Wentworth
Institute of Technology
Discrete wavelet transform : a signal processing approach /
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...
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
Singapore :
John Wiley & Sons, Inc.,
[2015]
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| Online Access: |
Full text (Wentworth users only) |
Table of Contents:
- 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.
- 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.