__**Provides easy learning and understanding of DWT from a signal processing point of view**__ * Presents DWT from a digital signal processing point of view, in contrast to the usual mathematical approach, making it highly accessible * Offers a comprehensive coverage of related topics, including convolution and correlation, Fourier transform, FIR filter, orthogonal and biorthogonal filters * Organized systematically, starting from the fundamentals of signal processing to the more advanced topics of DWT and Discrete Wavelet Packet Transform. * Written in a clear and concise manner with abundant examples, figures and detailed explanations * Features a companion website that has several MATLAB programs for the implementation of the DWT with commonly used filters __“This well-written textbook is an introduction to the theory of discrete wavelet transform (DWT) and its applications in digital signal and image processing.”__ -- Prof. Dr. Manfred Tasche - Institut für Mathematik, Uni Rostock Full review at https://zbmath.org/?q=an:06492561
Provides easy learning and understanding of DWT from a signal processing point of view
- Presents DWT from a digital signal processing point of view, in contrast to the usual mathematical approach, making it highly accessible
- Offers a comprehensive coverage of related topics, including convolution and correlation, Fourier transform, FIR filter, orthogonal and biorthogonal filters
- Organized systematically, starting from the fundamentals of signal processing to the more advanced topics of DWT and Discrete Wavelet Packet Transform.
- Written in a clear and concise manner with abundant examples, figures and detailed explanations
- Features a companion website that has several MATLAB programs for the implementation of the DWT with commonly used filters
"This well-written textbook is an introduction to the theory of discrete wavelet transform (DWT) and its applications in digital signal and image processing."
-- Prof. Dr. Manfred Tasche - Institut für Mathematik, Uni Rostock
Full review at https://zbmath.org/?q=an:06492561
Chapter 8 The Haar Discrete Wavelet Transform8.1 Introduction; 8.1.1 Signal Representation; 8.1.2 The Wavelet Transform Concept; 8.1.3 Fourier and Wavelet Transform Analyses; 8.1.4 Time-Frequency Domain; 8.2 The Haar Discrete Wavelet Transform; 8.2.1 The Haar DWT and the 2-Point DFT; 8.2.2 The Haar Transform Matrix; 8.3 The Time-Frequency Plane; 8.4 Wavelets from the Filter Coefficients; 8.4.1 Two Scale Relations; 8.5 The 2-D Haar Discrete Wavelet Transform; 8.6 Discontinuity Detection; 8.7 Summary; Exercises; Chapter 9 Orthogonal Filter Banks; 9.1 Haar Filter; 9.2 Daubechies Filter Cover; Title Page; Copyright; Contents; Preface; List of Abbreviations; Chapter 1 Introduction; 1.1 The Organization of This Book; Chapter 2 Signals; 2.1 Signal Classifications; 2.1.1 Periodic and Aperiodic Signals; 2.1.2 Even and Odd Signals; 2.1.3 Energy Signals; 2.1.4 Causal and Noncausal Signals; 2.2 Basic Signals; 2.2.1 Unit-Impulse Signal; 2.2.2 Unit-Step Signal; 2.2.3 The Sinusoid; 2.3 The Sampling Theorem and the Aliasing Effect; 2.4 Signal Operations; 2.4.1 Time Shifting; 2.4.2 Time Reversal; 2.4.3 Time Scaling; 2.5 Summary; Exercises; Chapter 3 Convolution and Correlation 3.1 Convolution3.1.1 The Linear Convolution; 3.1.2 Properties of Convolution; 3.1.3 The Periodic Convolution; 3.1.4 The Border Problem; 3.1.5 Convolution in the DWT; 3.2 Correlation; 3.2.1 The Linear Correlation; 3.2.2 Correlation and Fourier Analysis; 3.2.3 Correlation in the DWT; 3.3 Summary; Exercises; Chapter 4 Fourier Analysis of Discrete Signals; 4.1 Transform Analysis; 4.2 The Discrete Fourier Transform; 4.2.1 Parseval's Theorem; 4.3 The Discrete-Time Fourier Transform; 4.3.1 Convolution; 4.3.2 Convolution in the DWT; 4.3.3 Correlation; 4.3.4 Correlation in the DWT 4.3.5 Time Expansion4.3.6 Sampling Theorem; 4.3.7 Parseval's Theorem; 4.4 Approximation of the DTFT; 4.5 The Fourier Transform; 4.6 Summary; Exercises; Chapter 5 The z-Transform; 5.1 The z-Transform; 5.2 Properties of the z-Transform; 5.2.1 Linearity; 5.2.2 Time Shift of a Sequence; 5.2.3 Convolution; 5.3 Summary; Exercises; Chapter 6 Finite Impulse Response Filters; 6.1 Characterization; 6.1.1 Ideal Lowpass Filters; 6.1.2 Ideal Highpass Filters; 6.1.3 Ideal Bandpass Filters; 6.2 Linear Phase Response; 6.2.1 Even-Symmetric FIR Filters with Odd Number of Coefficients 6.2.2 Even-Symmetric FIR Filters with Even Number of Coefficients6.3 Summary; Exercises; Chapter 7 Multirate Digital Signal Processing; 7.1 Decimation; 7.1.1 Downsampling in the Frequency-Domain; 7.1.2 Downsampling Followed by Filtering; 7.2 Interpolation; 7.2.1 Upsampling in the Frequency-Domain; 7.2.2 Filtering Followed by Upsampling; 7.3 Two-Channel Filter Bank; 7.3.1 Perfect Reconstruction Conditions; 7.4 Polyphase Form of the Two-Channel Filter Bank; 7.4.1 Decimation; 7.4.2 Interpolation; 7.4.3 Polyphase Form of the Filter Bank; 7.5 Summary; Exercises Content: Signals -- Convolution and Correlation -- Fourier Analysis of Discrete Signals -- The -Transform -- Finite Impulse Response Filters -- Multirate Digital Signal Processing -- The Haar Discrete Wavelet Transform -- Orthogonal Filter Banks -- Biorthogonal Filter Banks -- Implementation of the Discrete Wavelet Transform -- The Discrete Wavelet Packet Transform -- The Discrete Stationary Wavelet Transform -- The Dual-Tree Discrete Wavelet Transform -- Image Compression -- Denoising.
