{"product_id":"discrete-wavelet-transform-9781119046066","title":"Discrete Wavelet Transform","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e\u003cp\u003e\u003ci\u003e\u003cb\u003eProvides easy learning and understanding of DWT from a signal processing point of view\u003c\/b\u003e\u003c\/i\u003e\u003c\/p\u003e \u003cul\u003e \u003cli\u003ePresents DWT from a digital signal processing point of view, in contrast to the usual mathematical approach, making it highly accessible\u003c\/li\u003e \u003cli\u003eOffers a comprehensive coverage of related topics, including convolution and correlation, Fourier transform, FIR filter, orthogonal and biorthogonal filters\u003c\/li\u003e \u003cli\u003eOrganized systematically, starting from the fundamentals of signal processing to the more advanced topics of DWT and Discrete Wavelet Packet Transform.\u003c\/li\u003e \u003cli\u003eWritten in a clear and concise manner with abundant examples, figures and detailed explanations\u003c\/li\u003e \u003cli\u003eFeatures a companion website that has several MATLAB programs for the implementation of the DWT with commonly used filters\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003e\u003ci\u003eThis well-written textbook is an introduction to the theory of discrete wavelet transform (DWT) and its applications in digital signal and image processing.\u003c\/i\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTrade Review\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003e\"Doubtless, this nice book will stimulate the practical education in the theory of DWT and its applications.\" (\u003ci\u003eZentralblatt MATH\u003c\/i\u003e, 2016)\u003c\/p\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003ePreface xi \u003cp\u003eList of Abbreviations xiii\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 The Organization of This Book 2\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Signals 5\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Signal Classifications 5\u003c\/p\u003e \u003cp\u003e2.1.1 Periodic and Aperiodic Signals 5\u003c\/p\u003e \u003cp\u003e2.1.2 Even and Odd Signals 6\u003c\/p\u003e \u003cp\u003e2.1.3 Energy Signals 7\u003c\/p\u003e \u003cp\u003e2.1.4 Causal and Noncausal Signals 9\u003c\/p\u003e \u003cp\u003e2.2 Basic Signals 9\u003c\/p\u003e \u003cp\u003e2.2.1 Unit-Impulse Signal 9\u003c\/p\u003e \u003cp\u003e2.2.2 Unit-Step Signal 10\u003c\/p\u003e \u003cp\u003e2.2.3 The Sinusoid 10\u003c\/p\u003e \u003cp\u003e2.3 The Sampling Theorem and the Aliasing Effect 12\u003c\/p\u003e \u003cp\u003e2.4 Signal Operations 13\u003c\/p\u003e \u003cp\u003e2.4.1 Time Shifting 13\u003c\/p\u003e \u003cp\u003e2.4.2 Time Reversal 14\u003c\/p\u003e \u003cp\u003e2.4.3 Time Scaling 14\u003c\/p\u003e \u003cp\u003e2.5 Summary 17\u003c\/p\u003e \u003cp\u003eExercises 17\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Convolution and Correlation 21\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Convolution 21\u003c\/p\u003e \u003cp\u003e3.1.1 The Linear Convolution 21\u003c\/p\u003e \u003cp\u003e3.1.2 Properties of Convolution 24\u003c\/p\u003e \u003cp\u003e3.1.3 The Periodic Convolution 25\u003c\/p\u003e \u003cp\u003e3.1.4 The Border Problem 25\u003c\/p\u003e \u003cp\u003e3.1.5 Convolution in the DWT 26\u003c\/p\u003e \u003cp\u003e3.2 Correlation 28\u003c\/p\u003e \u003cp\u003e3.2.1 The Linear Correlation 28\u003c\/p\u003e \u003cp\u003e3.2.2 Correlation and Fourier Analysis 29\u003c\/p\u003e \u003cp\u003e3.2.3 Correlation in the DWT 30\u003c\/p\u003e \u003cp\u003e3.3 Summary 31\u003c\/p\u003e \u003cp\u003eExercises 31\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Fourier Analysis of Discrete Signals 37\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Transform Analysis 37\u003c\/p\u003e \u003cp\u003e4.2 The Discrete Fourier Transform 38\u003c\/p\u003e \u003cp\u003e4.2.1 Parseval’s Theorem 43\u003c\/p\u003e \u003cp\u003e4.3 The Discrete-Time Fourier Transform 44\u003c\/p\u003e \u003cp\u003e4.3.1 Convolution 48\u003c\/p\u003e \u003cp\u003e4.3.2 Convolution in the DWT 48\u003c\/p\u003e \u003cp\u003e4.3.3 Correlation 50\u003c\/p\u003e \u003cp\u003e4.3.4 Correlation in the DWT 50\u003c\/p\u003e \u003cp\u003e4.3.5 Time Expansion 52\u003c\/p\u003e \u003cp\u003e4.3.6 Sampling Theorem 52\u003c\/p\u003e \u003cp\u003e4.3.7 Parseval’s Theorem 54\u003c\/p\u003e \u003cp\u003e4.4 Approximation of the DTFT 55\u003c\/p\u003e \u003cp\u003e4.5 The Fourier Transform 56\u003c\/p\u003e \u003cp\u003e4.6 Summary 56\u003c\/p\u003e \u003cp\u003eExercises 57\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Thez-Transform 59\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 The z-Transform 59\u003c\/p\u003e \u003cp\u003e5.2 Properties of the z-Transform 60\u003c\/p\u003e \u003cp\u003e5.2.1 Linearity 60\u003c\/p\u003e \u003cp\u003e5.2.2 Time Shift of a Sequence 61\u003c\/p\u003e \u003cp\u003e5.2.3 Convolution 61\u003c\/p\u003e \u003cp\u003e5.3 Summary 62\u003c\/p\u003e \u003cp\u003eExercises 62\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Finite Impulse Response Filters 63\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Characterization 63\u003c\/p\u003e \u003cp\u003e6.1.1 Ideal Lowpass Filters 64\u003c\/p\u003e \u003cp\u003e6.1.2 Ideal Highpass Filters 65\u003c\/p\u003e \u003cp\u003e6.1.3 Ideal Bandpass Filters 66\u003c\/p\u003e \u003cp\u003e6.2 Linear Phase Response 66\u003c\/p\u003e \u003cp\u003e6.2.1 Even-Symmetric FIR Filters with Odd Number of Coefficients 67\u003c\/p\u003e \u003cp\u003e6.2.2 Even-Symmetric FIR Filters with Even Number of Coefficients 68\u003c\/p\u003e \u003cp\u003e6.3 Summary 69\u003c\/p\u003e \u003cp\u003eExercises 69\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Multirate Digital Signal Processing 71\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Decimation 72\u003c\/p\u003e \u003cp\u003e7.1.1 Downsampling in the Frequency-Domain 72\u003c\/p\u003e \u003cp\u003e7.1.2 Downsampling Followed by Filtering 75\u003c\/p\u003e \u003cp\u003e7.2 Interpolation 77\u003c\/p\u003e \u003cp\u003e7.2.1 Upsampling in the Frequency-Domain 77\u003c\/p\u003e \u003cp\u003e7.2.2 Filtering Followed by Upsampling 78\u003c\/p\u003e \u003cp\u003e7.3 Two-Channel Filter Bank 79\u003c\/p\u003e \u003cp\u003e7.3.1 Perfect Reconstruction Conditions 81\u003c\/p\u003e \u003cp\u003e7.4 Polyphase Form of the Two-Channel Filter Bank 84\u003c\/p\u003e \u003cp\u003e7.4.1 Decimation 84\u003c\/p\u003e \u003cp\u003e7.4.2 Interpolation 87\u003c\/p\u003e \u003cp\u003e7.4.3 Polyphase Form of the Filter Bank 91\u003c\/p\u003e \u003cp\u003e7.5 Summary 94\u003c\/p\u003e \u003cp\u003eExercises 94\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 The Haar Discrete Wavelet Transform 97\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 Introduction 97\u003c\/p\u003e \u003cp\u003e8.1.1 Signal Representation 97\u003c\/p\u003e \u003cp\u003e8.1.2 The Wavelet Transform Concept 98\u003c\/p\u003e \u003cp\u003e8.1.3 Fourier and Wavelet Transform Analyses 98\u003c\/p\u003e \u003cp\u003e8.1.4 Time-Frequency Domain 99\u003c\/p\u003e \u003cp\u003e8.2 The Haar Discrete Wavelet Transform 100\u003c\/p\u003e \u003cp\u003e8.2.1 The Haar DWT and the 2-Point DFT 102\u003c\/p\u003e \u003cp\u003e8.2.2 The Haar Transform Matrix 103\u003c\/p\u003e \u003cp\u003e8.3 The Time-Frequency Plane 107\u003c\/p\u003e \u003cp\u003e8.4 Wavelets from the Filter Coefficients 111\u003c\/p\u003e \u003cp\u003e8.4.1 Two Scale Relations 116\u003c\/p\u003e \u003cp\u003e8.5 The 2-D Haar Discrete Wavelet Transform 118\u003c\/p\u003e \u003cp\u003e8.6 Discontinuity Detection 126\u003c\/p\u003e \u003cp\u003e8.7 Summary 127\u003c\/p\u003e \u003cp\u003eExercises 128\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Orthogonal Filter Banks 131\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Haar Filter 132\u003c\/p\u003e \u003cp\u003e9.2 Daubechies Filter 135\u003c\/p\u003e \u003cp\u003e9.3 Orthogonality Conditions 146\u003c\/p\u003e \u003cp\u003e9.3.1 Characteristics of Daubechies Lowpass Filters 149\u003c\/p\u003e \u003cp\u003e9.4 Coiflet Filter 150\u003c\/p\u003e \u003cp\u003e9.5 Summary 154\u003c\/p\u003e \u003cp\u003eExercises 155\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Biorthogonal Filter Banks 159\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Biorthogonal Filters 159\u003c\/p\u003e \u003cp\u003e10.2 5\/3 Spline Filter 163\u003c\/p\u003e \u003cp\u003e10.2.1 Daubechies Formulation 170\u003c\/p\u003e \u003cp\u003e10.3 4\/4 Spline Filter 170\u003c\/p\u003e \u003cp\u003e10.3.1 Daubechies Formulation 177\u003c\/p\u003e \u003cp\u003e10.4 CDF 9\/7 Filter 178\u003c\/p\u003e \u003cp\u003e10.5 Summary 183\u003c\/p\u003e \u003cp\u003eExercises 184\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Implementation of the Discrete Wavelet Transform 189\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Implementation of the DWT with Haar Filters 190\u003c\/p\u003e \u003cp\u003e11.1.1 1-Level Haar DWT 190\u003c\/p\u003e \u003cp\u003e11.1.2 2-Level Haar DWT 191\u003c\/p\u003e \u003cp\u003e11.1.3 1-Level Haar 2-D DWT 193\u003c\/p\u003e \u003cp\u003e11.1.4 The Signal-Flow Graph of the Fast Haar DWT Algorithms 194\u003c\/p\u003e \u003cp\u003e11.1.5 Haar DWT in Place 196\u003c\/p\u003e \u003cp\u003e11.2 Symmetrical Extension of the Data 198\u003c\/p\u003e \u003cp\u003e11.3 Implementation of the DWT with the D4 Filter 200\u003c\/p\u003e \u003cp\u003e11.4 Implementation of the DWT with Symmetrical Filters 203\u003c\/p\u003e \u003cp\u003e11.4.1 5\/3 Spline Filter 203\u003c\/p\u003e \u003cp\u003e11.4.2 CDF 9\/7 Filter 205\u003c\/p\u003e \u003cp\u003e11.4.3 4\/4 Spline Filter 208\u003c\/p\u003e \u003cp\u003e11.5 Implementation of the DWT using Factorized Polyphase Matrix 210\u003c\/p\u003e \u003cp\u003e11.5.1 Haar Filter 211\u003c\/p\u003e \u003cp\u003e11.5.2 D4 Filter 213\u003c\/p\u003e \u003cp\u003e11.5.3 5\/3 Spline Filter 216\u003c\/p\u003e \u003cp\u003e11.6 Summary 219\u003c\/p\u003e \u003cp\u003eExercises 219\u003c\/p\u003e \u003cp\u003e\u003cb\u003e12 The Discrete Wavelet Packet Transform 223\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e12.1 The Discrete Wavelet Packet Transform 223\u003c\/p\u003e \u003cp\u003e12.1.1 Number of Representations 226\u003c\/p\u003e \u003cp\u003e12.2 Best Representation 227\u003c\/p\u003e \u003cp\u003e12.2.1 Cost Functions 230\u003c\/p\u003e \u003cp\u003e12.3 Summary 233\u003c\/p\u003e \u003cp\u003eExercises 233\u003c\/p\u003e \u003cp\u003e\u003cb\u003e13 The Discrete Stationary Wavelet Transform 235\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e13.1 The Discrete Stationary Wavelet Transform 235\u003c\/p\u003e \u003cp\u003e13.1.1 The SWT 235\u003c\/p\u003e \u003cp\u003e13.1.2 The ISWT 236\u003c\/p\u003e \u003cp\u003e13.1.3 Algorithms for Computing the SWT and the ISWT 238\u003c\/p\u003e \u003cp\u003e13.1.4 2-D SWT 243\u003c\/p\u003e \u003cp\u003e13.2 Summary 244\u003c\/p\u003e \u003cp\u003eExercises 244\u003c\/p\u003e \u003cp\u003e\u003cb\u003e14 The Dual-Tree Discrete Wavelet Transform 247\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e14.1 The Dual-Tree Discrete Wavelet Transform 248\u003c\/p\u003e \u003cp\u003e14.1.1 Parseval’s Theorem 248\u003c\/p\u003e \u003cp\u003e14.2 The Scaling and Wavelet Functions 252\u003c\/p\u003e \u003cp\u003e14.3 Computation of the DTDWT 253\u003c\/p\u003e \u003cp\u003e14.4 Summary 262\u003c\/p\u003e \u003cp\u003eExercises 263\u003c\/p\u003e \u003cp\u003e\u003cb\u003e15 Image Compression 265\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e15.1 Lossy Image Compression 266\u003c\/p\u003e \u003cp\u003e15.1.1 Transformation 266\u003c\/p\u003e \u003cp\u003e15.1.2 Quantization 268\u003c\/p\u003e \u003cp\u003e15.1.3 Coding 270\u003c\/p\u003e \u003cp\u003e15.1.4 Compression Algorithm 273\u003c\/p\u003e \u003cp\u003e15.1.5 Image Reconstruction 277\u003c\/p\u003e \u003cp\u003e15.2 Lossless Image Compression 284\u003c\/p\u003e \u003cp\u003e15.3 Recent Trends in Image Compression 289\u003c\/p\u003e \u003cp\u003e15.3.1 The JPEG2000 Image Compression Standard 290\u003c\/p\u003e \u003cp\u003e15.4 Summary 290\u003c\/p\u003e \u003cp\u003eExercises 291\u003c\/p\u003e \u003cp\u003e\u003cb\u003e16 Denoising 295\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e16.1 Denoising 295\u003c\/p\u003e \u003cp\u003e16.1.1 Soft Thresholding 296\u003c\/p\u003e \u003cp\u003e16.1.2 Statistical Measures 297\u003c\/p\u003e \u003cp\u003e16.2 VisuShrink Denoising Algorithm 298\u003c\/p\u003e \u003cp\u003e16.3 Summary 303\u003c\/p\u003e \u003cp\u003eExercises 303\u003c\/p\u003e \u003cp\u003eBibliography 305\u003c\/p\u003e \u003cp\u003eAnswers to Selected Exercises 307\u003c\/p\u003e \u003cp\u003eIndex 319\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default 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