Ripples in Mathematics The Discrete Wavelet Transform

ISBN-10: 3540416625
ISBN-13: 9783540416623
Edition: 2001
List price: $89.99 Buy it from $16.72
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Description: This book gives an introduction to the discrete wavelet transform and some of its applications. It is based on a novel approach to discrete wavelets called lifting. The first part is a completely elementary introduction to the subject, and the  More...

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Book details

List price: $89.99
Copyright year: 2001
Publisher: Springer
Publication date: 6/6/2001
Binding: Paperback
Pages: 246
Size: 6.00" wide x 9.00" long x 0.50" tall
Weight: 0.836
Language: English

This book gives an introduction to the discrete wavelet transform and some of its applications. It is based on a novel approach to discrete wavelets called lifting. The first part is a completely elementary introduction to the subject, and the prerequisites for this part are knowledge of basic calculus and linear algebra. The second part requires some knowledge of Fourier series and digital signal analysis. The connections between lifting and filter theory are presented and the wavelet packet transforms are defined. The time-frequency plane is used for interpretation of signals. The problems with finite length signals are treated in detail. MATLAB is used as the computational environment for examples and implementation of transforms. The book is well suited for undergraduate mathematics and electrical engineering students and engineers in industry.

Introduction
Prerequisites
Guide to the Book
Background Information
A First Example
The Example
Generalizations
Exercises
The Discrete Wavelet Transform via Lifting
The First Example Again
De nition of Lifting
A Second Example
Lifting in General
DWT in General
Further Examples
Exercises
Analysis of Synthetic Signals
The Haar Transform
The CDF(2,2) Transform
Exercises
Interpretation
The First Example
Further Results on the Haar Transform
Interpretation of General DWT
Exercises
Two Dimensional Transforms
One Scale DWT in Two Dimensions
Interpretation and Examples
A 2D Transform Based on Lifting
Exercises
Lifting and Filters I
Fourier Series and the z-Transform
Lifting in the z-Transform Representation
Two Channel Filter Banks
Orthonormal and Biorthogonal Bases
Two Channel Filter Banks in the Time Domain
Summary of Results on Lifting and Filters
Properties of Orthogonal Filters
Some Examples
Exercises
Wavelet Packets
From Wavelets to Wavelet Packets
Choice of Basis
Cost Functions
Exercises
The Time-Frequency Plane
Sampling and Frequency Contents
De nition of the Time-Frequency Plane
Wavelet Packets and Frequency Contents
More about Time-Frequency Planes
More Fourier Analysis. The Spectrogram
Exercises
Finite Signals
The Extent of the Boundary Problem
DWT in Matrix Form
Gram-Schmidt Boundary Filters
Periodization
Moment Preserving Boundary Filters
Exercises
Implementation
Introduction to Software
Implementing the Haar Transform Through Lifting
Implementing the DWT Through Lifting
The Real Time Method
Filter Bank Implementation
Construction of Boundary Filters
Wavelet Packet Decomposition
Wavelet Packet Bases
Cost Functions
Exercises
Lifting and Filters II
The Three Basic Representations
From Matrix to Equation Form
From Equation to Filter Form
From Filters to Lifting Steps
Factoring Daubechies 4 into Lifting Steps
Factorizing Coi et 12 into Lifting Steps
Exercises
Wavelets in Matlab
Multiresolution Analysis
Frequency Properties of the Wavelet Transform
Wavelet Packets Used for Denoising
Best Basis Algorithm
Some Commands in Uvi Wave
Exercises
Applications and Outlook
Applications
Outlook
Some Web Sites
References
Index

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