Computational Signal Processing with Wavelets

Author: Anthony Teolis
Publisher: Birkhauser
Series: Applied and Numerical Harmonic Analysis

1998 * Hardcover * 332 pages

General Description

Computational Signal Processing with Wavelets examines both theoretical and practical aspects of computational signal processing using wavelets. Theoretically, an emphasis is placed on balancing the accessibility of the material with the level of mathematical rigor which sacrifices as little as possible of both. Computationally, wavelet signal processing algorithms are presented and applied to signal compression, digital communications, noise suppression, and signal identification. Numerical illustrations of these computational techniques are further provided with interactive MATLAB software.

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Interactive MATLAB Software (Free p-code)

Numerical examples used in the text are computed using a suite of object-oriented tools developed in MATLAB 5 called the Wavelet Signal Processing Workstation (WSPW).

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Audience

Mathematics and engineering students at the undergraduate and graduate levels will benefit greatly from the introductory treatment of the subject. Professionals and advanced students will find the overcomplete approach to signal representation and processing of great value.

Topics

This work is geared towards practical application and numerical implementation of wavelet-based algorithms supported by a solid mathematical foundation. Some of its main features are listed as follows.

1. An expository treatment of the following topics are included:
• continuous and discrete Fourier transforms,
• orthonormal and biorthogonal bases,
• frames, wavelet frames, and reconstruction,
• discrete wavelet transform and orthonormal wavelets,
• classical sampling theorem, and
• regular and irregular sampling and reconstruction.
2. A frame-based theory of the discretization and reconstruction of analog signals is developed in terms of the sampling of a continuous transform.
3. The continuous wavelet and Gabor transforms are introduced in a unified group-theoretic setting.
4. Concepts and techniques are numerically demonstrated through
• software reproducible examples,
• interactive graphical user interfaces, and
• over 120 traditional static figures;
5. Problem exercises are given at the end of each major chapter to reinforce concepts and ideas.
6. A new and efficient overcomplete wavelet transform is introduced and applied to the tasks of
• noise suppression,
• compression,
• digital communication, and
• identification;

Table of Contents

1. Introduction
2. Mathematical Preliminaries
3. Signal Representation and Frames
4. Continuous Wavelet Transform
5. Discrete Wavelet Transform
6. Overcomplete Wavelet Transform
7. Wavelet Signal Processing
8. Object-Oriented Wavelet Analysis with Matlab 5