Overview

This book reviews, extends, and applies wavelet theory, concentrating on the practical applications. Many pictures provide visualizations of wavelet theory and its new extentions, as well as relationships to established concepts. Wavelet theory is integrated with other general theories, including linear systems theory and template matching or matched filtering. These relationships create analogies with related research and connections to practical applications. In addition, by demonstrating the effectiveness of wavelet theory in these general applications, many other specific applications may be improved. Temporal and spatial signals and systems are considered. The properties of the wavelet transform representation are sensitive to the chosen mother wavelet (the kernel of the wavelet transform, analogous to the exponential function in a Fourier transform). These properties are examined and techniques for analyzing these sensitivities are presented.

Full Product Details

Author:   Randy K. Young
Publisher:   Springer
Imprint:   Springer
Edition:   1993 ed.
Volume:   189
Dimensions:   Width: 15.50cm , Height: 1.40cm , Length: 23.50cm
Weight:   1.150kg
ISBN:  

9780792392712

ISBN 10:   079239271
Pages:   223
Publication Date:   30 September 1992
Audience:   College/higher education ,  Professional and scholarly ,  Postgraduate, Research & Scholarly ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

Foreword.- Preface.- 1: Introduction/Background.- Wavelet Theory Basics - Scaling and Translation.- Appendix 1-A: Time Referencing.- 2: The Wavelet Transform.- Wavelet Transform Definitions and Operators.- Wavelet Transform Examples.- The Resolution of Identity.- Continuous Inverse Wavelet Transform Theorem.- Energy Distribution in the Wavelet Transform Domain.- Discrete Wavelet Transform (Continuous Time Wavelet Series).- Wideband Matched Filter Interpretation of the Lattice Density.- Review of the Inverse Discrete Wavelet Transform: Scale-translation Lattice Density and Mother WaveletConstraints.- Discrete Wavelet Mathematics - Rigorous Justification.- Discrete Time Wavelet Series.- Multiresolution, Orthogonal, and Biorthogonal WaveletTransforms (and PR-QMFs).- Discrete Time Wavelet Series - A Specific Structure.- Multiresolution.- Orthogonal and Biorthogonal Wavelet Transforms.- An Image Processing Example.- Appendix 2-A: Nonunique Wavelet Domain Representations.- 3: Practical Resolution, Gain, and Processing Structures.- Fourier/Narrowband Gain and Resolution Comparisons.- Multiple Mother Wavelets - Gain and Resolution PropertiesOnly.- Mother Wavelet Properties - Relationships to EstablishedTheories.- Signal Analysis - Time-frequency or time-scale Applications.- A Physical Interpretation of Scale-translation Resolution: Wideband Ambiguity Function Conditions.- Wideband Conditions.- Wideband Signals and the Analytic Signal Model.- Effective rms Time-bandwidth Product.- Wideband Systems and Signals.- Active and Passive Sensing.- Ambiguity Functions.- Reformulation of the WBCAF with Wavelet Transforms.- Properties of the Reformulated WBCAF.- Cross Wavelet Transforms and Signal Commonalities.- Appendix 3-A: Wideband/Narrowband Ambiguity Functions:Assumptions, Tradeoffsand Efficiencies.- Appendix 3-B: Narrowband Ambiguity Function Theory.- 4: Wavelet Theory Extensions and Ambiguity Functions.- Multiresolution/Orthogonal Wavelets versus UnconstrainedWavelets.- Sampling Grids.- Unconstrained Wavelet Transforms - Mother Wavelet Freedom.- The Mother Mapper Operator.- Unconstrained Wavelet Transforms/Mother Mapper OperatorProperties and Applications.- Mother Mapper Operator Applications.- Mother Mapper Operator - Final Considerations.- Further Research and Applications of the Mother Mapper Operator.- 5: Linear Systems Modelling with Wavelet Theory.- and Motivation.- Wideband/Nonstationary/Time-varying System Modelling.- The Wideband Signal Reflection Process.- Common Framework of System or Channel Characterizations.- The STV Wavelet Operator - Space-time-varying System Model.- STV Wavelet Operator’s Energy Distribution.- Estimation of the Wideband System Characterization.- Properties of the STV Wavelet Operator.- Examples of the STV Wavelet Operator.- Wideband Reflection: Comparing the LTI and STV Models.- Justification for the STV Operator Instead of Convolution forSignals Represented by Wavelet Transforms.- The STV Wavelet Operator in the Wavelet Transform Domain.- Space-time-varying System Identification Problem with Wideband/Nonstationary Input/Outputs.- Limitations of the STV Wavelet Operator - Time Referencing andNonlinear Time Variations.- Bi-wavelet System Representation: Time variation of the Time-varying System Model.- 6: Wideband Scattering and Environmental Imaging.- Scattering Theory.- General Scattering Function Background.- Narrowband Scattering Theory.- Wideband Correlation Receiver and its Output.- Wideband Point Scatterer Example.- Wideband Scattering Functions and Resolutions.- Physical Form of the WBCAF.- Time Delayand Scale Estimation.- WBAAF Moments and Assumptions.- Wideband Scattering Review.- Related Research.- References.

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