 1.2 Introduction 1 1.3 Book Objectives 2 1.4 DSP and ITS Applications 3 1.5 Application Case Studies Using DSP 4 1.6 Overview of Learning Objectives 12 1.7 Conventions Used in This Book 15 1.8 Chapter Summary 16 Chapter 2. Matlab for Signal Processing 19 2.1 Chapter Objectives 19 2.2 Introduction 19 2.3 What Is MATLAB? 19 2.4 Getting Started 20 2.5 Everything Is a Matrix 20 2.6 Interactive Use 21 2.7 Testing and Looping 23 2.8 Functions and Variables 25 2.9 Plotting and Graphing 30 2.10 Loading and Saving Data 31 2.11 Multidimensional Arrays 35 2.12 Bitwise Operators 37 2.13 Vectorizing Code 38 2.14 Using MATLAB for Processing Signals 40 2.15 Chapter Summary 43 Chapter 3. Sampled Signals and Digital Processing 45 3.1 Chapter Objectives 45 3.2 Introduction 45 3.3 Processing Signals Using Computer Algorithms 45 3.4 Digital Representation of Numbers 47 3.5 Sampling 61 3.6 Quantization 64 3.7 Image Display 74 3.8 Aliasing 81 3.9 Reconstruction 84 3.10 Block Diagrams and Difference Equations 88 3.11 Linearity, Superposition, and Time Invariance 92 3.12 Practical Issues and Computational Efficiency 95 3.13 Chapter Summary 98 Chapter 4. Random Signals 103 4.1 Chapter Objectives 103 4.2 Introduction 103 4.3 Random and Deterministic Signals 103 4.4 Random Number Generation 105 4.5 Statistical Parameters 106 4.6 Probability Functions 108 4.7 Common Distributions 112 4.8 Continuous and Discrete Variables 114 4.9 Signal Characterization 116 4.10 Histogram Operators 117 4.11 Median Filters 122 4.12 Chapter Summary 125 Chapter 5. Representing Signals and Systems 127 5.1 Chapter Objectives 127 5.2 Introduction 127 5.3 Discrete-Time Waveform Generation 127 5.4 The z Transform 137 5.5 Polynomial Approach 144 5.6 Poles, Zeros, and Stability 146 5.7 Transfer Functions and Frequency Response 152 5.8 Vector Interpretation of Frequency Response 153 5.9 Convolution 156 5.10 Chapter Summary 160 Chapter 6. Temporal and Spatial Signal Processing 165 6.1 Chapter Objectives 165 6.2 Introduction 165 6.3 Correlation 165 6.4 Linear Prediction 177 6.5 Noise Estimation and Optimal Filtering 183 6.6 Tomography 188 6.7 Chapter Summary 201 Chapter 7. Frequency Analysis of Signals 203 7.1 Chapter Objectives 203 7.2 Introduction 203 7.3 Fourier Series 203 7.4 How Do the Fourier Series Coefficient Equations Come About? 209 7.5 Phase-Shifted Waveforms 211 7.6 The Fourier Transform 212 7.7 Aliasing in Discrete-Time Sampling 231 7.8 The FFT as a Sample Interpolator 233 7.9 Sampling a Signal over a Finite Time Window 236 7.10 Time-Frequency Distributions 240 7.11 Buffering and Windowing 241 7.12 The FFT 243 7.13 The DCT 252 7.14 Chapter Summary 266 Chapter 8. Discrete-Time Filters 271 8.1 Chapter Objectives 271 8.2 Introduction 271 8.3 What Do We Mean by “Filtering”? 272 8.4 Filter Specification, Design, and Implementation 274 8.5 Filter Responses 282 8.6 Nonrecursive Filter Design 285 8.7 Ideal Reconstruction Filter 293 8.8 Filters with Linear Phase 294 8.9 Fast Algorithms for Filtering, Convolution, and Correlation 298 8.10 Chapter Summary 311 Chapter 9. Recursive Filters 315 9.1 Chapter Objectives 315 9.2 Introduction 315 9.3 Essential Analog System Theory 319 9.4 Continuous-Time Recursive Filters 326 9.5 Comparing Continuous-Time Filters 339 9.6 Converting Continuous-Time Filters to Discrete Filters 340 9.7 Scaling and Transformation of Continuous Filters 361 9.8 Summary of Digital Filter Design via Analog Approximation 371 9.9 Chapter Summary 372 Bibliography 375 Index 379

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Book SynopsisDespite our growing understanding of the properties and capabilities of nonlinear filters, there persists the belief among engineers that these filters are too complex to implement. This book debunks the myth that all nonlinear filters are complex with its coverage of the polynomial filter.Trade Review"A first-year graduate-level text that provides an overview of the state of the art in the area of nonlinear signal processing known as polynomial signal processing." (SciTech Book News Vol. 25, No. 2 June 2001) "The text is clear and easy to follow - an excellent way of getting started in this area." (Ultramicroscopy, Vol.87, 2001)Table of ContentsVolterra Series Expansions. Realization of Truncated Volterra Filters. Multidimensional Volterra Filters. Parameter Estimation. Frequency-Domain Methods for Volterra System Identification. Adaptive Truncated Volterra Filters. Recursive Polynomial Systems. Inversion and Time Series Analysis. Applications of Polynomial Filters. Some Related Topics and Recent Developments. Appendices. References. Index.

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Book SynopsisDescribes the operating principles of analog MOS integrated circuits and how to design and use such circuits. The initial section explores general properties of analog MOS integrated circuits and the math and physics background required. The remainder of the book is devoted to the design of circuits.Table of ContentsTransformation Methods. MOS Devices as Circuit Elements. MOS Operational Amplifiers. Switched-Capacitor Filters. Nonfiltering Applications of Switched-Capacitor Circuits. Nonideal Effects in Switched-Capacitor Circuits. Systems Considerations and Applications. Index.

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Book SynopsisUsing a pedagogical style along with detailed proofs and illustrative examples, this book opens a view to the largely unexplored area of nonlinear systems with uncertainties. The focus is on adaptive nonlinear control results introduced with the new recursive design methodology--adaptive backstepping.Table of ContentsSTATE FEEDBACK. Design Tools for Stabilization. Adaptive Backstepping Design. Tuning Functions Design. Modular Design with Passive Identifiers. Modular Design with Swapping Identifiers. OUTPUT FEEDBACK. Output-Feedback Design Tools. Tuning Functions Designs. Modular Designs. Linear Systems. Appendices. Bibliography. Index.

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Book SynopsisWith more and more information being transmitted over fiber optic cables, optical filtering is becoming crucial to the smooth operation of optical communication networks. This book presents digital signal processing techniques for the design of optical filters, covering filters used in narrow band filtering and optical signal processing.Table of ContentsFundamentals of Electromagnetic Waves and Waveguides. Digital Filter Concepts for Optical Filters. Multi-Stage MA Architectures. Multi- Stage AR Architectures. Multi-Stage ARMA Filters. Optical Measurements and Filter Analysis. Future Directions. Index.

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Book SynopsisModel-Based Signal Processing develops the "model-based approach" to signal processing for a variety of useful model sets including the popularly termed "physics-based" models. It presents a unique viewpoint of signal processing from the model-based perspective.Trade Review"Given its extensive, but very cohesive and accessible coverage…this book could be very well appreciated by both students and specialists in the field." (Computing Reviews.com, August 1, 2006) "...belongs in the library of every practicing signal processor." (Journal of the Acoustical Society of America, May 2006)Table of ContentsPreface. Acknowledgments. 1. Introduction. 2. Discrete Random Signals ans Systems. 3. Estimation Theory. 4. AR, MA, ARMAX, Lattice, Exponential, Wave Model-Based Processors. 5. Linear State-Space Model-Based Processors. 6. Nonlinear State-Space Model-Based Processors. 7. Adaptive AR, MA, ARMAX, Exponential Model-Based Processors. 8. Adaptive State-Space Model-Based Processors. 9. Applied Physics-Based Processors. Appendix A: Probability and Statistics Overview. Appendix B: Sequential MBP and UD-Factorization. Appendix C: SSpack_PC: An Interactive Model-Based Processing Software Package. Index.

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Book SynopsisExpertly combining the fields of computer architecture theory and digital signal processing (DSP), this comprehensive, single-volume resource provides everything circuit designers and computer professionals need to stay on top of the rapid changes in VLSI (Very Large Scale Integration) design for DSP.Trade Review"Globally there hardly exist more than a dozen book references on the subject of DSP hardware design. Among them…[Parhi's book is one of the] incontestable leaders, in both depth and breadth." (Analog Dialogue)Table of ContentsIntroduction to Digital Signal Processing Systems. Iteration Bound. Pipelining and Parallel Processing. Retiming. Unfolding. Folding. Systolic Architecture Design. Fast Convolution. Algorithmic Strength Reduction in Filters and Transforms. Pipelined and Parallel Recursive and Adaptive Filters. Scaling and Roundoff Noise. Digital Lattice Filter Structures. Bit-Level Arithmetic Architectures. Redundant Arithmetic. Numerical Strength Reduction. Synchronous, Wave, and Asynchronous Pipelines. Low-Power Design. Programmable Digital Signal Processors. Appendices. Index.

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Book SynopsisAn understanding of random processes is crucial to many engineering fields-including communication theory, computer vision, and digital signal processing in electrical and computer engineering, and vibrational theory and stress analysis in mechanical engineering.Trade Review"The reader will find an excellent presentation ranging from the basic concepts of probability theory to the advanced topics of RP, filtering, estimation and detection." (IIE Transactions on Operations Engineering)Table of ContentsPreface xv 1 Experiments and Probability 1 2 Random Variables 37 3 Estimation of Random Variables 133 4 Random Processes 179 5 Linear Systems: Random Processes 247 6 Nonlinear Systems: Random Processes 295 7 Optimum Linear Filters: The Wiener Approach 335 8 Optimum Linear Systems: The Kalman Approach 383 9 Detection Theory: Discrete Observation 423 10 Detection Theory: Continuous Observation 511 Appendixes Index 599

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Book SynopsisKalman filtering is a well-established topic in the field of control and signal processing and represents by far the most refined method for the design of neural networks. This book takes a nontraditional nonlinear approach and reflects the fact that most practical applications are nonlinear.Trade Review"Although the traditional approach to the subject is usually linear, this book recognizes and deals with the fact that real problems are most often nonlinear." (SciTech Book News, Vol. 25, No. 4, December 2001)Table of ContentsPreface. Contributors. Kalman Filters (S. Haykin). Parameter-Based Kalman Filter Training: Theory and Implementaion (G. Puskorius and L. Feldkamp). Learning Shape and Motion from Image Sequences (G. Patel, et al.). Chaotic Dynamics (G. Patel and S. Haykin). Dual Extended Kalman Filter Methods (E. Wan and A. Nelson). Learning Nonlinear Dynamical System Using the Expectation-Maximization Algorithm (S. Roweis and Z. Ghahramani). The Unscencted Kalman Filter (E. Wan and R. van der Merwe). Index.

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Book SynopsisWave scattering by discrete scatterers is an interdisciplinary area of research with many applications in such areas as atomic physics, medical imaging, geoscience and remote sensing. This three-volume work is an expanded and updated version of the authors 1985 book, Theory of Microwave Remote Sensing.Table of ContentsPREFACE xi CHAPTER 1 INTRODUCTION TO ELECTROMAGNETIC SCATTERING BY A SINGLE PARTICLE 1 1 Basic Scattering Parameters 2 1.1 Scattering Amplitudes and Cross Sections 2 1.2 Scattering Amplitude Matrix 6 2 Rayleigh Scattering 9 2.1 Rayleigh Scattering by a Small Particle 9 2.2 Rayleigh Scattering by a Sphere 10 2.3 Rayleigh Scattering by an Ellipsoid 12 2.4 Scattering Dyads 14 3 Integral Representations of Scattering and Born Approximation 16 3.1 Integral Expression for Scattering Amplitude 16 3.2 Born Approximation 18 4 Plane Waves, Cylindrical Waves, and Spherical Waves 21 4.1 Cartesian Coordinates: Plane Waves 21 4.2 Cylindrical Waves 22 4.3 Spherical Waves 24 5 Acoustic Scattering 30 6 Scattering by Spheres, Cylinders, and Disks 32 6.1 Mie Scattering 32 6.2 Scattering by a Finite Length Cylinder Using the Infinite Cylinder Approximation 41 6.3 Scattering by a Disk Based on the Infinite Disk Approximation 46 References and Additional Readings 52CHAPTER 2 BASIC THEORY OF ELECTROMAGNETIC SCATTERING 53 1 Dyadic Green's Function 54 1.1 Green's Functions 54 1.2 Plane Wave Representation 55 1.3 Cylindrical Waves 57 1.4 Spherical Waves 59 2 Huygens' Principle and Extinction Theorem 60 3 Active Remote Sensing and Bistatic Scattering Coefficients 66 4 Optical Theorem 68 5 Reciprocity and Symmetry 73 5.1 Reciprocity 73 5.2 Reciprocal Relations for Bistatic Scattering Coefficients and Scattering Amplitudes 75 5.3 Symmetry Relations for Dyadic Green's Function 79 6 Eulerian Angles of Rotation 81 7 T-Matrix 83 7.1 T-Matrix and Relation to Scattering Amplitudes 83 7.2 Unitarity and Symmetry 88 8 Extended Boundary Condition 91 8.1 Extended Boundary Condition Technique 91 8.2 Spheres 97 8.2.1 Scattering and Absorption for Arbitrary Excitation 100 8.2.2 Mie Scattering of Coated Sphere 102 8.3 Spheroids 104 References and Additional Readings 106CHAPTER 3 FUNDAMENTALS OF RANDOM SCATTERING 107 1 Radar Equation for Conglomeration of Scatterers 108 2 Stokes Parameters and Phase Matrices 116 2.1 Elliptical Polarization, Stokes Parameters, Partial Polarization 116 2.2 Stokes Matrix 123 2.3 Scattering per Unit Volume and Phase Matrix 124 2.4 Rayleigh Phase Matrix 127 2.5 Phase Matrix of Random Media 129 3 Fluctuating Fields 131 3.1 Coherent and Incoherent Fields 131 3.2 Probability Distribution of Scattered Fields and Polarimetric Description 132 4 Specific Intensity 140 5 Passive Remote Sensing 145 5.1 Planck's Radiation Law and Brightness Temperature 145 5.2 KirchhofT's Law 149 5.3 Fluctuation Dissipation Theorem 152 5.4 Emissivity of Four Stokes Parameters 155 6 Correlation Function of Fields 161 References and Additional Readings 165 CHAPTER 4 CHARACTERISTICS OF DISCRETE SCATTERERS AND ROUGH SURFACES 167 1 Ice 168 2 Snow 170 3 Vegetation 171 4 Atmosphere 172 5 Correlation Function and Pair Distribution Function 173 5.1 Correlation Function 174 5.2 Pair Distribution Function 176 6 Gaussian Rough Surface and Spectral Density 179 7 Soil and Rocky Surfaces 184 8 Ocean Surface 185 References and Additional Readings 195 CHAPTER 5 SCATTERING AND EMISSION BY LAYERED MEDIA 199 1 Incoherent Approach of Radiative Transfer 200 2 Wave Approach 203 2.1 Reflection and Transmission 203 2.2 Dyadic Green's Function for Stratified Medium 207 2.3 Brightness Temperatures for a Stratified Medium with Temperature Distribution 212 3 Comparison Between Incoherent Approach and Coherent Approach 217 4 Applications to Passive Remote Sensing of Soil 220 References and Additional Readings 229 CHAPTER 6 SINGLE SCATTERING AND APPLICATIONS 231 1 Single Scattering and Particle Position Correlation 232 2 Applications of Single Scattering 237 2.1 Synthetic Aperture Radar 237 2.2 Interferometric SAR 248 2.3 Active Remote Sensing of Half-Space Random Media 252 References and Additional Readings 258 CHAPTER 7 RADIATIVE TRANSFER THEORY 259 1 Scalar Radiative Transfer Theory 260 2 Vector Radiative Transfer Theory 269 2.1 Phase Matrix of Independent Scattering 269 2.2 Extinction Matrix 272 2.3 Emission Vector 275 2.4 Boundary Conditions 283 References and Additional Readings 286 CHAPTER 8 SOLUTION TECHNIQUES OF RADIATIVE TRANSFER THEORY 287 1 Iterative Method 288 1.1 Iterative Procedure 288 1.2 Integral Equation for Scattering Problems 293 1.3 Active Remote Sensing of a Half-Space of Spherical Particles 298 1.4 Active Remote Sensing of a Layer of Nonspherical Particles 303 1.4.1 Numerical Illustrations with Finite Dielectric Cylinders 310 1.5 Second-Order Scattering from Isotropic Point Scatterers 322 2 Discrete Ordinate-Eigenanalysis Method 324 2.1 Radiative Transfer Solution for Laminar Structures 324 2.2 Numerical Procedure of Discrete Ordinate Method: Normal Incidence 328 2.3 Active Remote Sensing: Oblique Incidence 337 2.4 Discrete Ordinate Method for Passive Remote Sensing 343 2.5 Passive Remote Sensing of a Three-Dimensional Random Medium 349 2.6 Passive Remote Sensing of a Layer of Mie Scatterers Overlying a Dielectric Half-Space 352 3 Invariant Imbedding 362 3.1 One-Dimensional Problem 363 3.2 Passive Remote Sensing of a Three-Dimensional Scattering Medium with Inhomogeneous Profiles 370 3.3 Passive Remote Sensing of a Three-Dimensional Random Medium 373 3.4 Thermal Emission of Layers of Spherical Scatterers in the Presence of Inhomogeneous Absorption and Temperature Profiles 374 4 Diffusion Approximation 380 References and Additional Readings 386 CHAPTER 9 ONE-DIMENSIONAL RANDOM ROUGH SURFACE SCATTERING 389 1 Introduction 390 2 Statistics of Random Rough Surface 392 2.1 Statistics, Correlation Function and Spectral Density 392 2.2 Characteristic Functions 396 3 Small Perturbation Method 397 3.1 Dirichlet Problem for One-Dimensional Surface 397 3.2 Neumann Problem for One-Dimensional Surface 403 4 Kirchhoff Approach 407 4.1 Dirichlet Problem for One-Dimensional Surface 408 4.2 Neumann Problem for One-Dimensional Surface 415 References and Additional Readings 417 INDEX 419

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Book SynopsisA timely and authoritative guide to the state of the art of wave scattering Scattering of Electromagnetic Waves offers in three volumes a complete and up-to-date treatment of wave scattering by random discrete scatterers and rough surfaces.Trade Review"this graduate textbook presents numerical simulation techniques and results for electromagnetic wave scattering in random media and rough surfaces..." (SciTech Book News, Vol. 25, No. 3, September 2001)Table of ContentsPREFACE xix CHAPTER 1 MONTE CARLO SIMULATIONS OF LAYERED MEDIA 1 1 One-Dimensional Layered Media with Permittivity Fluctuations 2 1.1 Continuous Random Medium 2 1.2 Generation of One-Dimensional Continuous Gaussian Random Medium 4 1.3 Numerical Results and Applications to Antarctica 5 2 Random Discrete Layering and Applications 8 References and Additional Readings 12 CHAPTER 2 INTEGRAL EQUATION FORMULATIONS AND BASIC NUMERICAL METHODS 13 1 Integral Equation Formulation for Scattering Problems 14 1.1 Surface Integral Equations 14 1.2 Volume Integral Equations 17 1.3 Dyadic Green's Function Singularity and Electrostatics 19 2 Method of Moments 23 3 Discrete Dipole Approximation (DDA) 27 3.1 Small Cubes 28 3.2 Radiative Corrections 29 3.3 Other Shapes 31 4 Product of Toeplitz Matrix and Column Vector 37 4.1 Discrete Fourier Transform and Convolutions 38 4.2 FFT for Product of Toeplitz Matrix and Column Vector 42 5 Conjugate Gradient Method 46 5.1 Steepest Descent Method 46 5.2 Real Symmetric Positive Definite Matrix 48 5.3 General Real Matrix and Complex Matrix 52 References and Additional Readings 57 CHAPTER 3 SCATTERING AND EMISSION BY A PERIODIC ROUGH SURFACE 61 1 Dirichlet Boundary Conditions 62 1.1 Surface Integral Equation 62 1.2 Floquet's Theorem and Bloch Condition 63 1.3 2-D Green's Function in 1-D Lattice 64 1.4 Bistatic Scattering Coefficients 67 2 Dielectric Periodic Surface: T-Matrix Method 68 2.1 Formulation in Longitudinal Field Components 69 2.2 Surface Field Integral Equations and Coupled Matrix Equations 74 2.3 Emissivity and Comparison with Experiments 81 3 Scattering of Waves Obliquely Incident on Periodic Rough Surfaces: Integral Equation Approach 85 3.1 Formulation 85 3.2 Polarimetric Brightness Temperatures 89 4 Ewald's Method 93 4.1 Preliminaries 93 4.2 3-D Green's Function in 3-D Lattices 98 4.3 3-D Green's Function in 2-D Lattices 102 4.4 Numerical Results 105 References and Additional Readings 110 CHAPTER 4 RANDOM ROUGH SURFACE SIMULATIONS 111 1 Perfect Electric Conductor (Non-Penetrable Surface) 114 1.1 Integral Equation 114 1.2 Matrix Equation: Dirichlet Boundary Condition (EFIE for TE Case) 1161.3 Tapering of Incident Waves and Calculation of Scattered Waves 118 1.4 Random Rough Surface Generation 124 1.4.1 Gaussian Rough Surface 124 1.4.2 Fractal Rough Surface 132 1.5 Neumann Boundary Condition (MFIE for TM Case) 134 2 Two-Media Problem 137 2.1 TE and TM Waves 139 2.2 Absorptivity, Emissivity and Reflectivity 141 2.3 Impedance Matrix Elements: Numerical Integrations 143 2.4 Simulation Results 145 2.4.1 Gaussian Surface and Comparisons with Analytical Methods 145 2.4.2 Dirichlet Case of Gaussian Surface with Ocean Spectrum and Fractal Surface 150 2.4.3 Bistatic Scattering for Two Media Problem with Ocean Spectrum 151 3 Topics of Numerical Simulations 154 3.1 Periodic Boundary Condition 154 3.2 MFIE for TE Case of PEC 158 3.3 Impedance Boundary Condition 161 4 Microwave Emission of Rough Ocean Surfaces 163 5 Waves Scattering from Real-Life Rough Surface Profiles 166 5.1 Introduction 166 5.2 Rough Surface Generated by Three Methods 167 5.3 Numerical Results of the Three Methods 169 References and Additional Readings 175 CHAPTER 5 FAST COMPUTATIONAL METHODS FOR SOLVING ROUGH SURFACE SCATTERING PROBLEMS 177 1 Banded Matrix Canonical Grid Method for Two-Dimensional Scattering for PEC Case 1791.1 Introduction 179 1.2 Formulation and Computational Procedure 180 1.3 Product of a Weak Matrix and a Surface Unknown Column Vector 187 1.4 Convergence and Neighborhood Distance 188 1.5 Results of Composite Surfaces and Grazing Angle Problems 189 2 Physics-Based Two-Grid Method for Lossy Dielectric Surfaces 196 2.1 Introduction 196 2.2 Formulation and Single-Grid Implementation 198 2.3 Physics-Based Two-Grid Method Combined with Banded Matrix Iterative Approach/Canonical Grid Method 200 2.4 Bistatic Scattering Coefficient and Emissivity 203 3 Steepest Descent Fast Multipole Method 212 3.1 Steepest Descent Path for Green's Function 213 3.2 Multi-Level Impedance Matrix Decomposition and Grouping 216 3.3 Multi-Level Discretization of Angles and Interpolation 222 3.4 Steepest Descent Expression of Multi-Level Impedance Matrix Elements 226 3.5 SDFMM Algorithm 235 3.6 Numerical Results 242 4 Method of Ordered Multiple Interactions (MOMI) 242 4.1 Matrix Equations Based on MFIE for TE and TM Waves for PEC 242 4.2 Iterative Approach 245 4.3 Numerical Results 247 5 Physics-Based Two-Grid Method Combined with the Multilevel Fast Multipole Method 249 5.1 Single Grid and PBTG 249 5.2 Computational Complexity of the Combined Algorithm of the PBTG with the MLFMM 252 5.3 Gaussian Rough Surfaces and CPU Comparison 254 5.4 Non-Gaussian Surfaces 257 References and Additional Readings 263 CHAPTER 6 THREE-DIMENSIONAL WAVE SCATTERING FROM TWO-DIMENSIONAL ROUGH SURFACES 267 1 Scattering by Non-Penetrable Media 270 1.1 Scalar Wave Scattering 270 1.1.1 Formulation and Numerical Method 270 1.1.2 Results and Discussion 273 1.1.3 Convergence of SMFSIA 277 1.2 Electromagnetic Wave Scattering by Perfectly Conducting Surfaces 278 1.2.1 Surface Integral Equation 278 1.2.2 Surface Integral Equation for Rough Surface Scattering 280 1.2.3 Computation Methods 281 1.2.4 Numerical Simulation Results 286 2 Integral Equations for Dielectric Surfaces 293 2.1 Electromagnetic Fields with Electric and Magnetic Sources 293 2.2 Physical Problem and Equivalent Exterior and Interior Problems 296 2.2.1 Equivalent Exterior Problem, Equivalent Currents and Integral Equations 296 2.2.2 Equivalent Interior Problem, Equivalent Currents and Integral Equations 298 2.3 Surface Integral Equations for Equivalent Surface Currents, Tangential and Normal Components of Fields 300 3 Two-Dimensional Rough Dielectric Surfaces with Sparse Matrix Canonical Grid Method 304 3.1 Integral Equation and SMCG Method 304 3.2 Numerical Results of Bistatic Scattering Coefficient 318 4 Scattering by Lossy Dielectric Surfaces with PBTG Method 326 4.1 Introduction 326 4.2 Formulation and Single Grid Implementation 328 4.3 Physics-Based Two-Grid Method 329 4.4 Numerical Results and Comparison with Second Order Perturbation Method 334 4.5 Numerical Simulations of Emissivity of Soils with Rough Surfaces at Microwave Frequencies 343 5 Four Stokes Parameters Based on Tangential Surface Fields 350 6 Parallel Implementation of SMCG on Low Cost Beowulf System 354 6.1 Introduction 354 6.2 Low-Cost Beowulf Cluster 355 6.3 Parallel Implementation of the SMCG Method and the PBTG Method 356 6.4 Numerical Results 360 References and Additional Readings 366 CHAPTER 7 VOLUME SCATTERING SIMULATIONS 371 1 Combining Simulations of Collective Volume Scattering Effects with Radiative Transfer Theory 373 2 Foldy-Lax Self-Consistent Multiple Scattering Equations 376 2.1 Final Exciting Field and Multiple Scattering Equation 376 2.2 Foldy-Lax Equations for Point Scatterers 379 2.3 The JV-Particle Scattering Amplitude 382 3 Analytical Solutions of Point Scatterers 382 3.1 Phase Function and Extinction Coefficient for Uniformly Distributed Point Scatterers 382 3.2 Scattering by Collection of Clusters 389 4 Monte Carlo Simulation Results of Point Scatterers 392 References and Additional Readings 401 CHAPTER 8 PARTICLE POSITIONS FOR DENSE MEDIA CHARACTERIZATIONS AND SIMULATIONS 403 1 Pair Distribution Functions and Structure Factors 404 1.1 Introduction 404 1.2 Percus Yevick Equation and Pair Distribution Function for Hard Spheres 406 1.3 Calculation of Structure Factor and Pair Distribution Function 409 2 Percus—Yevick Pair Distribution Functions for Multiple Sizes 411 3 Monte Carlo Simulations of Particle Positions 414 3.1 Metropolis Monte Carlo Technique 415 3.2 Sequential Addition Method 418 3.3 Numerical Results 418 4 Sticky Particles 424 4.1 Percus-Yevick Pair Distribution Function for Sticky Spheres 424 4.2 Pair Distribution Function of Adhesive Sphere Mixture 429 4.3 Monte Carlo Simulation of Adhesive Spheres 434 5 Particle Placement Algorithm for Spheroids 444 5.1 Contact Functions of Two Ellipsoids 445 5.2 Illustrations of Contact Functions 446 References and Additional Readings 450 CHAPTER 9 SIMULATIONS OF TWO-DIMENSIONAL DENSE MEDIA 453 1 Introduction 454 1.1 Extinction as a Function of Concentration 454 1.2 Extinction as a Function of Frequency 456 2 Random Positions of Cylinders 458 2.1 Monte Carlo Simulations of Positions of Hard Cylinders 458 2.2 Simulations of Pair Distribution Functions 460 2.3 Percus-Yevick Approximation of Pair Distribution Functions 461 2.4 Results of Simulations 463 2.5 Monte Carlo Simulations of Sticky Disks 463 3 Monte Carlo Simulations of Scattering by Cylinders 469 3.1 Scattering by a Single Cylinder 469 3.2 Foldy-Lax Multiple Scattering Equations for Cylinders 476 3.3 Coherent Field, Incoherent Field, and Scattering Coefficient 480 3.4 Scattered Field and Internal Field Formulations 481 3.5 Low Frequency Formulas 482 3.6 Independent Scattering 484 3.7 Simulation Results for Sticky and Non-Sticky Cylinders 485 4 Sparse-Matrix Canonical-Grid Method for Scattering by Many Cylinders 486 4.1 Introduction 486 4.2 The Two-Dimensional Scattering Problem of Many Dielectric Cylinders 489 4.3 Numerical Results of Scattering and CPU Comparisons 490 References and Additional Readings 493 CHAPTER 10 DENSE MEDIA MODELS AND THREE-DIMENSIONAL SIMULATIONS 495 1 Introduction 496 2 Simple Analytical Models For Scattering From a Dense Medium 496 2.1 Effective Permittivity 496 2.2 Scattering Attenuation and Coherent Propagation Constant 500 2.3 Coherent Reflection and Incoherent Scattering From a Half-Space of Scatterers 505 2.4 A Simple Dense Media Radiative Transfer Theory 510 3 Simulations Using Volume Integral Equations 512 3.1 Volume Integral Equation 512 3.2 Simulation of Densely Packed Dielectric Spheres 514 3.3 Densely Packed Spheroids 518 4 Numerical Simulations Using T-Matrix Formalism 533 4.1 Multiple Scattering Equations 533 4.2 Computational Considerations 541 4.3 Results and Comparisons with Analytic Theory 545 4.4 Simulation of Absorption Coefficient 547 References and Additional Readings 548 CHAPTER 11 ANGULAR CORRELATION FUNCTION AND DETECTION OF BURIED OBJECT 551 1 Introduction 552 2 Two-Dimensional Simulations of Angular Memory Effect and Detection of Buried Object 553 2.1 Introduction 553 2.2 Simple and General Derivation of Memory Effect 553 2.3 ACF of Random Rough Surfaces with Different Averaging Methods 555 2.4 Scattering by a Buried Object Under a Rough Surface 557 3 Angular Correlation Function of Scattering by a Buried Object Under a 2-D Random Rough Surface (3-D Scattering) 564 3.1 Introduction 564 3.2 Formulation of Integral Equations 565 3.3 Statistics of Scattered Fields 570 3.4 Numerical Illustrations of ACF and PACF 571 4 Angular Correlation Function Applied to Correlation Imaging in Target Detection 575 4.1 Introduction 575 4.2 Formulation of Imaging 578 4.3 Simulations of SAR Data and ACF Processing 580 References and Additional Readings 591 CHAPTER 12 MULTIPLE SCATTERING BY CYLINDERS IN THE PRESENCE OF BOUNDARIES 593 1 Introduction 594 2 Scattering by Dielectric Cylinders Above a Dielectric Half-Space 594 2.1 Scattering from a Layer of Vertical Cylinders: First-Order Solution 594 2.2 First- and Second-Order Solutions 603 2.3 Results of Monte Carlo Simulations 613 3 Scattering by Cylinders in the Presence of Two Reflective Boundaries 622 3.1 Vector Cylindrical Wave Expansion of Dyadic Green's Function Between Two Perfect Conductors 622 3.2 Dyadic Green's Function of a Cylindrical Scatterer Between Two PEC 629 3.3 Dyadic Green's Function with Multiple Cylinders 631 3.4 Excitation of Magnetic Ring Currents 635 3.4.1 First Order Solution 637 3.4.2 Numerical Results 638 References and Additional Readings 640 CHAPTER 13 ELECTROMAGNETIC WAVES SCATTERING BY VEGETATION 641 1 Introduction 642 2 Plant Modeling by Using L-Systems 644 2.1 Lindenmayer Systems 644 2.2 Turtle Interpretation of L-Systems 646 2.3 Computer Simulations of Stochastic L-Systems and Input Files 649 3 Scattering from Trees Generated by L-Systems Based on Coherent Addition Approximation 654 3.1 Single Scattering by a Particle in the Presence of Reflective Boundary 655 3.1.1 Electric Field and Dyadic Green's Function 655 3.1.2 Scattering by a Single Particle 656 3.2 Scattering by Trees 659 4 Coherent Addition Approximation with Attenuation 667 5 Scattering from Plants Generated by L-Systems Based on Discrete Dipole Approximation 669 5.1 Formulation of Discrete Dipole Approximation (DDA) Method 670 5.2 Scattering by Simple Trees 672 5.3 Scattering by Honda Trees 677 6 Rice Canopy Scattering Model 685 6.1 Model Description 685 6.2 Model Simulation 689 References and Additional Readings 691 INDEX 693

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Book SynopsisA timely and authoritative guide to the state of the art of wave scattering Scattering of Electromagnetic Waves offers in three volumes a complete and up-to-date treatment of wave scattering by random discrete scatterers and rough surfaces. Written by leading scientists who have made important contributions to wave scattering over three decades, this new work explains the principles, methods, and applications of this rapidly expanding, interdisciplinary field. It covers both introductory and advanced material and provides students and researchers in remote sensing as well as imaging, optics, and electromagnetic theory with a one-stop reference to a wealth of current research results. Plus, Scattering of Electromagnetic Waves contains detailed discussions of both analytical and numerical methods, including cutting-edge techniques for the recovery of earth/land parametric information. The three volumes are entitled respectively Theories and Applications, Numerical Simulation, andTrade Review"Here they [the authors] delve deeper into the topics raised in the first two volumes..." (SciTech Book News, Vol. 25, No. 3, September 2001)Table of ContentsPREFACE xiii CHAPTER 1 TWO-DIMENSIONAL RANDOM ROUGH SURFACE SCATTERING BASED ON SMALL PERTURBATION METHOD 1 1 Electromagnetic Wave Scattering by a Perfect Electric Conductor 2 1.1 Zeroth- and First-Order Solutions 7 1.2 Second-Order Solutions 11 2 Electromagnetic Wave Scattering by a Dielectric Rough Surface 18 2.1 Zeroth- and First-Order Solutions 27 2.2 Second-Order Solutions 36 3 Coherent Reflection, Emissivities, and Bistatic Scattering Coefficients of Random Dielectric Surfaces 47 3.1 Coherent Reflection 48 3.2 Emissivities of Four Stokes Parameters 51 3.3 Bistatic Scattering Coefficients 58 References and Additional Readings 61 CHAPTER 2 KIRCHHOFF APPROACH AND RELATED METHODS FOR ROUGH SURFACE SCATTERING 65 1 Kirchhoff Approach 66 1.1 Perfectly Conducting Rough Surface 66 1.2 Dielectric Rough Surfaces 72 1.3 Second-Order Slope Corrections 94 2 Phase Perturbation Method 101 3 Emissivity Based on Composite Surface Model 108 References and Additional Readings 118 CHAPTER 3 VOLUME SCATTERING: CASCADE OF LAYERS 121 1 Single Scattering Solution of a Thin Layer, Coherent Wave, and Effective Propagation Constant 122 2 Transition Operator 128 3 Electromagnetic Wave Case of a Thin Layer and Extinction Matrix 130 4 First- and Second-Order Solutions: Incoherent Waves 135 5 Cascading of Layers: From First- and Second-Order Wave Solutions to Radiative Transfer Equation 143 6 Effects of Clustering 150 References and Additional Readings 160 CHAPTER 4 ANALYTIC WAVE THEORY FOR A MEDIUM WITH PERMITTIVITY FLUCTUATIONS 161 1 Dyson's Equation for the Mean Field 162 1.1 Bilocal Approximation 167 1.2 Nonlinear Approximation 170 2 Second Moment of the Field 171 2.1 Bethe-Salpeter Equation 171 2.2 Energy Conservation 175 3 Strong Permittivity Fluctuations 178 3.1 Random Medium with Spherically Symmetric Correlation Function 179 3.2 Very Low Frequency Effective Permittivity 181 3.3 Effective Permittivity Under the Bilocal Approximation 182 3.4 Backscattering Coefficients 185 3.5 Results of Effective Permittivity and Bistatic Coefficients 187 References and Additional Readings 194 CHAPTER 5 MULTIPLE SCATTERING THEORY FOR DISCRETE SCATTERERS 197 1 Transition Operator 198 2 Multiple Scattering Equations 203 3 Approximations of Multiple Scattering Equations 204 3.1 Configurational Average of Multiple Scattering Equations 205 3.2 Effective Field Approximation (EFA, Foldy's Approximation) 207 3.3 Quasi-crystalline Approximation (QCA) 210 3.4 Coherent Potential (CP) 213 3.5 Quasi-crystalline Approximation with Coherent Potential (QCA-CP) 216 3.6 Low-Frequency Solutions 219 3.7 QCA-CP for Multiple Species of Particles 224 4 Ward's Identity and Energy Conservation 226 5 Derivation of Radiative Transfer Equation from Ladder Approximation 232 References and Additional Readings 241 CHAPTER 6 QUASI-CRYSTALLINE APPROXIMATION IN DENSE MEDIA SCATTERING 245 1 Scattering of Electromagnetic Waves from a Half-Space of Dielectric Scatterers— Normal Incidence 246 1.1 Coherent Wave Propagation 247 1.2 Effective Phase Velocity and Attenuation Rate in the Low-Frequency Limit 257 1.3 Dispersion Relations at Higher Frequencies 259 2 Scattering of Electromagnetic Waves from a Half-Space of Dielectric Scatterers—Oblique Incidence 266 2.1 Dispersion Relation and Coherent Reflected Wave 266 2.2 Vertically and Horizontally Polarized Incidence 275 3 Cases with Size Distributions 280 3.1 Coherent Field 281 3.2 Incoherent Field Using Distorted Born Approximation 287 4 Dense Media Radiative Transfer Theory Based on Quasi-crystalline Approximation 300 4.1 Phase Matrix, Extinction, Scattering, and Absorption Coefficients 301 4.2 Brightness Temperature Computed with QCA-based DMRT 307 4.3 Numerical Results for Sticky and Non-Sticky Particles 309 References and Additional Readings 319 CHAPTER 7 DENSE MEDIA SCATTERING 323 1 Introduction 324 2 Effective Propagation Constants, Mean Green's Function, and Mean Field for Half-Space DiscreteRandom Medium of Multiple Species 325 3 Derivation of Dense Media Radiative Transfer Equation (DMRT) 329 4 Dense Media Radiative Transfer Equations for Active Remote Sensing 340 5 General Relation between Active and Passive Remote Sensing with Temperature Distribution 344 6 Dense Media Radiative Transfer Equations for Passive Remote Sensing 349 7 Numerical Illustrations of Active and Passive Remote Sensing 351 References and Additional Readings 357 CHAPTER 8 BACKSCATTERING ENHANCEMENT 359 1 Introduction 360 1.1 Volume Scattering 361 1.2 Volume Scattering in the Presence of Reflective Boundary 362 2 Second-Order Volume Scattering Theory of Isotropic Point Scatterers 366 3 Summation of Ladder Terms and Cyclical Terms for Isotropic Point Scatterers 374 3.1 Formulation 375 3.2 Numerical Illustrations 380 4 Anisotropic Scatterers and Diffusion Approximation 385 4.1 Summation of Ladder Terms and Cyclical Terms 386 4.2 Unidirectional Point Source Green's Function 391 4.3 Second-Order Multiple-Scattering Theory 393 4.4 Diffusion Approximation 395 4.5 Numerical Results 399 References and Additional Readings 403 INDEX 407

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Book SynopsisAn outgrowth of the author''s extensive experience teaching senior and graduate level students, this is both a thorough introduction and a solid professional reference. * Material covered has been developed based on a 35-year research program associated with such systems as the Landsat satellite program and later satellite and aircraft programs. * Covers existing aircraft and satellite programs and several future programs *An Instructor''s Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department.Table of ContentsPreface. PART I: INTRODUCTION. Chapter 1. Introduction and Background. PART II: THE BASICS FOR CONVENTIONAL MULTISPECTRAL DATA. Chapter 2. Radiation and Sensor Systems in Remote Sensing. Chapter 3. Pattern Recognition in Remote Sensing. PART III: ADDITIONAL DETAILS. Chapter 4. Training a Classifier. Chapter 5. Hyperspectral Data Characteristics. Chapter 6. Feature Definition. Chapter 7. A Data Analysis Paradigm and Examples. Chapter 8. Use of Spatial Variations. Chapter 9. Noise in Remote Sensing Systems. Chapter 10. Multispectral Image Data Preprocessing. Appendix. An Outline of Probability Theory. Exercises. Index.

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Book SynopsisNeural networks consist of interconnected groups of neurons which function as processing units and aim to reconstruct the operation of the human brain.Table of ContentsPreface. Introduction. Fundamentals. Network Architectures for Prediction. Activation Functions Used in Neural Networks. Recurrent Neural Networks Architectures. Neural Networks as Nonlinear Adaptive Filters. Stability Issues in RNN Architectures. Data-Reusing Adaptive Learning Algorithms. A Class of Normalised Algorithms for Online Training of Recurrent Neural Networks. Convergence of Online Learning Algorithms in Neural Networks. Some Practical Considerations of Predictability and Learning Algorithms for Various Signals. Exploiting Inherent Relationships Between Parameters in Recurrent Neural Networks. Appendix A: The O Notation and Vector and Matrix Differentiation. Appendix B: Concepts from the Approximation Theory. Appendix C: Complex Sigmoid Activation Functions, Holomorphic Mappings and Modular Groups. Appendix D: Learning Algorithms for RNNs. Appendix E: Terminology Used in the Field of Neural Networks. Appendix F: On the A Posteriori Approach in Science and Engineering. Appendix G: Contraction Mapping Theorems. Appendix H: Linear GAS Relaxation. Appendix I: The Main Notions in Stability Theory. Appendix J: Deasonsonalising Time Series. References. Index.

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Book SynopsisA topical introduction on the ability of artificial neural networks to not only solve on-line a wide range of optimization problems but also to create new techniques and architectures. Provides in-depth coverage of mathematical modeling along with illustrative computer simulation results.Table of ContentsMathematical Preliminaries of Neurocomputing. Architectures and Electronic Implementation of Neural Network Models. Unconstrained Optimization and Learning Algorithms. Neural Networks for Linear, Quadratic Programming and Linear Complementarity Problems. A Neural Network Approach to the On-Line Solution of a System of Linear Algebraic Equations and Related Problems. Neural Networks for Matrix Algebra Problems. Neural Networks for Continuous, Nonlinear, Constrained Optimization Problems. Neural Networks for Estimation, Identification and Prediction. Neural Networks for Discrete and Combinatorial Optimization Problems. Appendices. Subject Index.

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Book SynopsisSignal analysis gives an insight into the properties of signals and stochastic processes by methodology. Linear transforms are integral to the continuing growth of signal processes as they characterize and classify signals. In particular, those transforms that provide time-frequency signal analysis are attracting greater numbers of researchers and are becoming an area of considerable importance. The key characteristic of these transforms, along with a certain time-frequency localization called the wavelet transform and various types of multirate filter banks, is their high computational efficiency. It is this computational efficiently which accounts for their increased application. This book provides a complete overview and introduction to signal analysis. It presents classical and modern signal analysis methods in a sequential structure starting with the background to signal theory. Progressing through the book the author introduces more advanced topics in an easy to understand style.Trade Review"...excellent and interesting reading for digital signal processing engineers and designers and for postgraduate students in electrical and computer faculties." (Mathematical Reviews, 2002d)Table of ContentsSignals and Signal Spaces. Integral Signal Representations. Discrete Signal Representations. Examples of Discrete Transforms. Transforms and Filters for Stochastic Processes. Filter Banks. Short-Time Fourier Analysis. Wavelet Transform. Non-Linear Time-Frequency Distributions. Bibliography. Index.

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Book SynopsisTime varying process identification (TVPI) techniques facilitate adaptive noise reduction, echo cancellation and predictive coding of signals. This treatment addresses the identification of time-varying characteristics of dynamic processes.Trade Review"...a comprehensive treatment...well-written and successful in combining mathematics and practical understanding of real world applications..." (Automatica, No.38, 2002)Table of ContentsModeling Essentials. Models of Nonstationary Processes. Process Segmentation. Weighted Least Squares. Least Mean Squares. Basis Functions. Kalman Filtering. Practical Issues. Epilogue. References. Index.

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Book SynopsisBrimming with top articles from experts in signal processing and biomedical engineering, Time Frequency and Wavelets in Biomedical Signal Processing introduces time--frequency, time--scale, wavelet transform methods, and their applications in biomedical signal processing.Table of ContentsList of Contributors. Preface. TIME-FREQUENCY ANALYSIS METHODS WITH BIOMEDICAL APPLICATIONS. Recent Advances in Time-Frequency Representations: SomeTheoretical Foundation (W. Williams). Biological Applications and Interpretations of Time-Frequency Signal Analysis (W. Williams). The Application of Advanced Time-Frequency Analysis Techniques to Doppler Ultrasound (S. Marple, et al.). Analysis of ECG Late Potentials Using Time-Frequency Methods (H. Dickhaus & H. Heinrich). Time-Frequency Distributions Applied to Uterine EMG: Characterization and Assessment (J. Duchene & D. Devedeux). Time-Frequency Analyses of the Electrogastrogram (Z. Lin and J. Chen). Recent Advances in Time-Frequency and Time-Scale Methods (C. Mello & M. Akay). WAVELETS, WAVELET PACKETS, AND MATCHING PURSUITS WITH BIOMEDICAL APPLICATIONS. Fast Algorithms for Wavelet Transform Computation (O. Rioul & P. Duhamel). Analysis of Cellular Vibrations in the Living Cochlea Using the Continuous Wavelet Transform and the Short-Time Fourier Transform (M. Teich, et al.). Alterative Processing Method Using Gabor Wavelets and the Wavelet Transform for the Analysis of Phonocardiogram Signals (M. Matalgah, et al.). Wavelet Feature Extraction from Neurophysiological Signals (M. Sun & R. Sclabassi). Experiments with Adapted Wavelet De-Noising for Medical Signals and Images (R. Coifman & M. Wickerhauser). Speech Enhancement for Hearing Aids (J. Rutledge). From Continuous Wavelet Transform to Wavelet Packets: Application to the Estimation of Pulmonary Microvascular Pressure (M. Karrakchou & M. Kunt). In Pursuit of Time-Frequency Representation of Brain Signals (P. Durka & K. Blinowska). EEG Spike Directors Based on Different Decompositions: A Comparative Study (L. Senhadji, et al.). WAVELETS AND MEDICAL IMAGING. A Discrete Dyadic Wavelet Transform for Multidimensional Feature Analysis (I. Koren & A. Laine). Hexagonal QMF Banks and Wavelets (S. Schuler & A. Laine). Inversion of the Radon Transform under Wavelet Constraints (B. Sahiner & A. Yagle). Wavelets Applied to Mammograms (W. Richardson). Hybrid Wavelet Transform for Image Enhancement forComputer-Assisted Diagnosis and Telemedicine Applications (L. Clarke, et al.). Medical Image Enhancement Using Wavelet Transform and Arithmetic Coding (P. Saipetch, et al.). Adapted Wavelet Encoding in Functional Magnetic Resonance Imaging (D. Healy, et al.). A Tutorial Overview of a Stabilization Algorithm for Limited-Angle Tomography (T. Olson). Wavelet Compression of Medical Images (A. Manduca). WAVELETS, NEURAL NETWORKS, AND FRACTALS. Single Side Scaling Wavelet Frame and Neural Network (Q. Zhang). Analysis of Evoked Potentials Using Wavelet Networks (H. Heinrich & H. Dickhaus). Self-Organizing Wavelet-Based Neural Networks (K. Kobayashi). On Wavelets and Fractal Processes (P. Flandrin). Fractal Analysis of Heart Rate Variability (R. Fischer & M. Akay). Index. Editor's Biography.

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Book SynopsisIn view of the extensive development of CCS 7 and fast-paced growth of ISDN in telecommunication networks throughout the world, this valuable resource serves as a timely reference and guide. Practical and up-to-date, Engineering Networks for Synchronization, CCS 7, and ISDN provides in-depth instruction on three important and closely related elements of the modern digital network: network synchronization, CCITT Common Channel Signaling System No. 7 (CCS 7), and Narrowband ISDN.Table of ContentsSeries Editor's Note. Foreword. Preface. Introduction. Digital Network Synchronization: Basic Concepts. Planning, Testing, and Monitoring Network Synchronization. CCS 7: General Description. Introduction to ISDN. Functions of the CCS 7 Signaling Link Level. Signaling Network Functions in CCS 7. ISDN: Services and Protocols. CCS 7 ISDN User Part. CCS 7 Planning and Implementation. Testing in CCS 7. Packet and Frame Mode Services in the ISDN. Planning and Implementation the ISDN. Testing in the ISDN. Timing in SONET and SDH. Appendix 1: Ordering Information. Appendix 2: List of ISUP Messages. Index. About the Author.

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Book Synopsis

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Book SynopsisA realistic and comprehensive review of joint approaches to machine learning and signal processing algorithms, with application to communications, multimedia, and biomedical engineering systems Digital Signal Processing with Kernel Methods reviews the milestones in the mixing of classical digital signal processing models and advanced kernel machines statistical learning tools. It explains the fundamental concepts from both fields of machine learning and signal processing so that readers can quickly get up to speed in order to begin developing the concepts and application software in their own research. Digital Signal Processing with Kernel Methods provides a comprehensive overview of kernel methods in signal processing, without restriction to any application field. It also offers example applications and detailed benchmarking experiments with real and synthetic datasets throughout. Readers can find further worked examples with Matlab source code on a website developed by the authors: hTable of ContentsAbout the Authors xiii Preface xvii Acknowledgements xxi List of Abbreviations xxiii Part I Fundamentals and Basic Elements 1 1 From Signal Processing to Machine Learning 3 1.1 A New Science is Born: Signal Processing 3 1.1.1 Signal Processing Before Being Coined 3 1.1.2 1948: Birth of the Information Age 4 1.1.3 1950s: Audio Engineering Catalyzes Signal Processing 4 1.2 From Analog to Digital Signal Processing 5 1.2.1 1960s: Digital Signal Processing Begins 5 1.2.2 1970s: Digital Signal Processing Becomes Popular 6 1.2.3 1980s: Silicon Meets Digital Signal Processing 6 1.3 Digital Signal Processing Meets Machine Learning 7 1.3.1 1990s: New Application Areas 7 1.3.2 1990s: Neural Networks, Fuzzy Logic, and Genetic Optimization 7 1.4 Recent Machine Learning in Digital Signal Processing 8 1.4.1 Traditional Signal Assumptions Are No Longer Valid 8 1.4.2 Encoding Prior Knowledge 8 1.4.3 Learning and Knowledge from Data 9 1.4.4 From Machine Learning to Digital Signal Processing 9 1.4.5 From Digital Signal Processing to Machine Learning 10 2 Introduction to Digital Signal Processing 13 2.1 Outline of the Signal Processing Field 13 2.1.1 Fundamentals on Signals and Systems 14 2.1.2 Digital Filtering 21 2.1.3 Spectral Analysis 24 2.1.4 Deconvolution 28 2.1.5 Interpolation 30 2.1.6 System Identification 31 2.1.7 Blind Source Separation 36 2.2.3 Sparsity, Compressed Sensing, and Dictionary Learning 44 2.3 Multidimensional Signals and Systems 48 2.3.1 Multidimensional Signals 49 2.3.2 Multidimensional Systems 51 2.4 Spectral Analysis on Manifolds 52 2.4.1 Theoretical Fundamentals 52 2.4.2 Laplacian Matrices 54 2.5 Tutorials and Application Examples 57 2.5.1 Real and Complex Signal Processing and Representations 57 2.5.2 Convolution, Fourier Transform, and Spectrum 63 2.5.3 Continuous-Time Signals and Systems 67 2.5.4 Filtering Cardiac Signals 70 2.5.5 Nonparametric Spectrum Estimation 74 2.5.6 Parametric Spectrum Estimation 77 2.5.7 Source Separation 81 2.5.8 Time–Frequency Representations and Wavelets 84 2.5.9 Examples for Spectral Analysis on Manifolds 87 2.6 Questions and Problems 94 3 Signal Processing Models 97 3.1 Introduction 97 3.2 Vector Spaces, Basis, and Signal Models 98 3.2.1 Basic Operations for Vectors 98 3.2.2 Vector Spaces 100 3.2.3 Hilbert Spaces 101 3.2.4 Signal Models 102 3.2.5 Complex Signal Models 104 3.2.6 Standard Noise Models in Digital Signal Processing 105 3.2.7 The Role of the Cost Function 107 3.2.8 The Role of the Regularizer 109 3.3 Digital Signal Processing Models 111 3.3.1 Sinusoidal Signal Models 112 3.3.2 System Identification Signal Models 113 3.3.3 Sinc Interpolation Models 116 3.3.4 Sparse Deconvolution 120 3.3.5 Array Processing 121 3.4 Tutorials and Application Examples 122 3.4.1 Examples of Noise Models 123 3.4.2 Autoregressive Exogenous System Identification Models 132 3.4.3 Nonlinear System Identification Using Volterra Models 138 3.4.4 Sinusoidal Signal Models 140 3.4.5 Sinc-based Interpolation 144 3.4.6 Sparse Deconvolution 152 3.4.7 Array Processing 157 3.5 Questions and Problems 160 3.A MATLABsimpleInterp Toolbox Structure 161 4 Kernel Functions and Reproducing Kernel Hilbert Spaces 165 4.1 Introduction 165 4.2 Kernel Functions and Mappings 169 4.2.1 Measuring Similarity with Kernels 169 4.2.2 Positive-Definite Kernels 169 4.2.3 Reproducing Kernel in Hilbert Space and Reproducing Property 170 4.2.4 Mercer’s Theorem 173 4.3 Kernel Properties 174 4.3.1 Tikhonov’s Regularization 175 4.3.2 Representer Theorem and Regularization Properties 176 4.3.3 Basic Operations with Kernels 178 4.4 Constructing Kernel Functions 179 4.4.1 Standard Kernels 179 4.4.2 Properties of Kernels 180 4.4.3 Engineering Signal Processing Kernels 181 4.5 Complex Reproducing Kernel in Hilbert Spaces 184 4.6 Support Vector Machine Elements for Regression and Estimation 186 4.6.1 Support Vector Regression Signal Model and Cost Function 186 4.6.2 Minimizing Functional 187 4.7 Tutorials and Application Examples 191 4.7.1 Kernel Calculations and Kernel Matrices 191 4.7.2 Basic Operations with Kernels 194 4.7.3 Constructing Kernels 197 4.7.4 Complex Kernels 199 4.7.5 Application Example for Support Vector Regression Elements 202 4.8 Concluding Remarks 205 4.9 Questions and Problems 205 Part II Function Approximation and Adaptive Filtering 209 5 A Support Vector Machine Signal Estimation Framework 211 5.1 Introduction 211 5.2 A Framework for Support Vector Machine Signal Estimation 213 5.3 Primal Signal Models for Support Vector Machine Signal Processing 216 5.3.1 Nonparametric Spectrum and System Identification 218 5.3.2 Orthogonal Frequency Division Multiplexing Digital Communications 220 5.3.3 Convolutional Signal Models 222 5.3.4 Array Processing 225 5.4 Tutorials and Application Examples 227 5.4.1 Nonparametric Spectral Analysis with Primal Signal Models 227 5.4.2 System Identification with Primal Signal Model ;;-filter 228 5.4.3 Parametric Spectral Density Estimation with Primal Signal Models 230 5.4.4 Temporal Reference Array Processing with Primal Signal Models 231 5.4.5 Sinc Interpolation with Primal Signal Models 233 6 Reproducing Kernel Hilbert Space Models for Signal Processing 241 6.1 Introduction 241 6.2 Reproducing Kernel Hilbert Space Signal Models 242 6.2.1 Kernel Autoregressive Exogenous Identification 244 6.2.2 Kernel Finite Impulse Response and the ;;-Filter 247 6.2.3 Kernel Array Processing with Spatial Reference 248 6.2.4 Kernel Semiparametric Regression 249 6.3 Tutorials and Application Examples 258 6.3.1 Nonlinear System Identification with Support Vector Machine–Autoregressive and Moving Average 258 6.3.2 Nonlinear System Identification with the ;;-filter 260 6.3.3 Electric Network Modeling with Semiparametric Regression 264 6.3.4 Promotional Data 272 6.3.5 Spatial and Temporal Antenna Array Kernel Processing 275 6.4 Questions and Problems 279 7 Dual Signal Models for Signal Processing 281 7.1 Introduction 281 7.2 Dual Signal Model Elements 281 7.3 Dual Signal Model Instantiations 283 7.3.1 Dual Signal Model for Nonuniform Signal Interpolation 283 7.3.2 Dual Signal Model for Sparse Signal Deconvolution 284 7.3.3 Spectrally Adapted Mercer Kernels 285 7.4 Tutorials and Application Examples 289 7.4.1 Nonuniform Interpolation with the Dual Signal Model 290 7.4.2 Sparse Deconvolution with the Dual Signal Model 292 7.4.3 Doppler Ultrasound Processing for Fault Detection 294 7.4.4 Spectrally Adapted Mercer Kernels 296 7.4.5 Interpolation of Heart Rate Variability Signals 304 7.4.6 Denoising in Cardiac Motion-Mode Doppler Ultrasound Images 309?m 7.4.7 Indoor Location from Mobile Devices Measurements 316 7.4.8 Electroanatomical Maps in Cardiac Navigation Systems 322 7.5 Questions and Problems 331 8 Advances in Kernel Regression and Function Approximation 333 8.1 Introduction 333 8.2 Kernel-Based Regression Methods 333 8.2.1 Advances in Support Vector Regression 334 8.2.2 Multi-output Support Vector Regression 338 8.2.3 Kernel Ridge Regression 339 8.2.4 Kernel Signal-To-Noise Regression 341 8.2.5 Semisupervised Support Vector Regression 343 8.2.6 Model Selection in Kernel Regression Methods 345 8.4.1 Comparing Support Vector Regression, Relevance Vector Machines, and Gaussian Process Regression 360 8.4.2 Profile-Dependent Support Vector Regression 362 8.4.3 Multi-output Support Vector Regression 364 8.4.4 Kernel Signal-to-Noise Ratio Regression 366 8.4.5 Semisupervised Support Vector Regression 368 8.4.6 Bayesian Nonparametric Model 369 8.4.7 Gaussian Process Regression 370 8.4.8 Relevance Vector Machines 379 8.5 Concluding Remarks 382 8.6 Questions and Problems 383 9 Adaptive Kernel Learning for Signal Processing 387 9.1 Introduction 387 9.2 Linear Adaptive Filtering 387 9.2.1 Least Mean Squares Algorithm 388 9.2.2 Recursive Least-Squares Algorithm 389 9.3 Kernel Adaptive Filtering 392 9.4 Kernel Least Mean Squares 392 9.4.1 Derivation of Kernel Least Mean Squares 393 9.4.2 Implementation Challenges and Dual Formulation 394 9.5.3 Prediction of the Mackey–Glass Time Series with Kernel Recursive Least Squares 401 9.5.4 Beyond the Stationary Model 402 9.5.5 Example on Nonlinear Channel Identification and Reconvergence 405 9.6 Explicit Recursivity for Adaptive Kernel Models 406 9.6.1 Recursivity in Hilbert Spaces 406 9.6.2 Recursive Filters in Reproducing Kernel Hilbert Spaces 408 9.7 Online Sparsification with Kernels 411 9.7.1 Sparsity by Construction 411 9.7.2 Sparsity by Pruning 413 9.8 Probabilistic Approaches to Kernel Adaptive Filtering 414 9.8.1 Gaussian Processes and Kernel Ridge Regression 415 9.8.2 Online Recursive Solution for Gaussian Processes Regression 416 9.8.3 Kernel Recursive Least Squares Tracker 417 9.8.4 Probabilistic Kernel Least Mean Squares 418 9.9 Further Reading 418 9.9.1 Selection of Kernel Parameters 418 9.9.2 Multi-Kernel Adaptive Filtering 419 9.9.3 Recursive Filtering in Kernel Hilbert Spaces 419 9.10 Tutorials and Application Examples 419 9.10.1 Kernel Adaptive Filtering Toolbox 420 9.10.2 Prediction of a Respiratory Motion Time Series 421 9.10.3 Online Regression on the KIN?h?eK Dataset 423 9.10.4 The Mackey–Glass Time Series 425 9.10.5 Explicit Recursivity on Reproducing Kernel in Hilbert Space and Electroencephalogram Prediction 427 9.10.6 Adaptive Antenna Array Processing 428 9.11 Questions and Problems 430 Part III Classification, Detection, and Feature Extraction 433 10 Support Vector Machine and Kernel Classification Algorithms 435 10.1 Introduction 435 10.2 Support Vector Machine and Kernel Classifiers 435 10.2.1 Support Vector Machines 435 10.2.2 Multiclass and Multilabel Support Vector Machines 441 10.2.3 Least-Squares Support Vector Machine 447 10.2.4 Kernel Fisher’s Discriminant Analysis 448 10.3 Advances in Kernel-Based Classification 452 10.3.1 Large Margin Filtering 452 10.3.2 Semisupervised Learning 454 10.3.3 Multiple Kernel Learning 460 10.3.4 Structured-Output Learning 462 10.3.5 Active Learning 468 10.4 Large-Scale Support Vector Machines 477 10.4.1 Large-Scale Support Vector Machine Implementations 477 10.4.2 Random Fourier Features 478 10.4.3 Parallel Support Vector Machine 480 10.4.4 Outlook 483 10.5 Tutorials and Application Examples 485 10.5.1 Examples of Support Vector Machine Classification 485 10.5.2 Example of Least-Squares Support Vector Machine 492 10.5.3 Kernel-Filtering Support Vector Machine for Brain–Computer Interface Signal Classification 493 10.5.4 Example of Laplacian Support Vector Machine 494 10.5.5 Example of Graph-Based Label Propagation 498 10.5.6 Examples of Multiple Kernel Learning 498 10.6 Concluding Remarks 501 10.7 Questions and Problems 502 11 Clustering and Anomaly Detection with Kernels 503 11.1 Introduction 503 11.2 Kernel Clustering 506 11.2.1 Kernelization of the Metric 506 11.2.2 Clustering in Feature Spaces 508 11.3 Domain Description Via Support Vectors 514 11.3.1 Support Vector Domain Description 514 11.3.2 One-Class Support Vector Machine 515 11.3.3 Relationship Between Support Vector Domain Description and Density Estimation 516 11.3.4 Semisupervised One-Class Classification 517 11.4 Kernel Matched Subspace Detectors 518 11.4.1 Kernel Orthogonal Subspace Projection 518 11.4.2 Kernel Spectral Angle Mapper 520 11.5 Kernel Anomaly Change Detection 522 11.5.1 Linear Anomaly Change Detection Algorithms 522 11.5.2 Kernel Anomaly Change Detection Algorithms 523 11.6 Hypothesis Testing with Kernels 525 11.6.1 Distribution Embeddings 526 11.6.3 Maximum Mean Discrepancy 527 11.6.3 One-Class Support Measure Machine 528 11.7 Tutorials and Application Examples 529 11.7.1 Example on Kernelization of the Metric 529 11.7.2 Example on Kernel k-Means 530 11.7.3 Domain Description Examples 531 11.7.4 Kernel Spectral Angle Mapper and Kernel Orthogonal Subspace Projection Examples 534 11.7.5 Example of Kernel Anomaly Change Detection Algorithms 536 11.7.6 Example on Distribution Embeddings and Maximum Mean Discrepancy 540 11.8 Concluding Remarks 541 11.9 Questions and Problems 542 12 Kernel Feature Extraction in Signal Processing 543 12.1 Introduction 543 12.2 Multivariate Analysis in Reproducing Kernel Hilbert Spaces 545 12.2.1 Problem Statement and Notation 545 12.2.2 Linear Multivariate Analysis 546 12.2.3 Kernel Multivariate Analysis 549 12.2.4 Multivariate Analysis Experiments 551 12.3 Feature Extraction with Kernel Dependence Estimates 555 12.3.1 Feature Extraction Using Hilbert–Schmidt Independence Criterion 556 12.3.2 Blind Source Separation Using Kernels 563 12.4 Extensions for Large-Scale and Semisupervised Problems 570 12.4.2 Efficiency with the Incomplete Cholesky Decomposition 570 12.4.3 Efficiency with Random Fourier Features 570 12.4.3 Sparse Kernel Feature Extraction 571 12.4.4 Semisupervised Kernel Feature Extraction 573 12.5 Domain Adaptation with Kernels 575 12.5.1 Kernel Mean Matching 578 12.5.2 Transfer Component Analysis 579 12.5.3 Kernel Manifold Alignment 581 12.5.4 Relations between Domain Adaptation Methods 585 12.5.5 Experimental Comparison between Domain Adaptation Methods 12.6 Concluding Remarks 587 12.7 Questions and Problems 588 References 589Index 631

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Book SynopsisThe modern financial industry has been required to deal with large and diverse portfolios in a variety of asset classes often with limited market data available.Table of ContentsList of Contributors xiii Preface xv 1 Overview 1 Ali N. Akansu, Sanjeev R. Kulkarni, and Dmitry Malioutov 1.1 Introduction 1 1.2 A Bird’s-Eye View of Finance 2 1.2.1 Trading and Exchanges 4 1.2.2 Technical Themes in the Book 5 1.3 Overview of the Chapters 6 1.3.1 Chapter 2: “Sparse Markowitz Portfolios” by Christine De Mol 6 1.3.2 Chapter 3: “Mean-Reverting Portfolios: Tradeoffs between Sparsity and Volatility” by Marco Cuturi and Alexandre d’Aspremont 7 1.3.3 Chapter 4: “Temporal Causal Modeling” by Prabhanjan Kambadur, Aurélie C. Lozano, and Ronny Luss 7 1.3.4 Chapter 5: “Explicit Kernel and Sparsity of Eigen Subspace for the AR(1) Process” by Mustafa U. Torun, Onur Yilmaz and Ali N. Akansu 7 1.3.5 Chapter 6: “Approaches to High-Dimensional Covariance and Precision Matrix Estimation” by Jianqing Fan, Yuan Liao, and Han Liu 7 1.3.6 Chapter 7: “Stochastic Volatility: Modeling and Asymptotic Approaches to Option Pricing and Portfolio Selection” by Matthew Lorig and Ronnie Sircar 7 1.3.7 Chapter 8: “Statistical Measures of Dependence for Financial Data” by David S. Matteson, Nicholas A. James, and William B. Nicholson 8 1.3.8 Chapter 9: “Correlated Poisson Processes and Their Applications in Financial Modeling” by Alexander Kreinin 8 1.3.9 Chapter 10: “CVaR Minimizations in Support Vector Machines” by Junya Gotoh and Akiko Takeda 8 1.3.10 Chapter 11: “Regression Models in Risk Management” by Stan Uryasev 8 1.4 Other Topics in Financial Signal Processing and Machine Learning 9 References 9 2 Sparse Markowitz Portfolios 11 ChristineDeMol 2.1 Markowitz Portfolios 11 2.2 Portfolio Optimization as an Inverse Problem: The Need for Regularization 13 2.3 Sparse Portfolios 15 2.4 Empirical Validation 17 2.5 Variations on the Theme 18 2.5.1 Portfolio Rebalancing 18 2.5.2 Portfolio Replication or Index Tracking 19 2.5.3 Other Penalties and Portfolio Norms 19 2.6 Optimal Forecast Combination 20 Acknowlegments 21 References 21 3 Mean-Reverting Portfolios 23 Marco Cuturi and Alexandre d’Aspremont 3.1 Introduction 23 3.1.1 Synthetic Mean-Reverting Baskets 24 3.1.2 Mean-Reverting Baskets with Sufficient Volatility and Sparsity 24 3.2 Proxies for Mean Reversion 25 3.2.1 Related Work and Problem Setting 25 3.2.2 Predictability 26 3.2.3 Portmanteau Criterion 27 3.2.4 Crossing Statistics 28 3.3 Optimal Baskets 28 3.3.1 Minimizing Predictability 29 3.3.2 Minimizing the Portmanteau Statistic 29 3.3.3 Minimizing the Crossing Statistic 29 3.4 Semidefinite Relaxations and Sparse Components 30 3.4.1 A Semidefinite Programming Approach to Basket Estimation 30 3.4.2 Predictability 30 3.4.3 Portmanteau 31 3.4.4 Crossing Stats 31 3.5 Numerical Experiments 32 3.5.1 Historical Data 32 3.5.2 Mean-reverting Basket Estimators 33 3.5.3 Jurek and Yang (2007) Trading Strategy 33 3.5.4 Transaction Costs 33 3.5.5 Experimental Setup 36 3.5.6 Results 36 3.6 Conclusion 39 References 39 4 Temporal Causal Modeling 41 Prabhanjan Kambadur, Aurélie C. Lozano, and Ronny Luss 4.1 Introduction 41 4.2 TCM 46 4.2.1 Granger Causality and Temporal Causal Modeling 46 4.2.2 Grouped Temporal Causal Modeling Method 47 4.2.3 Synthetic Experiments 49 4.3 Causal Strength Modeling 51 4.4 Quantile TCM (Q-TCM) 52 4.4.1 Modifying Group OMP for Quantile Loss 52 4.4.2 Experiments 53 4.5 TCM with Regime Change Identification 55 4.5.1 Model 56 4.5.2 Algorithm 58 4.5.3 Synthetic Experiments 60 4.5.4 Application: Analyzing Stock Returns 62 4.6 Conclusions 63 References 64 5 Explicit Kernel and Sparsity of Eigen Subspace for the AR(1) Process 67 Mustafa U. Torun, Onur Yilmaz, and Ali N. Akansu 5.1 Introduction 67 5.2 Mathematical Definitions 68 5.2.1 Discrete AR(1) Stochastic Signal Model 68 5.2.2 Orthogonal Subspace 69 5.3 Derivation of Explicit KLT Kernel for a Discrete AR(1) Process 72 5.3.1 A Simple Method for Explicit Solution of a Transcendental Equation 73 5.3.2 Continuous Process with Exponential Autocorrelation 74 5.3.3 Eigenanalysis of a Discrete AR(1) Process 76 5.3.4 Fast Derivation of KLT Kernel for an AR(1) Process 79 5.4 Sparsity of Eigen Subspace 82 5.4.1 Overview of Sparsity Methods 83 5.4.2 pdf-Optimized Midtread Quantizer 84 5.4.3 Quantization of Eigen Subspace 86 5.4.4 pdf of Eigenvector 87 5.4.5 Sparse KLT Method 89 5.4.6 Sparsity Performance 91 5.5 Conclusions 97 References 97 6 Approaches to High-Dimensional Covariance and Precision Matrix Estimations 100 Jianqing Fan, Yuan Liao, and Han Liu 6.1 Introduction 100 6.2 Covariance Estimation via Factor Analysis 101 6.2.1 Known Factors 103 6.2.2 Unknown Factors 104 6.2.3 Choosing the Threshold 105 6.2.4 Asymptotic Results 105 6.2.5 A Numerical Illustration 107 6.3 Precision Matrix Estimation and Graphical Models 109 6.3.1 Column-wise Precision Matrix Estimation 110 6.3.2 The Need for Tuning-insensitive Procedures 111 6.3.3 TIGER: A Tuning-insensitive Approach for Optimal Precision Matrix Estimation 112 6.3.4 Computation 114 6.3.5 Theoretical Properties of TIGER 114 6.3.6 Applications to Modeling Stock Returns 115 6.3.7 Applications to Genomic Network 118 6.4 Financial Applications 119 6.4.1 Estimating Risks of Large Portfolios 119 6.4.2 Large Panel Test of Factor Pricing Models 121 6.5 Statistical Inference in Panel Data Models 126 6.5.1 Efficient Estimation in Pure Factor Models 126 6.5.2 Panel Data Model with Interactive Effects 127 6.5.3 Numerical Illustrations 130 6.6 Conclusions 131 References 131 7 Stochastic Volatility 135 Matthew Lorig and Ronnie Sircar 7.1 Introduction 135 7.1.1 Options and Implied Volatility 136 7.1.2 Volatility Modeling 137 7.2 Asymptotic Regimes and Approximations 141 7.2.1 Contract Asymptotics 142 7.2.2 Model Asymptotics 142 7.2.3 Implied Volatility Asymptotics 143 7.2.4 Tractable Models 145 7.2.5 Model Coefficient Polynomial Expansions 146 7.2.6 Small “Vol of Vol” Expansion 152 7.2.7 Separation of Timescales Approach 152 7.2.8 Comparison of the Expansion Schemes 154 7.3 Merton Problem with Stochastic Volatility: Model Coefficient Polynomial Expansions 155 7.3.1 Models and Dynamic Programming Equation 155 7.3.2 Asymptotic Approximation 157 7.3.3 Power Utility 159 7.4 Conclusions 160 Acknowledgements 160 References 160 8 Statistical Measures of Dependence for Financial Data 162 David S. Matteson, Nicholas A. James, and William B. Nicholson 8.1 Introduction 162 8.2 Robust Measures of Correlation and Autocorrelation 164 8.2.1 Transformations and Rank-Based Methods 166 8.2.2 Inference 169 8.2.3 Misspecification Testing 171 8.3 Multivariate Extensions 174 8.3.1 Multivariate Volatility 175 8.3.2 Multivariate Misspecification Testing 176 8.3.3 Granger Causality 176 8.3.4 Nonlinear Granger Causality 177 8.4 Copulas 179 8.4.1 Fitting Copula Models 180 8.4.2 Parametric Copulas 181 8.4.3 Extending beyond Two Random Variables 183 8.4.4 Software 185 8.5 Types of Dependence 185 8.5.1 Positive and Negative Dependence 185 8.5.2 Tail Dependence 187 References 188 9 Correlated Poisson Processes and Their Applications in Financial Modeling 191 Alexander Kreinin 9.1 Introduction 191 9.2 Poisson Processes and Financial Scenarios 193 9.2.1 Integrated Market–Credit Risk Modeling 193 9.2.2 Market Risk and Derivatives Pricing 194 9.2.3 Operational Risk Modeling 194 9.2.4 Correlation of Operational Events 195 9.3 Common Shock Model and Randomization of Intensities 196 9.3.1 Common Shock Model 196 9.3.2 Randomization of Intensities 196 9.4 Simulation of Poisson Processes 197 9.4.1 Forward Simulation 197 9.4.2 Backward Simulation 200 9.5 Extreme Joint Distribution 207 9.5.1 Reduction to Optimization Problem 207 9.5.2 Monotone Distributions 208 9.5.3 Computation of the Joint Distribution 214 9.5.4 On the Frechet–Hoeffding Theorem 215 9.5.5 Approximation of the Extreme Distributions 217 9.6 Numerical Results 219 9.6.1 Examples of the Support 219 9.6.2 Correlation Boundaries 221 9.7 Backward Simulation of the Poisson-Wiener Process 222 9.8 Concluding Remarks 227 Acknowledgments 228 Appendix A 229 A. 1 Proof of Lemmas 9.2 and 9.3 229 A.1.1 Proof of Lemma 9.2 229 A.1.2 Proof of Lemma 9.3 230 References 231 10 CVaR Minimizations in Support Vector Machines 233 Jun-ya Gotoh and Akiko Takeda 10.1 What Is CVaR? 234 10.1.1 Definition and Interpretations 234 10.1.2 Basic Properties of CVaR 238 10.1.3 Minimization of CVaR 240 10.2 Support Vector Machines 242 10.2.1 Classification 242 10.2.2 Regression 246 10.3 ν-SVMs as CVaR Minimizations 247 10.3.1 ν-SVMs as CVaR Minimizations with Homogeneous Loss 247 10.3.2 ν-SVMs as CVaR Minimizations with Nonhomogeneous Loss 251 10.3.3 Refining the ν-Property 253 10.4 Duality 256 10.4.1 Binary Classification 256 10.4.2 Geometric Interpretation of ν-SVM 257 10.4.3 Geometric Interpretation of the Range of ν for ν-SVC 258 10.4.4 Regression 259 10.4.5 One-class Classification and SVDD 259 10.5 Extensions to Robust Optimization Modelings 259 10.5.1 Distributionally Robust Formulation 259 10.5.2 Measurement-wise Robust Formulation 261 10.6 Literature Review 262 10.6.1 CVaR as a Risk Measure 263 10.6.2 From CVaR Minimization to SVM 263 10.6.3 From SVM to CVaR Minimization 263 10.6.4 Beyond CVaR 263 References 264 11 Regression Models in Risk Management 266 Stan Uryasev 11.1 Introduction 267 11.2 Error and Deviation Measures 268 11.3 Risk Envelopes and Risk Identifiers 271 11.3.1 Examples of Deviation Measures D, Corresponding Risk Envelopes Q, and Sets of Risk Identifiers QD(X) 272 11.4 Error Decomposition in Regression 273 11.5 Least-Squares Linear Regression 275 11.6 Median Regression 277 11.7 Quantile Regression and Mixed Quantile Regression 281 11.8 Special Types of Linear Regression 283 11.9 Robust Regression 284 References, Further Reading, and Bibliography 287 Index 289

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Book SynopsisFeatures inexpensive ARM Cortex-M4 microcontroller development systems available from Texas Instruments and STMicroelectronics. This book presents a hands-on approach to teaching Digital Signal Processing (DSP) with real-time examples using the ARM Cortex-M4 32-bit microprocessor. Real-time examples using analog input and output signals are provided, giving visible (using an oscilloscope) and audible (using a speaker or headphones) results. Signal generators and/or audio sources, e.g. iPods, can be used to provide experimental input signals. The text also covers the fundamental concepts of digital signal processing such as analog-to-digital and digital-to-analog conversion, FIR and IIR filtering, Fourier transforms, and adaptive filtering. Digital Signal Processing Using the ARM Cortex-M4: Uses a large number of simple example programs illustrating DSP concepts in real-time, in an electrical engineering laboratory setting Includes exTable of ContentsPreface xi 1 ARM® CORTEX® - M4 Development Systems 1 1.1 Introduction 1 1.1.1 Audio Interfaces 2 1.1.2 Texas Instruments TM4C123 LaunchPad and STM32F407 Discovery Development Kits 2 1.1.3 Hardware and Software Tools 6 Reference 7 2 Analog Input and Output 9 2.1 Introduction 9 2.1.1 Sampling, Reconstruction, and Aliasing 9 2.2 TLV320AIC3104 (AIC3104) Stereo Codec for Audio Input and Output 10 2.3 WM5102 Audio Hub Codec for Audio Input and Output 12 2.4 Programming Examples 12 2.5 Real-Time Input and Output Using Polling, Interrupts, and Direct Memory Access (DMA) 12 2.5.1 I2S Emulation on the TM4C123 15 2.5.2 Program Operation 15 2.5.3 Running the Program 16 2.5.4 Changing the Input Connection to LINE IN 16 2.5.5 Changing the Sampling Frequency 16 2.5.6 Using the Digital MEMS Microphone on the Wolfson Audio Card 20 2.5.7 Running the Program 21 2.5.8 Running the Program 23 2.5.9 DMA in the TM4C123 Processor 26 2.5.10 Running the Program 30 2.5.11 Monitoring Program Execution 30 2.5.12 Measuring the Delay Introduced by DMA-Based I/O 30 2.5.13 DMA in the STM32F407 Processor 34 2.5.14 Running the Program 35 2.5.15 Measuring the Delay Introduced by DMA-Based I/O 35 2.5.16 Running the Program 46 2.6 Real-Time Waveform Generation 46 2.6.1 Running the Program 49 2.6.2 Out-of-Band Noise in the Output of the AIC3104 Codec (tm4c123_sine48_intr.c). 49 2.6.3 Running the Program 53 2.6.4 Running the Program 62 2.6.5 Running the Program 69 2.7 Identifying the Frequency Response of the DAC Using Pseudorandom Noise 70 2.7.1 Programmable De-Emphasis in the AIC3104 Codec 72 2.7.2 Programmable Digital Effects Filters in the AIC3104 Codec 72 2.8 Aliasing 78 2.8.1 Running the Program 83 2.9 Identifying the Frequency Response of the DAC Using An Adaptive Filter 83 2.9.1 Running the Program 84 2.10 Analog Output Using the STM32F407’S 12-BIT DAC 91 References 96 3 Finite Impulse Response Filters 97 3.1 Introduction to Digital Filters 97 3.1.1 The FIR Filter 97 3.1.2 Introduction to the z-Transform 99 3.1.3 Definition of the z-Transform 100 3.1.4 Properties of the z-Transform 108 3.1.5 z-Transfer Functions 111 3.1.6 Mapping from the s-Plane to the z-Plane 111 3.1.7 Difference Equations 112 3.1.8 Frequency Response and the z-Transform 113 3.1.9 The Inverse z-Transform 114 3.2 Ideal Filter Response Classifications: LP, HP, BP, BS 114 3.2.1 Window Method of FIR Filter Design 114 3.2.2 Window Functions 116 3.2.3 Design of Ideal High-Pass Band-Pass and Band-Stop FIR Filters Using the Window Method 120 3.3 Programming Examples 123 3.3.1 Altering the Coefficients of the Moving Average Filter 132 3.3.2 Generating FIR Filter Coefficient Header Files Using MATLAB 137 4 Infinite Impulse Response Filters 163 4.1 Introduction 163 4.2 IIR Filter Structures 164 4.2.1 Direct Form I Structure 164 4.2.2 Direct Form II Structure 165 4.2.3 Direct Form II Transpose 166 4.2.4 Cascade Structure 168 4.2.5 Parallel Form Structure 169 4.3 Impulse Invariance 171 4.4 Bilinear Transformation 171 4.4.1 Bilinear Transform Design Procedure 172 4.5 Programming Examples 173 4.5.1 Design of a Simple IIR Low-Pass Filter 173 Reference 216 5 Fast Fourier Transform 217 5.1 Introduction 217 5.2 Development of the FFT Algorithm with RADIX-2 218 5.3 Decimation-in-Frequency FFT Algorithm with RADIX-2 219 5.4 Decimation-in-Time FFT Algorithm with RADIX-2 222 5.4.1 Reordered Sequences in the Radix-2 FFT and Bit-Reversed Addressing 224 5.5 Decimation-in-Frequency FFT Algorithm with RADIX-4 226 5.6 Inverse Fast Fourier Transform 227 5.7 Programming Examples 228 5.7.1 Twiddle Factors 233 5.8 Frame- or Block-Based Programming 239 5.8.1 Running the Program 242 5.8.2 Spectral Leakage 244 5.9 Fast Convolution 252 5.9.1 Running the Program 256 5.9.2 Execution Time of Fast Convolution Method of FIR Filter Implementation 256 Reference 261 6 Adaptive Filters 263 6.1 Introduction 263 6.2 Adaptive Filter Configurations 264 6.2.1 Adaptive Prediction 264 6.2.2 System Identification or Direct Modeling 265 6.2.3 Noise Cancellation 265 6.2.4 Equalization 266 6.3 Performance Function 267 6.3.1 Visualizing the Performance Function 269 6.4 Searching for the Minimum 270 6.5 Least Mean Squares Algorithm 270 6.5.1 LMS Variants 272 6.5.2 Normalized LMS Algorithm 272 6.6 Programming Examples 273 6.6.1 Using CMSIS DSP Function arm_lms_f32() 280 Index 299

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Book SynopsisAn important working resource for engineers and researchers involved in the design, development, and implementation of signal processing systems The last decade has seen a rapid expansion of the use of field programmable gate arrays (FPGAs) for a wide range of applications beyond traditional digital signal processing (DSP) systems. Written by a team of experts working at the leading edge of FPGA research and development, this second edition of FPGA-based Implementation of Signal Processing Systems has been extensively updated and revised to reflect the latest iterations of FPGA theory, applications, and technology. Written from a system-level perspective, it features expert discussions of contemporary methods and tools used in the design, optimization and implementation of DSP systems using programmable FPGA hardware. And it provides a wealth of practical insightsalong with illustrative case studies and timely real-world examplesof critical concern to engineers Table of ContentsPreface xv List of Abbreviations xxi 1 Introduction to Field Programmable Gate Arrays 1 1.1 Introduction 1 1.2 Field Programmable Gate Arrays 2 1.3 Influence of Programmability 6 1.4 Challenges of FPGAs 8 Bibliography 9 2 DSP Basics 11 2.1 Introduction 11 2.2 Definition of DSP Systems 12 2.3 DSP Transformations 16 2.4 Filters 20 2.5 Adaptive Filtering 29 2.6 Final Comments 38 Bibliography 38 3 Arithmetic Basics 41 3.1 Introduction 41 3.2 Number Representations 42 3.3 Arithmetic Operations 47 3.4 Alternative Number Representations 55 3.5 Division 59 3.6 Square Root 60 3.7 Fixed-Point versus Floating-Point 64 3.8 Conclusions 66 Bibliography 67 4 Technology Review 70 4.1 Introduction 70 4.2 Implications of Technology Scaling 71 4.3 Architecture and Programmability 72 4.4 DSP Functionality Characteristics 74 4.5 Microprocessors 76 4.6 DSP Processors 82 4.7 Graphical Processing Units 86 4.8 System-on-Chip Solutions 88 4.9 Heterogeneous Computing Platforms 91 4.10 Conclusions 92 Bibliography 92 5 Current FPGA Technologies 94 5.1 Introduction 94 5.2 Toward FPGAs 95 5.3 Altera Stratix® V and 10 FPGA Family 98 5.4 Xilinx UltrascaleTM/Virtex-7 FPGA Families 103 5.5 Xilinx Zynq FPGA Family 107 5.6 Lattice iCE40isp FPGA Family 108 5.7 MicroSemi RTG4 FPGA Family 111 5.8 Design Stratregies for FPGA-based DSP Systems 112 5.9 Conclusions 114 Bibliography 114 6 Detailed FPGA Implementation Techniques 116 6.1 Introduction 116 6.2 FPGA Functionality 117 6.3 Mapping to LUT-Based FPGA Technology 123 6.4 Fixed-Coefficient DSP 125 6.5 Distributed Arithmetic 130 6.6 Reduced-Coefficient Multiplier 133 6.7 Conclusions 137 Bibliography 138 7 Synthesis Tools for FPGAs 140 7.1 Introduction 140 7.2 High-Level Synthesis 141 7.3 Xilinx Vivado 143 7.4 Control Logic Extraction Phase Example 144 7.5 Altera SDK for OpenCL 145 7.6 Other HLS Tools 147 7.7 Conclusions 150 Bibliography 150 8 Architecture Derivation for FPGA-based DSP Systems 152 8.1 Introduction 152 8.2 DSP Algorithm Characteristics 153 8.3 DSP Algorithm Representations 157 8.4 Pipelining DSP Systems 160 8.5 Parallel Operation 170 8.6 Conclusions 178 Bibliography 179 9 Complex DSP Core Design for FPGA 180 9.1 Introduction 180 9.2 Motivation for Design for Reuse 181 9.3 Intellectual Property Cores 182 9.4 Evolution of IP Cores 184 9.5 Parameterizable (Soft) IP Cores 187 9.6 IP Core Integration 195 9.7 Current FPGA-based IP Cores 197 9.8 Watermarking IP 198 9.9 Summary 198 Bibliography 199 10 AdvancedModel-Based FPGA Accelerator Design 200 10.1 Introduction 200 10.2 Dataflow Modeling of DSP Systems 201 10.3 Architectural Synthesis of Custom Circuit Accelerators from DFGs 204 10.4 Model-Based Development of Multi-Channel Dataflow Accelerators 205 10.5 Model-Based Development for Memory-Intensive Accelerators 219 10.6 Summary 223 References 223 11 Adaptive Beamformer Example 225 11.1 Introduction to Adaptive Beamforming 226 11.2 Generic Design Process 226 11.3 Algorithm to Architecture 231 11.4 Efficient Architecture Design 235 11.5 Generic QR Architecture 240 11.6 Retiming the Generic Architecture 246 11.7 Parameterizable QR Architecture 253 11.8 Generic Control 266 11.9 Beamformer Design Example 269 11.10 Summary 271 References 271 12 FPGA Solutions for Big Data Applications 273 12.1 Introduction 273 12.2 Big Data 274 12.3 Big Data Analytics 275 12.4 Acceleration 280 12.5 k-Means Clustering FPGA Implementation 283 12.6 FPGA-Based Soft Processors 286 12.7 System Hardware 290 12.8 Conclusions 293 Bibliography 293 13 Low-Power FPGA Implementation 296 13.1 Introduction 296 13.2 Sources of Power Consumption 297 13.3 FPGA Power Consumption 300 13.4 Power Consumption Reduction Techniques 302 13.5 Dynamic Voltage Scaling in FPGAs 303 13.6 Reduction in Switched Capacitance 305 13.7 Final Comments 316 Bibliography 317 14 Conclusions 319 14.1 Introduction 319 14.2 Evolution in FPGA Design Approaches 320 14.3 Big Data and the Shift toward Computing 320 14.4 Programming Flow for FPGAs 321 14.5 Support for Floating-Point Arithmetic 322 14.6 Memory Architectures 322 Bibliography 323 Index 325

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Book SynopsisAn Innovative Approach to Multidimensional Signals and Systems Theory for Image and Video Processing In this volume, Eric Dubois further develops the theory of multi-D signal processing wherein input and output are vector-value signals. With this framework, he introduces the reader to crucial concepts in signal processing such as continuous- and discrete-domain signals and systems, discrete-domain periodic signals, sampling and reconstruction, light and color, random field models, image representation and more. While most treatments use normalized representations for non-rectangular sampling, this approach obscures much of the geometrical and scale information of the signal. In contrast, Dr. Dubois uses actual units of space-time and frequency. Basis-independent representations appear as much as possible, and the basis is introduced where needed to perform calculations or implementations. Thus, lattice theory is developed from the beginning and rectangular samplTable of ContentsAbout the Companion Website xiii 1 Introduction 1 2 Continuous-Domain Signals and Systems 5 2.1 Introduction 5 2.2 Multidimensional Signals 7 2.2.1 Zero–One Functions 7 2.2.2 Sinusoidal Signals 7 2.2.3 Real Exponential Functions 10 2.2.4 Zone Plate 10 2.2.5 Singularities 12 2.2.6 Separable and Isotropic Functions 13 2.3 Visualization of Two-Dimensional Signals 13 2.4 Signal Spaces and Systems 14 2.5 Continuous-Domain Linear Systems 15 2.5.1 Linear Systems 15 2.5.2 Linear Shift-Invariant Systems 19 2.5.3 Response of a Linear System 20 2.5.4 Response of a Linear Shift-Invariant System 20 2.5.5 Frequency Response of an LSI System 22 2.6 The Multidimensional Fourier Transform 22 2.6.1 Fourier Transform Properties 23 2.6.2 Evaluation of Multidimensional Fourier Transforms 27 2.6.3 Two-Dimensional Fourier Transform of Polygonal Zero–One Functions 30 2.6.4 Fourier Transform of a Translating Still Image 33 2.7 Further Properties of Differentiation and Related Systems 33 2.7.1 Directional Derivative 34 2.7.2 Laplacian 34 2.7.3 Filtered Derivative Systems 35 Problems 37 3 Discrete-Domain Signals and Systems 41 3.1 Introduction 41 3.2 Lattices 42 3.2.1 Basic Definitions 42 3.2.2 Properties of Lattices 44 3.2.3 Examples of 2D and 3D Lattices 44 3.3 Sampling Structures 46 3.4 Signals Defined on Lattices 47 3.5 Special Multidimensional Signals on a Lattice 48 3.5.1 Unit Sample 48 3.5.2 Sinusoidal Signals 49 3.6 Linear Systems Over Lattices 51 3.6.1 Response of a Linear System 51 3.6.2 Frequency Response 52 3.7 Discrete-Domain Fourier Transforms Over a Lattice 52 3.7.1 Definition of the Discrete-Domain Fourier Transform 52 3.7.2 Properties of the Multidimensional Fourier Transform Over a Lattice Λ 53 3.7.3 Evaluation of Forward and Inverse Discrete-Domain Fourier Transforms 57 3.8 Finite Impulse Response (FIR) Filters 59 3.8.1 Separable Filters 66 Problems 67 4 Discrete-Domain Periodic Signals 69 4.1 Introduction 69 4.2 Periodic Signals 69 4.3 Linear Shift-Invariant Systems 72 4.4 Discrete-Domain Periodic Fourier Transform 73 4.5 Properties of the Discrete-Domain Periodic Fourier Transform 77 4.6 Computation of the Discrete-Domain Periodic Fourier Transform 81 4.6.1 Direct Computation 81 4.6.2 Selection of Coset Representatives 82 4.7 Vector Space Representation of Images Based on the Discrete-Domain Periodic Fourier Transform 87 4.7.1 Vector Space Representation of Signals with Finite Extent 87 4.7.2 Block-Based Vector-Space Representation 88 Problems 90 5 Continuous-Domain Periodic Signals 93 5.1 Introduction 93 5.2 Continuous-Domain Periodic Signals 93 5.3 Linear Shift-Invariant Systems 94 5.4 Continuous-Domain Periodic Fourier Transform 96 5.5 Properties of the Continuous-Domain Periodic Fourier Transform 96 5.6 Evaluation of the Continuous-Domain Periodic Fourier Transform 100 Problems 105 6 Sampling, Reconstruction and Sampling Theorems for Multidimensional Signals 107 6.1 Introduction 107 6.2 Ideal Sampling and Reconstruction of Continuous-Domain Signals 107 6.3 Practical Sampling 110 6.4 Practical Reconstruction 112 6.5 Sampling and Periodization of Multidimensional Signals and Transforms 113 6.6 Inverse Fourier Transforms 116 6.6.1 Inverse Discrete-Domain Aperiodic Fourier Transform 117 6.6.2 Inverse Continuous-Domain Periodic Fourier Transform 118 6.6.3 Inverse Continuous-Domain Fourier Transform 119 6.7 Signals and Transforms with Finite Support 119 6.7.1 Continuous-Domain Signals with Finite Support 119 6.7.2 Discrete-Domain Aperiodic Signals with Finite Support 120 6.7.3 Band-Limited Continuous-Domain Γ-Periodic Signals 121 Problems 121 7 Light and Color Representation in Imaging Systems 125 7.1 Introduction 125 7.2 Light 125 7.3 The Space of Light Stimuli 128 7.4 The Color Vector Space 129 7.4.1 Properties of Metamerism 130 7.4.2 Algebraic Condition for Metameric Equivalence 132 7.4.3 Extension of Metameric Equivalence to A 135 7.4.4 Definition of the Color Vector Space 135 7.4.5 Bases for the Vector Space C 137 7.4.6 Transformation of Primaries 138 7.4.7 The CIE Standard Observer 140 7.4.8 Specification of Primaries 142 7.4.9 Physically Realizable Colors 144 7.5 Color Coordinate Systems 147 7.5.1 Introduction 147 7.5.2 Luminance and Chromaticity 147 7.5.3 Linear Color Representations 153 7.5.4 Perceptually Uniform Color Coordinates 155 7.5.5 Display Referred Coordinates 157 7.5.6 Luma-Color-Difference Representation 158 Problems 158 8 Processing of Color Signals 163 8.1 Introduction 163 8.2 Continuous-Domain Systems for Color Images 163 8.2.1 Continuous-Domain Color Signals 163 8.2.2 Continuous-Domain Systems for Color Signals 166 8.2.3 Frequency Response and Fourier Transform 168 8.3 Discrete-Domain Color Images 173 8.3.1 Color Signals With All Components on a Single Lattice 173 8.3.1.1 Sampling a Continuous-Domain Color Signal Using a Single Lattice 175 8.3.1.2 S-CIELAB Error Criterion 175 8.3.2 Color Signals With Different Components on Different Sampling Structures 180 8.4 Color Mosaic Displays 188 9 Random Field Models 193 9.1 Introduction 193 9.2 What is a Random Field? 194 9.3 Image Moments 195 9.3.1 Mean, Autocorrelation, Autocovariance 195 9.3.2 Properties of the Autocorrelation Function 198 9.3.3 Cross-Correlation 199 9.4 Power Density Spectrum 199 9.4.1 Properties of the Power Density Spectrum 200 9.4.2 Cross Spectrum 201 9.4.3 Spectral Density Matrix 201 9.5 Filtering and Sampling of WSS Random Fields 202 9.5.1 LSI Filtering of a Scalar WSS Random Field 202 9.5.2 Why is Sf(u) Called a Power Density Spectrum? 204 9.5.3 LSI Filtering of a WSS Color Random Field 205 9.5.4 Sampling of a WSS Continuous-Domain Random Field 206 9.6 Estimation of the Spectral Density Matrix 207 Problems 214 10 Analysis and Design of Multidimensional FIR Filters 215 10.1 Introduction 215 10.2 Moving Average Filters 215 10.3 Gaussian Filters 217 10.4 Band-pass and Band-stop Filters 220 10.5 Frequency-Domain Design of Multidimensional FIR Filters 225 10.5.1 FIR Filter Design Using Windows 226 10.5.2 FIR Filter Design Using Least-pth Optimization 229 Problems 236 11 Changing the Sampling Structure of an Image 237 11.1 Introduction 237 11.2 Sublattices 237 11.3 Upsampling 239 11.4 Downsampling 245 11.5 Arbitrary Sampling Structure Conversion 248 11.5.1 Sampling Structure Conversion Using a Common Superlattice 248 11.5.2 Polynomial Interpolation 251 Problems 254 12 Symmetry Invariant Signals and Systems 255 12.1 LSI Systems Invariant to a Group of Symmetries 255 12.1.1 Symmetries of a Lattice 255 12.1.2 Symmetry-Group Invariant Systems 258 12.1.3 Spaces of Symmetric Signals 261 12.2 Symmetry-Invariant Discrete-Domain Periodic Signals and Systems 269 12.2.1 Symmetric Discrete-Domain Periodic Signals 270 12.2.2 Discrete-Domain Periodic Symmetry-Invariant Systems 271 12.2.3 Discrete-Domain Symmetry-Invariant Periodic Fourier Transform 273 12.3 Vector-Space Representation of Images Based on the Symmetry-Invariant Periodic Fourier Transform 282 13 Lattices 289 13.1 Introduction 289 13.2 Basic Definitions 289 13.3 Properties of Lattices 293 13.4 Reciprocal Lattice 294 13.5 Sublattices 295 13.6 Cosets and the Quotient Group 296 13.7 Basis Transformations 298 13.7.1 Elementary Column Operations 299 13.7.2 Hermite Normal Form 300 13.8 Smith Normal Form 302 13.9 Intersection and Sum of Lattices 304 Appendix A: Equivalence Relations 311 Appendix B: Groups 313 Appendix C: Vector Spaces 315 Appendix D: Multidimensional Fourier Transform Properties 319 References 323 Index 329

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Book SynopsisDelivers an appropriate mix of theory and applications to help readers understand the process and problems of image and signal analysis Maintaining a comprehensive and accessible treatment of the concepts, methods, and applications of signal and image data transformation, this Second Edition of Discrete Fourier Analysis and Wavelets: Applications to Signal and Image Processing features updated and revised coverage throughout with an emphasis on key and recent developments in the field of signal and image processing. Topical coverage includes: vector spaces, signals, and images; the discrete Fourier transform; the discrete cosine transform; convolution and filtering; windowing and localization; spectrograms; frames; filter banks; lifting schemes; and wavelets. Discrete Fourier Analysis and Wavelets introduces a new chapter on framesa new technology in which signals, images, and other data are redundantly measured. This redundancy allows for more sopTable of ContentsPreface xvii Acknowledgments xxi 1 Vector Spaces, Signals, and Images 1 1.1 Overview 1 1.2 Some Common Image Processing Problems 1 1.2.1 Applications 2 1.2.1.1 Compression 2 1.2.1.2 Restoration 2 1.2.1.3 Edge Detection 3 1.2.1.4 Registration 3 1.2.2 Transform-Based Methods 3 1.3 Signals and Images 3 1.3.1 Signals 4 1.3.2 Sampling, Quantization Error, and Noise 5 1.3.3 Grayscale Images 6 1.3.4 Sampling Images 8 1.3.5 Color 9 1.3.6 Quantization and Noise for Images 9 1.4 Vector Space Models for Signals and Images 10 1.4.1 Examples—Discrete Spaces 11 1.4.2 Examples—Function Spaces 14 1.5 Basic Waveforms—The Analog Case 16 1.5.1 The One-Dimensional Waveforms 16 1.5.2 2D Basic Waveforms 19 1.6 Sampling and Aliasing 20 1.6.1 Introduction 20 1.6.2 Aliasing for Complex Exponential Waveforms 22 1.6.3 Aliasing for Sines and Cosines 23 1.6.4 The Nyquist Sampling Rate 24 1.6.5 Aliasing in Images 24 1.7 Basic Waveforms—The Discrete Case 25 1.7.1 Discrete Basic Waveforms for Finite Signals 25 1.7.2 Discrete Basic Waveforms for Images 27 1.8 Inner Product Spaces and Orthogonality 28 1.8.1 Inner Products and Norms 28 1.8.1.1 Inner Products 28 1.8.1.2 Norms 29 1.8.2 Examples 30 1.8.3 Orthogonality 33 1.8.4 The Cauchy–Schwarz Inequality 34 1.8.5 Bases and Orthogonal Decomposition 35 1.8.5.1 Bases 35 1.8.5.2 Orthogonal and Orthonormal Bases 37 1.8.5.3 Parseval’s Identity 39 1.9 Signal and Image Digitization 39 1.9.1 Quantization and Dequantization 40 1.9.1.1 The General Quantization Scheme 41 1.9.1.2 Dequantization 42 1.9.1.3 Measuring Error 42 1.9.2 Quantifying Signal and Image Distortion More Generally 43 1.10 Infinite-Dimensional Inner Product Spaces 45 1.10.1 Example: An Infinite-Dimensional Space 45 1.10.2 Orthogonal Bases in Inner Product Spaces 46 1.10.3 The Cauchy–Schwarz Inequality and Orthogonal Expansions 48 1.10.4 The Basic Waveforms and Fourier Series 49 1.10.4.1 Complex Exponential Fourier Series 49 1.10.4.2 Sines and Cosines 52 1.10.4.3 Fourier Series on Rectangles 53 1.10.5 Hilbert Spaces and L2(a, b ) 53 1.10.5.1 Expanding the Space of Functions 53 1.10.5.2 Complications 54 1.10.5.3 A Converse to Parseval 55 1.11 Matlab Project 55 Exercises 60 2 The Discrete Fourier Transform 71 2.1 Overview 71 2.2 The Time Domain and Frequency Domain 71 2.3 A Motivational Example 73 2.3.1 A Simple Signal 73 2.3.2 Decomposition into BasicWaveforms 74 2.3.3 Energy at Each Frequency 74 2.3.4 Graphing the Results 75 2.3.5 Removing Noise 77 2.4 The One-Dimensional DFT 78 2.4.1 Definition of the DFT 78 2.4.2 Sample Signal and DFT Pairs 80 2.4.2.1 An Aliasing Example 80 2.4.2.2 Square Pulses 81 2.4.2.3 Noise 82 2.4.3 Suggestions on Plotting DFTs 84 2.4.4 An Audio Example 84 2.5 Properties of the DFT 85 2.5.1 Matrix Formulation and Linearity 85 2.5.1.1 The DFT as a Matrix 85 2.5.1.2 The Inverse DFT as a Matrix 87 2.5.2 Symmetries for Real Signals 88 2.6 The Fast Fourier transform 90 2.6.1 DFT Operation Count 90 2.6.2 The FFT 91 2.6.3 The Operation Count 92 2.7 The Two-Dimensional DFT 93 2.7.1 Interpretation and Examples of the 2-D DFT 96 2.8 Matlab Project 97 2.8.1 Audio Explorations 97 2.8.2 Images 99 Exercises 101 3 The Discrete Cosine Transform 105 3.1 Motivation for the DCT—Compression 105 3.2 Other Compression Issues 106 3.3 Initial Examples—Thresholding 107 3.3.1 Compression Example 1: A Smooth Function 108 3.3.2 Compression Example 2: A Discontinuity 109 3.3.3 Compression Example 3 110 3.3.4 Observations 112 3.4 The Discrete Cosine Transform 112 3.4.1 DFT Compression Drawbacks 112 3.4.2 The Discrete Cosine Transform 113 3.4.2.1 Symmetric Reflection 113 3.4.2.2 DFT of the Extension 113 3.4.2.3 DCT/IDCT Derivation 114 3.4.2.4 Definition of the DCT and IDCT 115 3.4.3 Matrix Formulation of the DCT 116 3.5 Properties of the DCT 116 3.5.1 BasicWaveforms for the DCT 116 3.5.2 The Frequency Domain for the DCT 117 3.5.3 DCT and Compression Examples 117 3.6 The Two-Dimensional DCT 120 3.7 Block Transforms 121 3.8 JPEG Compression 123 3.8.1 Overall Outline 123 3.8.2 DCT and Quantization Details 124 3.8.3 The JPEG Dog 128 3.8.4 Sequential versus Progressive Encoding 128 3.9 Matlab Project 131 Exercises 134 4 Convolution and Filtering 139 4.1 Overview 139 4.2 One-Dimensional Convolution 139 4.2.1 Example: Low-Pass Filtering and Noise Removal 139 4.2.2 Convolution 142 4.2.2.1 Convolution Definition 142 4.2.2.2 Convolution Properties 143 4.3 Convolution Theorem and Filtering 146 4.3.1 The Convolution Theorem 146 4.3.2 Filtering and Frequency Response 147 4.3.2.1 Filtering Effect on BasicWaveforms 147 4.3.3 Filter Design 150 4.4 2D Convolution—Filtering Images 152 4.4.1 Two-Dimensional Filtering and Frequency Response 152 4.4.2 Applications of 2D Convolution and Filtering 153 4.4.2.1 Noise Removal and Blurring 153 4.4.2.2 Edge Detection 154 4.5 Infinite and Bi-Infinite Signal Models 156 4.5.1 L2(ℕ) and L2(ℤ) 158 4.5.1.1 The Inner Product Space L2(ℕ) 158 4.5.1.2 The Inner Product Space L2(ℤ) 159 4.5.2 Fourier Analysis in L2(ℤ) and L2(ℕ) 160 4.5.2.1 The Discrete Time Fourier Transform in L2(ℤ) 160 4.5.2.2 Aliasing and the Nyquist Frequency in L2(ℤ) 161 4.5.2.3 The Fourier Transform on L2(ℕ)) 163 4.5.3 Convolution and Filtering in L2(ℤ) and L2(ℕ) 163 4.5.3.1 The Convolution Theorem 164 4.5.4 The z-Transform 166 4.5.4.1 Two Points of View 166 4.5.4.2 Algebra of z-Transforms; Convolution 167 4.5.5 Convolution in ℂN versus L2(ℤ) 168 4.5.5.1 Some Notation 168 4.5.5.2 Circular Convolution and z-Transforms 169 4.5.5.3 Convolution in ℂN from Convolution in L2(ℤ) 170 4.5.6 Some Filter Terminology 171 4.5.7 The Space L2(ℤ × ℤ) 172 4.6 Matlab Project 172 4.6.1 Basic Convolution and Filtering 172 4.6.2 Audio Signals and Noise Removal 174 4.6.3 Filtering Images 175 Exercises 176 5 Windowing and Localization 185 5.1 Overview: Nonlocality of the DFT 185 5.2 Localization via Windowing 187 5.2.1 Windowing 187 5.2.2 Analysis of Windowing 188 5.2.2.1 Step 1: Relation of X and Y 189 5.2.2.2 Step 2: Effect of Index Shift 190 5.2.2.3 Step 3: N-Point versus M-Point DFT 191 5.2.3 Spectrograms 192 5.2.4 Other Types of Windows 196 5.3 Matlab Project 198 5.3.1 Windows 198 5.3.2 Spectrograms 199 Exercises 200 6 Frames 205 6.1 Introduction 205 6.2 Packet Loss 205 6.3 Frames—Using more Dot Products 208 6.4 Analysis and Synthesis with Frames 211 6.4.1 Analysis and Synthesis 211 6.4.2 Dual Frame and Perfect Reconstruction 213 6.4.3 Partial Reconstruction 214 6.4.4 Other Dual Frames 215 6.4.5 Numerical Concerns 216 6.4.5.1 Condition Number of a Matrix 217 6.5 Initial Examples of Frames 218 6.5.1 Circular Frames in ℝ2 218 6.5.2 Extended DFT Frames and Harmonic Frames 219 6.5.3 Canonical Tight Frame 221 6.5.4 Frames for Images 222 6.6 More on the Frame Operator 222 6.7 Group-Based Frames 225 6.7.1 Unitary Matrix Groups and Frames 225 6.7.2 Initial Examples of Group Frames 228 6.7.2.1 Platonic Frames 228 6.7.2.2 Symmetric Group Frames 230 6.7.2.3 Harmonic Frames 232 6.7.3 Gabor Frames 232 6.7.3.1 Flipped Gabor Frame 237 6.8 Frame Applications 237 6.8.1 Packet Loss 239 6.8.2 Redundancy and other duals 240 6.8.3 Spectrogram 241 6.9 Matlab Project 242 6.9.1 Frames and Frame Operator 243 6.9.2 Analysis and Synthesis 245 6.9.3 Condition Number 246 6.9.4 Packet Loss 246 6.9.5 Gabor Frames 246 Exercises 247 7 Filter Banks 251 7.1 Overview 251 7.2 The Haar Filter Bank 252 7.2.1 The One-Stage Two-Channel Filter Bank 252 7.2.2 Inverting the One-stage Transform 256 7.2.3 Summary of Filter Bank Operation 257 7.3 The General One-stage Two-channel Filter Bank 260 7.3.1 Formulation for Arbitrary FIR Filters 260 7.3.2 Perfect Reconstruction 261 7.3.3 Orthogonal Filter Banks 263 7.4 Multistage Filter Banks 264 7.5 Filter Banks for Finite Length Signals 267 7.5.1 Extension Strategy 267 7.5.2 Analysis of Periodic Extension 269 7.5.2.1 Adapting the Analysis Transform to Finite Length 270 7.5.2.2 Adapting the Synthesis Transform to Finite Length 272 7.5.2.3 Other Extensions 274 7.5.3 Matrix Formulation of the Periodic Case 274 7.5.4 Multistage Transforms 275 7.5.4.1 Iterating the One-stage Transform 275 7.5.4.2 Matrix Formulation of Multistage Transform 277 7.5.4.3 Reconstruction from Approximation Coefficients 278 7.5.5 Matlab Implementation of Discrete Wavelet Transforms 281 7.6 The 2D Discrete Wavelet Transform and JPEG 2000 281 7.6.1 Two-dimensional Transforms 281 7.6.2 Multistage Transforms for Two-dimensional Images 282 7.6.3 Approximations and Details for Images 286 7.6.4 JPEG 2000 288 7.7 Filter Design 289 7.7.1 Filter Banks in the z-domain 290 7.7.1.1 Downsampling and Upsampling in the z-domain 290 7.7.1.2 Filtering in the Frequency Domain 290 7.7.2 Perfect Reconstruction in the z-frequency Domain 290 7.7.3 Filter Design I: Synthesis from Analysis 292 7.7.4 Filter Design II: Product Filters 295 7.7.5 Filter Design III: More Product Filters 297 7.7.6 Orthogonal Filter Banks 299 7.7.6.1 Design Equations for an Orthogonal Bank 299 7.7.6.2 The Product Filter in the Orthogonal Case 300 7.7.6.3 Restrictions on P(z); Spectral Factorization 301 7.7.6.4 Daubechies Filters 301 7.8 Matlab Project 303 7.8.1 Basics 303 7.8.2 Audio Signals 304 7.8.3 Images 305 7.9 Alternate Matlab Project 306 7.9.1 Basics 306 7.9.2 Audio Signals 307 7.9.3 Images 307 Exercises 309 8 Lifting for Filter Banks and Wavelets 319 8.1 Overview 319 8.2 Lifting for the Haar Filter Bank 319 8.2.1 The Polyphase Analysis 320 8.2.2 Inverting the Polyphase Haar Transform 321 8.2.3 Lifting Decomposition for the Haar Transform 322 8.2.4 Inverting the Lifted Haar Transform 324 8.3 The Lifting Theorem 324 8.3.1 A Few Facts About Laurent Polynomials 325 8.3.1.1 The Width of a Laurent Polynomial 325 8.3.1.2 The Division Algorithm 325 8.3.2 The Lifting Theorem 326 8.4 Polyphase Analysis for Filter Banks 330 8.4.1 The Polyphase Decomposition and Convolution 331 8.4.2 The Polyphase Analysis Matrix 333 8.4.3 Inverting the Transform 334 8.4.4 Orthogonal Filters 338 8.5 Lifting 339 8.5.1 Relation Between the Polyphase Matrices 339 8.5.2 Factoring the Le Gall 5/3 Polyphase Matrix 341 8.5.3 Factoring the Haar Polyphase Matrix 343 8.5.4 Efficiency 345 8.5.5 Lifting to Design Transforms 346 8.6 Matlab Project 351 8.6.1 Laurent Polynomials 351 8.6.2 Lifting for CDF(2,2) 354 8.6.3 Lifting the D4 Filter Bank 356 Exercises 356 9 Wavelets 361 9.1 Overview 361 9.1.1 Chapter Outline 361 9.1.2 Continuous from Discrete 361 9.2 The Haar Basis 363 9.2.1 Haar Functions as a Basis for L2(0, 1) 364 9.2.1.1 Haar Function Definition and Graphs 364 9.2.1.2 Orthogonality 367 9.2.1.3 Completeness in L2(0, 1) 368 9.2.2 Haar Functions as an Orthonormal Basis for L2(ℝ) 372 9.2.3 Projections and Approximations 374 9.3 Haar Wavelets Versus the Haar Filter Bank 376 9.3.1 Single-stage Case 377 9.3.1.1 Functions from Sequences 377 9.3.1.2 Filter Bank Analysis/Synthesis 377 9.3.1.3 Haar Expansion and Filter Bank Parallels 378 9.3.2 Multistage Haar Filter Bank and Multiresolution 380 9.3.2.1 Some Subspaces and Bases 381 9.3.2.2 Multiresolution and Orthogonal Decomposition 381 9.3.2.3 Direct Sums 382 9.3.2.4 Connection to Multistage Haar Filter Banks 384 9.4 Orthogonal Wavelets 386 9.4.1 Essential Ingredients 386 9.4.2 Constructing a Multiresolution Analysis: The Dilation Equation 387 9.4.3 Connection to Orthogonal Filters 389 9.4.4 Computing the Scaling Function 390 9.4.5 Scaling Function Existence and Properties 394 9.4.5.1 Fixed Point Iteration and the Cascade Algorithm 394 9.4.5.2 Existence of the Scaling Function 395 9.4.5.3 The Support of the Scaling Function 397 9.4.5.4 Back to Multiresolution 399 9.4.6 Wavelets 399 9.4.7 Wavelets and the Multiresolution Analysis 404 9.4.7.1 Final Remarks on Orthogonal Wavelets 406 9.5 Biorthogonal Wavelets 407 9.5.1 Biorthogonal Scaling Functions 408 9.5.2 Biorthogonal Wavelets 409 9.5.3 Decomposition of L2(ℝ) 409 9.6 Matlab Project 411 9.6.1 Orthogonal Wavelets 411 9.6.2 Biorthogonal Wavelets 414 Exercises 414 Bibliography 421 Appendix: Solutions to Exercises 423 Index 439

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Book SynopsisA problem-solving approach to statistical signal processing for practicing engineers, technicians, and graduate students This book takes a pragmatic approach in solving a set of common problems engineers and technicians encounter when processing signals.Table of ContentsList of Figures xvii List of Tables xxiii Preface xxv List of Abbreviations xxix How to Use the Book xxxi About the Companion Website xxxiii Prerequisites xxxv Why are there so many matrixes in this book? xxxvii 1 Manipulations on Matrixes 1 1.1 Matrix Properties 1 1.1.1 Elementary Operations 2 1.2 Eigen-Decomposition 6 1.3 Eigenvectors in Everyday Life 9 1.3.1 Conversations in a Noisy Restaurant 9 1.3.2 Power Control in a Cellular System 12 1.3.3 Price Equilibrium in the Economy 14 1.4 Derivative Rules 15 1.4.1 Derivative with respect to x 16 1.4.2 Derivative with respect to x 17 1.4.3 Derivative with respect to the Matrix X 18 1.5 Quadratic Forms 19 1.6 Diagonalization of a Quadratic Form 20 1.7 Rayleigh Quotient 21 1.8 Basics of Optimization 22 1.8.1 Quadratic Function with Simple Linear Constraint (M=1) 23 1.8.2 Quadratic Function with Multiple Linear Constraints 23 Appendix A: Arithmetic vs. Geometric Mean 24 2 Linear Algebraic Systems 27 2.1 Problem Definition and Vector Spaces 27 2.1.1 Vector Spaces in Tomographic Radiometric Inversion 29 2.2 Rotations 31 2.3 Projection Matrixes and Data-Filtering 33 2.3.1 Projections and Commercial FM Radio 34 2.4 Singular Value Decomposition (SVD) and Subspaces 34 2.4.1 How to Choose the Rank of Afor Gaussian Model? 35 2.5 QR and Cholesky Factorization 36 2.6 Power Method for Leading Eigenvectors 38 2.7 Least Squares Solution of Overdetermined Linear Equations 39 2.8 Efficient Implementation of the LS Solution 41 2.9 Iterative Methods 42 3 Random Variables in Brief 45 3.1 Probability Density Function (pdf), Moments, and Other Useful Properties 45 3.2 Convexity and Jensen Inequality 49 3.3 Uncorrelatedness and Statistical Independence 49 3.4 Real-Valued Gaussian Random Variables 51 3.5 Conditional pdf for Real-Valued Gaussian Random Variables 54 3.6 Conditional pdf in Additive Noise Model 56 3.7 Complex Gaussian Random Variables 56 3.7.1 Single Complex Gaussian Random Variable 56 3.7.2 Circular Complex Gaussian Random Variable 57 3.7.3 Multivariate Complex Gaussian Random Variables 58 3.8 Sum of Square of Gaussians: Chi-Square 59 3.9 Order Statistics for N rvs 60 4 Random Processes and Linear Systems 63 4.1 Moment Characterizations and Stationarity 64 4.2 Random Processes and Linear Systems 66 4.3 Complex-Valued Random Processes 68 4.4 Pole-Zero and Rational Spectra (Discrete-Time) 69 4.4.1 Stability of LTI Systems 70 4.4.2 Rational PSD 71 4.4.3 Paley–Wiener Theorem 72 4.5 Gaussian Random Process (Discrete-Time) 73 4.6 Measuring Moments in Stochastic Processes 75 Appendix A: Transforms for Continuous-Time Signals 76 Appendix B: Transforms for Discrete-Time Signals 79 5 Models and Applications 83 5.1 Linear Regression Model 84 5.2 Linear Filtering Model 86 5.2.1 Block-Wise Circular Convolution 88 5.2.2 Discrete Fourier Transform and Circular Convolution Matrixes 89 5.2.3 Identification and Deconvolution 90 5.3 MIMO systems and Interference Models 91 5.3.1 DSL System 92 5.3.2 MIMO in Wireless Communication 92 5.4 Sinusoidal Signal 97 5.5 Irregular Sampling and Interpolation 97 5.5.1 Sampling With Jitter 100 5.6 Wavefield Sensing System 101 6 Estimation Theory 105 6.1 Historical Notes 105 6.2 Non-Bayesian vs. Bayesian 106 6.3 Performance Metrics and Bounds 107 6.3.1 Bias 107 6.3.2 Mean Square Error (MSE) 108 6.3.3 Performance Bounds 109 6.4 Statistics and Sufficient Statistics 110 6.5 MVU and BLU Estimators 111 6.6 BLUE for Linear Models 112 6.7 Example: BLUE of the Mean Value of Gaussian rvs 114 7 Parameter Estimation 117 7.1 Maximum Likelihood Estimation (MLE) 117 7.2 MLE for Gaussian Model 119 7.2.1 Additive Noise Model with 119 7.2.2 Additive Noise Model with 120 7.2.3 Additive Noise Model with Multiple Observations with Known 121 7.2.3.1 Linear Model 121 7.2.3.2 Model 122 7.2.3.3 Model 123 7.2.4 Model 123 7.2.5 Additive Noise Model with Multiple Observations with Unknown 124 7.3 Other Noise Models 125 7.4 MLE and Nuisance Parameters 126 7.5 MLE for Continuous-Time Signals 128 7.5.1 Example: Amplitude Estimation 129 7.5.2 MLE for Correlated Noise 130 7.6 MLE for Circular Complex Gaussian 131 7.7 Estimation in Phase/Frequency Modulations 131 7.7.1 MLE Phase Estimation 132 7.7.2 Phase Locked Loops 133 7.8 Least Square (LS) Estimation 135 7.8.1 Weighted LS with 136 7.8.2 LS Estimation and Linear Models 137 7.8.3 Under or Over-Parameterizing? 138 7.8.4 Constrained LS Estimation 139 7.9 Robust Estimation 140 8 Cramér–Rao Bound 143 8.1 Cramér–Rao Bound and Fisher Information Matrix 143 8.1.1 CRB for Scalar Problem (P=1) 143 8.1.2 CRB and Local Curvature of Log-Likelihood 144 8.1.3 CRB for Multiple Parameters (p 1) 144 8.2 Interpretation of CRB and Remarks 146 8.2.1 Variance of Each Parameter 146 8.2.2 Compactness of the Estimates 146 8.2.3 FIM for Known Parameters 147 8.2.4 Approximation of the Inverse of FIM 148 8.2.5 Estimation Decoupled From FIM 148 8.2.6 CRB and Nuisance Parameters 149 8.2.7 CRB for Non-Gaussian rv and Gaussian Bound 149 8.3 CRB and Variable Transformations 150 8.4 FIM for Gaussian Parametric Model 151 8.4.1 FIM for with 151 8.4.2 FIM for Continuous-Time Signals in Additive White Gaussian Noise 152 8.4.3 FIM for Circular Complex Model 152 Appendix A: Proof of CRB 154 Appendix B: FIM for Gaussian Model 156 Appendix C: Some Derivatives for MLE and CRB Computations 157 9 MLE and CRB for Some Selected Cases 159 9.1 Linear Regressions 159 9.2 Frequency Estimation 162 9.3 Estimation of Complex Sinusoid 164 9.3.1 Proper, Improper, and Non-Circular Signals 165 9.4 Time of Delay Estimation 166 9.5 Estimation of Max for Uniform pdf 170 9.6 Estimation of Occurrence Probability for Binary pdf 172 9.7 How to Optimize Histograms? 173 9.8 Logistic Regression 176 10 Numerical Analysis and Montecarlo Simulations 179 10.1 System Identification and Channel Estimation 181 10.1.1 Matlab Code and Results 184 10.2 Frequency Estimation 184 10.2.1 Variable (Coarse/Fine) Sampling 187 10.2.2 Local Parabolic Regression 189 10.2.3 Matlab Code and Results 190 10.3 Time of Delay Estimation 192 10.3.1 Granularity of Sampling in ToD Estimation 193 10.3.2 Matlab Code and Results 194 10.4 Doppler-Radar System by Frequency Estimation 196 10.4.1 EM Method 197 10.4.2 Matlab Code and Results 199 11 Bayesian Estimation 201 11.1 Additive Linear Model with Gaussian Noise 203 11.1.1 Gaussian A-priori: 204 11.1.2 Non-Gaussian A-Priori 206 11.1.3 Binary Signals: MMSE vs. MAP Estimators 207 11.1.4 Example: Impulse Noise Mitigation 210 11.2 Bayesian Estimation in Gaussian Settings 212 11.2.1 MMSE Estimator 213 11.2.2 MMSE Estimator for Linear Models 213 11.3 LMMSE Estimation and Orthogonality 215 11.4 Bayesian CRB 218 11.5 Mixing Bayesian and Non-Bayesian 220 11.5.1 Linear Model with Mixed Random/Deterministic Parameters 220 11.5.2 Hybrid CRB 222 11.6 Expectation-Maximization (EM) 223 11.6.1 EM of the Sum of Signals in Gaussian Noise 224 11.6.2 EM Method for the Time of Delay Estimation of Multiple Waveforms 227 11.6.3 Remarks 228 Appendix A: Gaussian Mixture pdf 229 12 Optimal Filtering 231 12.1 Wiener Filter 231 12.2 MMSE Deconvolution (or Equalization) 233 12.3 Linear Prediction 234 12.3.1 Yule–Walker Equations 235 12.4 LS Linear Prediction 237 12.5 Linear Prediction and AR Processes 239 12.6 Levinson Recursion and Lattice Predictors 241 13 Bayesian Tracking and Kalman Filter 245 13.1 Bayesian Tracking of State in Dynamic Systems 246 13.1.1 Evolution of the A-posteriori pdf 247 13.2 Kalman Filter (KF) 249 13.2.1 KF Equations 251 13.2.2 Remarks 253 13.3 Identification of Time-Varying Filters in Wireless Communication 255 13.4 Extended Kalman Filter (EKF) for Non-Linear Dynamic Systems 257 13.5 Position Tracking by Multi-Lateration 258 13.5.1 Positioning and Noise 260 13.5.2 Example of Position Tracking 263 13.6 Non-Gaussian Pdf and Particle Filters264 14 Spectral Analysis 267 14.1 Periodogram 268 14.1.1 Bias of the Periodogram 268 14.1.2 Variance of the Periodogram 271 14.1.3 Filterbank Interpretation 273 14.1.4 Pdf of the Periodogram (White Gaussian Process) 274 14.1.5 Bias and Resolution 275 14.1.6 Variance Reduction and WOSA 278 14.1.7 Numerical Example: Bandlimited Process and (Small) Sinusoid 280 14.2 Parametric Spectral Analysis 282 14.2.1 MLE and CRB 284 14.2.2 General Model for AR, MA, ARMA Spectral Analysis 285 14.3 AR Spectral Analysis 286 14.3.1 MLE and CRB 286 14.3.2 A Good Reason to Avoid Over-Parametrization in AR 289 14.3.3 Cramér–Rao Bound of Poles in AR Spectral Analysis 291 14.3.4 Example: Frequency Estimation by AR Spectral Analysis 293 14.4 MA Spectral Analysis 296 14.5 ARMA Spectral Analysis 298 14.5.1 Cramér–Rao Bound for ARMA Spectral Analysis 300 Appendix A: Which Sample Estimate of the Autocorrelation to Use? 302 Appendix B: Eigenvectors and Eigenvalues of Correlation Matrix 303 Appendix C: Property of Monic Polynomial 306 Appendix D: Variance of Pole in AR(1) 307 15 Adaptive Filtering 309 15.1 Adaptive Interference Cancellation 311 15.2 Adaptive Equalization in Communication Systems 313 15.2.1 Wireless Communication Systems in Brief 313 15.2.2 Adaptive Equalization 315 15.3 Steepest Descent MSE Minimization 317 15.3.1 Convergence Analysis and Step-Size 318 15.3.2 An Intuitive View of Convergence Conditions 320 15.4 From Iterative to Adaptive Filters 323 15.5 LMS Algorithm and Stochastic Gradient 324 15.6 Convergence Analysis of LMS Algorithm 325 15.6.1 Convergence in the Mean 326 15.6.2 Convergence in the Mean Square 326 15.6.3 Excess MSE 329 15.7 Learning Curve of LMS 331 15.7.1 Optimization of the Step-Size 332 15.8 NLMS Updating and Non-Stationarity 333 15.9 Numerical Example: Adaptive Identification 334 15.10 RLS Algorithm 338 15.10.1 Convergence Analysis 339 15.10.2 Learning Curve of RLS 341 15.11 Exponentially-Weighted RLS 342 15.12 LMS vs. RLS 344 Appendix A: Convergence in Mean Square 344 16 Line Spectrum Analysis 347 16.1 Model Definition 349 16.1.1 Deterministic Signals 350 16.1.2 Random Signals 350 16.1.3 Properties of Structured Covariance 351 16.2 Maximum Likelihood and Cramér–Rao Bounds 352 16.2.1 Conditional ML 353 16.2.2 Cramér–Rao Bound for Conditional Model 354 16.2.3 Unconditional ML 356 16.2.4 Cramér–Rao Bound for Unconditional Model 356 16.2.5 Conditional vs. Unconditional Model & Bounds 357 16.3 High-Resolution Methods 357 16.3.1 Iterative Quadratic ML (IQML) 358 16.3.2 Prony Method 360 16.3.3 MUSIC 360 16.3.4 ESPRIT 363 16.3.5 Model Order 365 17 Equalization in Communication Engineering 367 17.1 Linear Equalization 369 17.1.1 Zero Forcing (ZF) Equalizer 370 17.1.2 Minimum Mean Square Error (MMSE) Equalizer 371 17.1.3 Finite-Length/Finite-Block Equalizer 371 17.2 Non-Linear Equalization 372 17.2.1 ZF-DFE 373 17.2.2 MMSE–DFE 374 17.2.3 Finite-Length MMSE–DFE 375 17.2.4 Asymptotic Performance for Infinite-Length Equalizers 376 17.3 MIMO Linear Equalization 377 17.3.1 ZF MIMO Equalization 377 17.3.2 MMSE MIMO Equalization 379 17.4 MIMO–DFE Equalization 379 17.4.1 Cholesky Factorization and Min/Max Phase Decomposition 379 17.4.2 MIMO–DFE 380 18 2D Signals and Physical Filters 383 18.1 2D Sinusoids 384 18.1.1 Moiré Pattern 386 18.2 2D Filtering 388 18.2.1 2D Random Fields 390 18.2.2 Wiener Filtering 391 18.2.3 Image Acquisition and Restoration 392 18.3 Diffusion Filtering 394 18.3.1 Evolution vs. Time: Fourier Method 394 18.3.2 Extrapolation of the Density 395 18.3.3 Effect of Phase-Shift 396 18.4 Laplace Equation and Exponential Filtering 398 18.5 Wavefield Propagation 400 18.5.1 Propagation/Backpropagation 400 18.5.2 Wavefield Extrapolation and Focusing 402 18.5.3 Exploding Reflector Model 402 18.5.4 Wavefield Extrapolation 404 18.5.5 Wavefield Focusing (or Migration) 406 Appendix A: Properties of 2D Signals 406 Appendix B: Properties of 2D Fourier Transform 410 Appendix C: Finite Difference Method for PDE-Diffusion 412 19 Array Processing 415 19.1 Narrowband Model 415 19.1.1 Multiple DoAs and Multiple Sources 419 19.1.2 Sensor Spacing Design 420 19.1.3 Spatial Resolution and Array Aperture 421 19.2 Beamforming and Signal Estimation 422 19.2.1 Conventional Beamforming 425 19.2.2 Capon Beamforming (MVDR) 426 19.2.3 Multiple-Constraint Beamforming 429 19.2.4 Max-SNR Beamforming 431 19.3 DoA Estimation 432 19.3.1 ML Estimation and CRB 433 19.3.2 Beamforming and Root-MVDR 434 20 Multichannel Time of Delay Estimation 435 20.1 Model Definition for ToD 440 20.2 High Resolution Method for ToD (L=1) 441 20.2.1 ToD in the Fourier Transformed Domain 441 20.2.2 CRB and Resolution 444 20.3 Difference of ToD (DToD) Estimation 445 20.3.1 Correlation Method for DToD 445 20.3.2 Generalized Correlation Method 448 20.4 Numerical Performance Analysis of DToD 452 20.5 Wavefront Estimation: Non-Parametric Method (L=1) 454 20.5.1 Wavefront Estimation in Remote Sensing and Geophysics 456 20.5.2 Narrowband Waveforms and 2D Phase Unwrapping 457 20.5.3 2D Phase Unwrapping in Regular Grid Spacing 458 20.6 Parametric ToD Estimation and Wideband Beamforming 460 20.6.1 Delay and Sum Beamforming 462 20.6.2 Wideband Beamforming After Fourier Transform 464 20.7 Appendix A: Properties of the Sample Correlations 465 20.8 Appendix B: How to Delay a Discrete-Time Signal? 466 20.9 Appendix C: Wavefront Estimation for 2D Arrays 467 21 Tomography 467 21.1 X-ray Tomography 471 21.1.1 Discrete Model 471 21.1.2 Maximum Likelihood 473 21.1.3 Emission Tomography 473 21.2 Algebraic Reconstruction Tomography (ART) 475 21.3 Reconstruction From Projections: Fourier Method 475 21.3.1 Backprojection Algorithm 476 21.3.2 How Many Projections to Use? 479 21.4 Traveltime Tomography 480 21.5 Internet (Network) Tomography 483 21.5.1 Latency Tomography 484 21.5.2 Packet-Loss Tomography 484 22 Cooperative Estimation 487 22.1 Consensus and Cooperation 490 22.1.1 Vox Populi: The Wisdom of Crowds 490 22.1.2 Cooperative Estimation as Simple Information Consensus 490 22.1.3 Weighted Cooperative Estimation ( ) 493 22.1.4 Distributed MLE ( ) 495 22.2 Distributed Estimation for Arbitrary Linear Models (p>1) 496 22.2.1 Centralized MLE 497 22.2.2 Distributed Weighted LS 498 22.2.3 Distributed MLE 500 22.2.4 Distributed Estimation for Under-Determined Systems 501 22.2.5 Stochastic Regressor Model 503 22.2.6 Cooperative Estimation in the Internet of Things (IoT) 503 22.2.7 Example: Iterative Distributed Estimation 505 22.3 Distributed Synchronization 506 22.3.1 Synchrony-States for Analog and Discrete-Time Clocks 507 22.3.2 Coupled Clocks 510 22.3.3 Internet Synchronization and the Network Time Protocol (NTP) 512 Appendix A: Basics of Undirected Graphs 515 23 Classification and Clustering 521 23.1 Historical Notes 522 23.2 Classification 523 23.2.1 Binary Detection Theory 523 23.2.2 Binary Classification of Gaussian Distributions 528 23.3 Classification of Signals in Additive Gaussian Noise 529 23.3.1 Detection of Known Signal 531 23.3.2 Classification of Multiple Signals 532 23.3.3 Generalized Likelihood Ratio Test (GLRT) 533 23.3.4 Detection of Random Signals 535 23.4 Bayesian Classification 536 23.4.1 To Classify or Not to Classify? 537 23.4.2 Bayes Risk 537 23.5 Pattern Recognition and Machine Learning 538 23.5.1 Linear Discriminant 539 23.5.2 Least Squares Classification 540 23.5.3 Support Vectors Principle 541 23.6 Clustering 543 23.6.1 K-Means Clustering 544 23.6.2 EM Clustering 545 References 549 Index 557

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Book SynopsisA bridge between the application of subspace-based methods for parameter estimation in signal processing and subspace-based system identification in control systems Model-Based Processing: An Applied Subspace Identification Approach provides expert insight on developing models for designing model-based signal processors (MBSP) employing subspace identification techniques to achieve model-based identification (MBID) and enables readers to evaluate overall performance using validation and statistical analysis methods. Focusing on subspace approaches to system identification problems, this book teaches readers to identify models quickly and incorporate them into various processing problems including state estimation, tracking, detection, classification, controls, communications, and other applications that require reliable models that can be adapted to dynamic environments. The extraction of a model from data is vital to numerous applications, from thTable of ContentsPreface xiii Acknowledgements xxi Glossary xxiii 1 Introduction 1 1.1 Background 1 1.2 Signal Estimation 2 1.3 Model-Based Processing 8 1.4 Model-Based Identification 16 1.5 Subspace Identification 20 1.6 Notation and Terminology 22 1.7 Summary 24 MATLAB Notes 25 References 25 Problems 26 2 Random Signals and Systems 29 2.1 Introduction 29 2.2 Discrete Random Signals 32 2.3 Spectral Representation of Random Signals 36 2.4 Discrete Systems with Random Inputs 40 2.4.1 Spectral Theorems 41 2.4.2 ARMAX Modeling 42 2.5 Spectral Estimation 44 2.5.1 Classical (Nonparametric) Spectral Estimation 44 2.5.1.1 Correlation Method (Blackman–Tukey) 45 2.5.1.2 Average Periodogram Method (Welch) 46 2.5.2 Modern (Parametric) Spectral Estimation 47 2.5.2.1 Autoregressive (All-Pole) Spectral Estimation 48 2.5.2.2 Autoregressive Moving Average Spectral Estimation 51 2.5.2.3 Minimum Variance Distortionless Response (MVDR) Spectral Estimation 52 2.5.2.4 Multiple Signal Classification (MUSIC) Spectral Estimation 55 2.6 Case Study: Spectral Estimation of Bandpass Sinusoids 59 2.7 Summary 61 MATLAB Notes 61 References 62 Problems 64 3 State-Space Models for Identification 69 3.1 Introduction 69 3.2 Continuous-Time State-Space Models 69 3.3 Sampled-Data State-Space Models 73 3.4 Discrete-Time State-Space Models 74 3.4.1 Linear Discrete Time-Invariant Systems 77 3.4.2 Discrete Systems Theory 78 3.4.3 Equivalent Linear Systems 82 3.4.4 Stable Linear Systems 83 3.5 Gauss–Markov State-Space Models 83 3.5.1 Discrete-Time Gauss–Markov Models 83 3.6 Innovations Model 89 3.7 State-Space Model Structures 90 3.7.1 Time-Series Models 91 3.7.2 State-Space and Time-Series Equivalence Models 91 3.8 Nonlinear (Approximate) Gauss–Markov State-Space Models 97 3.9 Summary 101 MATLAB Notes 102 References 102 Problems 103 4 Model-Based Processors 107 4.1 Introduction 107 4.2 Linear Model-Based Processor: Kalman Filter 108 4.2.1 Innovations Approach 110 4.2.2 Bayesian Approach 114 4.2.3 Innovations Sequence 116 4.2.4 Practical Linear Kalman Filter Design: Performance Analysis 117 4.2.5 Steady-State Kalman Filter 125 4.2.6 Kalman Filter/Wiener Filter Equivalence 128 4.3 Nonlinear State-Space Model-Based Processors 129 4.3.1 Nonlinear Model-Based Processor: Linearized Kalman Filter 130 4.3.2 Nonlinear Model-Based Processor: Extended Kalman Filter 133 4.3.3 Nonlinear Model-Based Processor: Iterated–Extended Kalman Filter 138 4.3.4 Nonlinear Model-Based Processor: Unscented Kalman Filter 141 4.3.5 Practical Nonlinear Model-Based Processor Design: Performance Analysis 148 4.3.6 Nonlinear Model-Based Processor: Particle Filter 151 4.3.7 Practical Bayesian Model-Based Design: Performance Analysis 160 4.4 Case Study: 2D-Tracking Problem 166 4.5 Summary 173 MATLAB Notes 173 References 174 Problems 177 5 Parametrically Adaptive Processors 185 5.1 Introduction 185 5.2 Parametrically Adaptive Processors: Bayesian Approach 186 5.3 Parametrically Adaptive Processors: Nonlinear Kalman Filters 187 5.3.1 Parametric Models 188 5.3.2 Classical Joint State/Parametric Processors: Augmented Extended Kalman Filter 190 5.3.3 Modern Joint State/Parametric Processor: Augmented Unscented Kalman Filter 198 5.4 Parametrically Adaptive Processors: Particle Filter 201 5.4.1 Joint State/Parameter Estimation: Particle Filter 201 5.5 Parametrically Adaptive Processors: Linear Kalman Filter 208 5.6 Case Study: Random Target Tracking 214 5.7 Summary 222 MATLAB Notes 223 References 223 Problems 226 6 Deterministic Subspace Identification 231 6.1 Introduction 231 6.2 Deterministic Realization Problem 232 6.2.1 Realization Theory 233 6.2.2 Balanced Realizations 238 6.2.3 Systems Theory Summary 239 6.3 Classical Realization 241 6.3.1 Ho–Kalman Realization Algorithm 241 6.3.2 SVD Realization Algorithm 243 6.3.2.1 Realization: Linear Time-Invariant Mechanical Systems 246 6.3.3 Canonical Realization 251 6.3.3.1 Invariant System Descriptions 251 6.3.3.2 Canonical Realization Algorithm 257 6.4 Deterministic Subspace Realization: Orthogonal Projections 264 6.4.1 Subspace Realization: Orthogonal Projections 266 6.4.2 Multivariable Output Error State-Space (MOESP) Algorithm 271 6.5 Deterministic Subspace Realization: Oblique Projections 274 6.5.1 Subspace Realization: Oblique Projections 278 6.5.2 Numerical Algorithms for Subspace State-Space System Identification (N4SID) Algorithm 280 6.6 Model Order Estimation and Validation 285 6.6.1 Order Estimation: SVD Approach 286 6.6.2 Model Validation 289 6.7 Case Study: Structural Vibration Response 295 6.8 Summary 299 MATLAB Notes 300 References 300 Problems 303 7 Stochastic Subspace Identification 309 7.1 Introduction 309 7.2 Stochastic Realization Problem 312 7.2.1 Correlated Gauss–Markov Model 312 7.2.2 Gauss–Markov Power Spectrum 313 7.2.3 Gauss–Markov Measurement Covariance 314 7.2.4 Stochastic Realization Theory 315 7.3 Classical Stochastic Realization via the Riccati Equation 317 7.4 Classical Stochastic Realization via Kalman Filter 321 7.4.1 Innovations Model 321 7.4.2 Innovations Power Spectrum 322 7.4.3 Innovations Measurement Covariance 323 7.4.4 Stochastic Realization: Innovations Model 325 7.5 Stochastic Subspace Realization: Orthogonal Projections 330 7.5.1 Multivariable Output Error State-SPace (MOESP) Algorithm 334 7.6 Stochastic Subspace Realization: Oblique Projections 342 7.6.1 Numerical Algorithms for Subspace State-Space System Identification (N4SID) Algorithm 346 7.6.2 Relationship: Oblique (N4SID) and Orthogonal (MOESP) Algorithms 351 7.7 Model Order Estimation and Validation 353 7.7.1 Order Estimation: Stochastic Realization Problem 354 7.7.1.1 Order Estimation: Statistical Methods 356 7.7.2 Model Validation 362 7.7.2.1 Residual Testing 363 7.8 Case Study: Vibration Response of a Cylinder: Identification and Tracking 369 7.9 Summary 378 MATLAB NOTES 378 References 379 Problems 382 8 Subspace Processors for Physics-Based Application 391 8.1 Subspace Identification of a Structural Device 391 8.1.1 State-Space Vibrational Systems 392 8.1.1.1 State-Space Realization 394 8.1.2 Deterministic State-Space Realizations 396 8.1.2.1 Subspace Approach 396 8.1.3 Vibrational System Processing 398 8.1.4 Application: Vibrating Structural Device 400 8.1.5 Summary 404 8.2 MBID for Scintillator System Characterization 405 8.2.1 Scintillation Pulse Shape Model 407 8.2.2 Scintillator State-Space Model 409 8.2.3 Scintillator Sampled-Data State-Space Model 410 8.2.4 Gauss–Markov State-Space Model 411 8.2.5 Identification of the Scintillator Pulse Shape Model 412 8.2.6 Kalman Filter Design: Scintillation/Photomultiplier System 414 8.2.6.1 Kalman Filter Design: Scintillation/Photomultiplier Data 416 8.2.7 Summary 417 8.3 Parametrically Adaptive Detection of Fission Processes 418 8.3.1 Fission-Based Processing Model 419 8.3.2 Interarrival Distribution 420 8.3.3 Sequential Detection 422 8.3.4 Sequential Processor 422 8.3.5 Sequential Detection for Fission Processes 424 8.3.6 Bayesian Parameter Estimation 426 8.3.7 Sequential Bayesian Processor 427 8.3.8 Particle Filter for Fission Processes 429 8.3.9 SNM Detection and Estimation: Synthesized Data 430 8.3.10 Summary 433 8.4 Parametrically Adaptive Processing for Shallow Ocean Application 435 8.4.1 State-Space Propagator 436 8.4.2 State-Space Model 436 8.4.2.1 Augmented State-Space Models 438 8.4.3 Processors 441 8.4.4 Model-Based Ocean Acoustic Processing 444 8.4.4.1 Adaptive PF Design: Modal Coefficients 445 8.4.4.2 Adaptive PF Design: Wavenumbers 447 8.4.5 Summary 450 8.5 MBID for Chirp Signal Extraction 452 8.5.1 Chirp-like Signals 453 8.5.1.1 Linear Chirp 453 8.5.1.2 Frequency-Shift Key (FSK) Signal 455 8.5.2 Model-Based Identification: Linear Chirp Signals 457 8.5.2.1 Gauss–Markov State-Space Model: Linear Chirp 457 8.5.3 Model-Based Identification: FSK Signals 459 8.5.3.1 Gauss–Markov State-Space Model: FSK Signals 460 8.5.4 Summary 462 References 462 Appendix A Probability and Statistics Overview 467 A.1 Probability Theory 467 A.2 Gaussian Random Vectors 473 A.3 Uncorrelated Transformation: Gaussian Random Vectors 473 A.4 Toeplitz Correlation Matrices 474 A.5 Important Processes 474 References 476 Appendix B Projection Theory 477 B.1 Projections: Deterministic Spaces 477 B.2 Projections: Random Spaces 478 B.3 Projection: Operators 479 B.3.1 Orthogonal (Perpendicular) Projections 479 B.3.2 Oblique (Parallel) Projections 481 References 483 Appendix C Matrix Decompositions 485 C.1 Singular-Value Decomposition 485 C.2 QR-Decomposition 487 C.3 LQ-Decomposition 487 References 488 Appendix D Output-Only Subspace Identification 489 References 492 Index 495

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Book SynopsisAn Introduction to Audio Content Analysis Enables readers to understand the algorithmic analysis of musical audio signals with AI-driven approaches An Introduction to Audio Content Analysis serves as a comprehensive guide on audio content analysis explaining how signal processing and machine learning approaches can be utilized for the extraction of musical content from audio. It gives readers the algorithmic understanding to teach a computer to interpret music signals and thus allows for the design of tools for interacting with music. The work ties together topics from audio signal processing and machine learning, showing how to use audio content analysis to pick up musical characteristics automatically. A multitude of audio content analysis tasks related to the extraction of tonal, temporal, timbral, and intensity-related characteristics of the music signal are presented. Each task is introduced from both a musical and a technical perspective, detailing the algorithmic approach as well as providing practical guidance on implementation details and evaluation. To aid in reader comprehension, each task description begins with a short introduction to the most important musical and perceptual characteristics of the covered topic, followed by a detailed algorithmic model and its evaluation, and concluded with questions and exercises. For the interested reader, updated supplemental materials are provided via an accompanying website. Written by a well-known expert in the music industry, sample topics covered in Introduction to Audio Content Analysis include: Digital audio signals and their representation, common time-frequency transforms, audio featuresPitch and fundamental frequency detection, key and chordRepresentation of dynamics in music and intensity-related featuresBeat histograms, onset and tempo detection, beat histograms, and detection of structure in music, and sequence alignmentAudio fingerprinting, musical genre, mood, and instrument classification An invaluable guide for newcomers to audio signal processing and industry experts alike, An Introduction to Audio Content Analysis covers a wide range of introductory topics pertaining to music information retrieval and machine listening, allowing students and researchers to quickly gain core holistic knowledge in audio analysis and dig deeper into specific aspects of the field with the help of a large amount of references.Table of ContentsAuthor Biography xvii Preface xix Acronyms xxi List of Symbols xxv Source Code Repositories xxix 1 Introduction 1 Part I Fundamentals of Audio Content Analysis 9 2 Analysis of Audio Signals 11 3 Input Representation 17 4 Inference 91 5 Data 107 Part II Music Transcription 127 7 Tonal Analysis 129 8 Intensity217 9 Temporal Analysis 229 10 Alignment 281 Part III Music Identification, Classification, and Assessment 303 11 Audio Fingerprinting 305 12 Music Similarity Detection and Music Genre Classification 317 13 Mood Recognition 337 14 Musical Instrument Recognition 347 15 Music Performance Assessment 355 Part IV Appendices 365 Appendix A Fundamentals 367 Appendix B Fourier Transform 385 Appendix C Principal Component Analysis 405 Appendix D Linear Regression 409 Appendix E Software for Audio Analysis 411 Appendix F Datasets 417 Index 425

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