Discrete wavelet transform : a signal processing approach / / D. Sundararajan

• Record Nr.: UNINA9910820918403321
• Autore: Sundararajan D.
• Pubbl/distr/stampa: Hoboken, New Jersey : , : Wiley, , 2015; ©2015
• ISBN: 1-119-11311-3; 1-119-04607-6; 1-119-04608-4
• Descrizione fisica: 1 online resource (340 p.)
• Disciplina: 515/.2433
• Soggetti: Wavelets (Mathematics); Signal processing; Geometric tomography
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: 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 Convolution 3.1.1 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 Expansion 4.3.6 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 Coefficients 6.3 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; Chapter 8 The Haar Discrete Wavelet Transform 8.1 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; 9.3 Orthogonality Conditions