Wavelet Tour of Signal Processing

ISBN-10: 012466606X
ISBN-13: 9780124666061
Edition: 2nd 1999 (Revised)
List price: $97.95
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Description: A Wavelet Tour of Signal Processing begins with a presentation of the wonders of the Fourier transform and then describes its failures for transient signal processing. It presents local time-frequency methods and the related mathematical tools.

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Book details

List price: $97.95
Edition: 2nd
Copyright year: 1999
Publisher: Elsevier Science & Technology Books
Publication date: 9/3/1999
Binding: Hardcover
Pages: 620
Size: 5.98" wide x 9.02" long x 0.52" tall
Weight: 2.596
Language: English

A Wavelet Tour of Signal Processing begins with a presentation of the wonders of the Fourier transform and then describes its failures for transient signal processing. It presents local time-frequency methods and the related mathematical tools.

Preface
Preface to the Second Edition
Notation
Introduction to a Transient World
Fourier Kingdom
Time-Frequency Wedding
Windowed Fourier Transform
Wavelet Transform
Bases of Time-Frequency Atoms
Wavelet Bases and Filter Banks
Tilings of Wavelet Packet and Local Cosine Bases
Bases for What?
Approximation
Estimation
Compression
Travel Guide
Reproducible Computational Science
Road Map
Fourier Kingdom
Linear Time-Invariant Filtering
Impulse Response
Transfer Functions
Fourier Integrals
Fourier Transform in L (R)
Fourier Transform in L (R)
Examples
Properties
Regularity and Decay
Uncertainty Principle
Total Variation
Two-Dimensional Fourier Transform
Problems
Discrete Revolution
Sampling Analog Signals
Whittaker Sampling Theorem
Aliasing
General Sampling Theorems
Discrete Time-Invariant Filters
Impulse Response and Transfer Function
Fourier Series
Finite Signals
Circular Convolutions
Discrete Fourier Transform
Fast Fourier Transform
Fast Convolutions
Discrete Image Processing
Two-Dimensional Sampling Theorem
Discrete Image Filtering
Circular Convolutions and Fourier Basis
Problems
Time Meets Frequency
Time-Frequency Atoms
Windowed Fourier Transform
Completeness and Stability
Choice of Window
Discrete Windowed Fourier Transform
Wavelet Transforms
Real Wavelets
Analytic Wavelets
Discrete Wavelets
Instantaneous Frequency
Windowed Fourier Ridges
Wavelet Ridges
Quadratic Time-Frequency Energy
Wigner-Ville Distribution
Interferences and Positivity
Cohen's Class
Discrete Wigner-Ville Computations
Problems
Frames
Frame Theory
Frame Definition and Sampling
Pseudo Inverse
Inverse Frame Computations
Frame Projector and Noise Reduction
Windowed Fourier Frames
Wavelet Frames
Translation Invariance
Dyadic Wavelet Transform
Wavelet Design
"Algorithme a Trous"
Oriented Wavelets for a Vision
Problems
Wavelet Zoom
Lipschitz Regularity
Lipschitz Definition and Fourier Analysis
Wavelet Vanishing Moments
Regularity Measurements with Wavelets
Wavelet Transform Modulus Maxima
Detection of Singularities
Reconstruction From Dyadic Maxima
Multiscale Edge Detection
Wavelet Maxima for Images
Fast Multiscale Edge Computations
Multifractals
Fractal Sets and Self-Similar Functions
Singularity Spectrum
Fractal Noise
Problems
Wavelet Bases
Orthogonal Wavelet Bases
Multiresolution Approximations
Scaling Function
Conjugate Mirror Filters
In Which Orthogonal Wavelets Finally Arrive
Classes of Wavelet Bases
Choosing a Wavelet
Shannon, Meyer and Battle-Lemarie Wavelets
Daubechies Compactly Supported Wavelets
Wavelets and Filter Banks
Fast Orthogonal Wavelet Transform
Perfect Reconstruction Filter Banks
Biorthogonal Bases of I (Z)
Biorthogonal Wavelet Bases
Construction of Biorthogonal Wavelet Bases
Biorthogonal Wavelet Design
Compactly Supported Biorthogonal Wavelets
Lifting Wavelets
Wavelet Bases on an Interval
Periodic Wavelets
Folded Wavelets
Boundary Wavelets
Multiscale Interpolations
Interpolation and Sampling Theorems
Interpolation Wavelet Basis
Separable Wavelet Bases
Separable Multiresolutions
Two-Dimensional Wavelet Bases
Fast Two-Dimensional Wavelet Transform
Wavelet Bases in Higher Dimensions
Problems
Wavelet Packet and Local Cosine Bases
Wavelet Packets
Wavelet Packet Tree
Time-Frequency Localization
Particular Wavelet Packet Bases
Wavelet Packet Filter Banks
Image Wavelet Packets
Wavelet Packet Quad-Tree
Separable Filter Banks
Block Transforms
Block Bases
Cosine Bases
Discrete Cosine Bases
Fast Discrete Cosine Transforms
Lapped Orthogonal Transforms
Lapped Projectors
Lapped Orthogonal Bases
Local Cosine Bases
Discrete Lapped Transforms
Local Cosine Trees
Binary Tree of Cosine Bases
Tree of Discrete Bases
Image Cosine Quad-Tree
Problems
An Approximation Tour
Linear Approximations
Linear Approximation Error
Linear Fourier Approximations
Linear Multiresolution Approximations
Karhunen-Loeve Approximations
Non-Linear Approximations
Non-Linear Approximation Error
Wavelet Adaptive Grids
Besov Spaces
Image Approximations with Wavelets
Adaptive Basis Selection
Best Basis and Schur Concavity
Fast Best Basis Search in Trees
Wavelet Packet and Local Cosine Best Bases
Approximations with Pursuits
Basis Pursuit
Matching Pursuit
Orthogonal Matching Pursuit
Problems
Estimations are Approximations
Bayes Versus Minimax
Bayes Estimation
Minimax Estimation
Diagonal Estimation in a Basis
Diagonal Estimation with Oracles
Thresholding Estimation
Thresholding Refinements
Wavelet Thresholding
Best Basis Thresholding
Minimax Optimality
Linear Diagonal Minimax Estimation
Orthosymmetric Sets
Nearly Minimax with Wavelets
Restoration
Estimation in Arbitary Gaussian Noise
Inverse Problems and Deconvolution
Coherent Estimation
Coherent Basis Thresholding
Coherent Matching Pursuit
Spectrum Estimation
Power Spectrum
Approximate Karhunen-Loeve Search
Locally Stationary Processes
Problems
Transform Coding
Signal Compression
State of the Art
Compression in Orthonormal Bases
Distortion Rate of Quantization
Entropy Coding
Scalar Quantization
High Bit Rate Compression
Bit Allocation
Optimal Basis and Karhunen-Loeve
Transparent Audio Code
Image Compression
Deterministic Distortion Rate
Wavelet Image Coding
Block Cosine Image Coding
Embedded Transform Coding
Minimax Distortion Rate
Video Signals
Optical Flow
MPEG Video Compression
Problems
Mathematical Complements
Functions and Integration
Banach and Hilbert Spaces
Bases of Hilbert Spaces
Linear Operators
Separable Spaces and Bases
Random Vectors and Covariance Operators
Diracs
Software Toolboxes
WaveLab
LastWave
Freeware Wavelet Toolboxes
Bibliography
Index

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