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Wavelet transforms and their applications

Author: Lokenath Debnath
Publisher: Boston : Birkhäuser, ©2002.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

Places emphasis on the logical development of fundamental ideas and systematic treatment of wavelet analysis and its applications to a variety of problems as encountered in various interdisciplinary  Read more...

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Lokenath Debnath
ISBN: 0817642048 3764342048 9783764342043 9780817642044
OCLC Number: 46791141
Description: xv, 565 pages : illustrations ; 24 cm
Contents: Ch. 1. Brief Historical Introduction --
Fourier Series and Fourier Transforms --
Gabor Transforms --
The Wigner-Ville Distribution and Time-Frequency Signal Analysis --
Wavelet Transforms --
Wavelet Bases and Multiresolution Analysis --
Applications of Wavelet Transforms --
Ch. 2. Hilbert Spaces and Orthonormal Systems --
Normed Spaces --
The L[superscript p] Spaces --
Generalized Functions with Examples --
Definition and Examples of an Inner Product Space --
Norm in an Inner Product Space --
Definition and Examples of a Hilbert Space --
Strong and Weak Convergences --
Orthogonal and Orthonormal Systems --
Properties of Orthonormal Systems --
Trigonometric Fourier Series --
Orthogonal Complements and the Projection Theorem --
Linear Funtionals and the Riesz Representation Theorem --
Separable Hilbert Spaces --
Linear Operators on Hilbert Spaces --
Eigenvalues and Eigenvectors of an Operator --
Ch. 3. Fourier Transforms and Their Applications --
Fourier Transforms in L[superscript 1][Riemann integral] --
Basic Properties of Fourier Transforms --
Fourier Transforms in L[superscript 2][Riemann integral] --
Poisson's Summation Formula --
The Shannon Sampling Theorem and Gibbs's Phenomenon --
Heisenberg's Uncertainty Principle --
Applications of Fourier Transforms in Mathematical Statistics --
Applications of Fourier Transforms to Ordinary Differential Equations --
Solutions of Integral Equations --
Solutions of Partial Differential Equations --
Applications of Multiple Fourier Transforms to Partial Differential Equations --
Construction of Green's Functions by the Fourier Transform Method --
Ch. 4. The Gabor Transform and Time-Frequency Signal Analysis --
Classification of Signals and the Joint Time-Frequency Analysis of Signals --
Definition and Examples of the Gabor Transforms --
Basic Properties of Gabor Transforms --
Frames and Frame Operators --
Discrete Gabor Transforms and the Gabor Representation Problem --
The Zak Transform and Time-Frequency Signal Analysis --
Basic Properties of Zak Transforms --
Applications of Zak Transforms and the Balian-Low Theorem --
Ch. 5. The Wigner-Ville Distribution and Time-Frequency Signal Analysis --
Definitions and Examples of the Wigner-Ville Distribution --
Basic Properties of the Wigner-Ville Distribution --
The Wigner-Ville Distribution of Analytic Signals and Band-Limited Signals --
Definitions and Examples of the Woodward Ambiguity Functions --
Basic Properties of Ambiguity Functions --
The Ambiguity Transformation and Its Properties --
Discrete Wigner-Ville Distributions --
Cohen's Class of Time-Frequency Distributions --
Ch. 6. Wavelet Transforms and Basic Properties --
Continuous Wavelet Transforms and Examples --
Basic Properties of Wavelet Transforms --
The Discrete Wavelet Transforms --
Orthonormal Wavelets --
Ch. 7. Multiresolution Analysis and Construction of Wavelets --
Definition of Multiresolution Analysis and Examples --
Properties of Scaling Functions and Orthonormal Wavelet Bases --
Construction of Orthonormal Wavelets --
Daubechies' Wavelets and Algorithms --
Discrete Wavelet Transforms and Mallat's Pyramid Algorithm --
Ch. 8. Newland's Harmonic Wavelets --
Harmonic Wavelets --
Properties of Harmonic Scaling Functions --
Wavelet Expansions and Parseval's Formula --
Ch. 9. Wavelet Transform Analysis of Turbulence --
Fourier Transforms in Turbulence and the Navier-Stokes Equations --
Fractals, Multifractals, and Singularities in Turbulence --
Farge's Wavelet Transform Analysis of Turbulence --
Adaptive Wavelet Method for Analysis of Turbulent Flows --
Meneveau's Wavelet Analysis of Turbulence.
Other Titles: Wavelet transforms & their applications
Responsibility: Lokenath Debnath.

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