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Wavelet theory and its applications

Author: Randy K Young
Publisher: Boston : Kluwer Academic Publishers, ©1993.
Series: Kluwer international series in engineering and computer science, SECS 189.; Kluwer international series in engineering and computer science., VLSI, computer architecture, and digital signal processing.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:

A proliferation of research papers and a couple of books, written in English (there is an earlier book written in French), have emerged on the subject.

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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Randy K Young
ISBN: 079239271X 9780792392712
OCLC Number: 26300533
Language Note: English.
Description: xiv, 223 pages : illustrations ; 25 cm.
Contents: Ch. 1. Introduction/Background --
Wavelet Theory Basics --
Scaling and Translation --
Appendix 1-A: Time Referencing --
Ch. 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 Wavelet Constraints --
Discrete Wavelet Mathematics --
Rigorous Justification --
Discrete Time Wavelet Series --
Multiresolution, Orthogonal, and Biorthogonal Wavelet Transforms (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 --
Ch. 3. Practical Resolution, Gain, and Processing Structures --
Fourier/Narrowband Gain and Resolution Comparisons --
Multiple Mother Wavelets --
Gain and Resolution Properties Only --
Mother Wavelet Properties --
Relationships to Established Theories --
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, Tradeoffs and Efficiencies --
Appendix 3-B: Narrowband Ambiguity Function Theory --
Ch. 4. Wavelet Theory Extensions and Ambiguity Functions --
Multiresolution/Orthogonal Wavelets versus Unconstrained Wavelets --
Sampling Grids --
Unconstrained Wavelet Transforms --
Mother Wavelet Freedom --
The Mother Mapper Operator --
Unconstrained Wavelet Transforms/Mother Mapper Operator Properties and Applications --
Mother Mapper Operator Applications --
Mother Mapper Operator --
Final Considerations --
Further Research and Applications of the Mother Mapper Operator --
Ch. 5. Linear Systems Modelling with Wavelet Theory --
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 for Signals 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 and Nonlinear Time Variations --
Bi-wavelet System Representation: Time variation of the Time-varying System Model --
Ch. 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 Delay and Scale Estimation --
WBAAF Moments and Assumptions --
Wideband Scattering Review.
Series Title: Kluwer international series in engineering and computer science, SECS 189.; Kluwer international series in engineering and computer science., VLSI, computer architecture, and digital signal processing.
Responsibility: by Randy K. Young.
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