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Computational Signal Processing with Wavelets (Applied and Numerical Harmonic Analysis)


Computational Signal Processing with Wavelets (Applied and Numerical Harmonic Analysis) Cover


Synopses & Reviews

Publisher Comments:

This unique resource examines the conceptual, computational, and practical aspects of applied signal processing using wavelets.  With this book, readers will understand and be able to use the power and utility of new wavelet methods in science and engineering problems and analysis.  The text is written in a clear, accessible style avoiding unnecessary abstractions and details.  From a computational perspective, wavelet signal processing algorithms are presented and applied to signal compression, noise suppression, and signal identification.  Numerical illustrations of these computational techniques are further provided with interactive software (MATLAB code) that is available on the world wide web.  Topics and Features: * Continuous wavelet and Gabor transforms * Frame-based theory of discretization and reconstruction of analog signals is developed * New and efficient "overcomplete" wavelet transform is introduced and applied * Numerical illustrations with an object-oriented computational perspective using the Wavelet Signal Processing Workstation (MATLAB code) available This book is an excellent resource for information and computational tools needed to use wavelets in many types of signal processing problems.  Graduates, professionals, and practitioners in engineering, computer science, geophysics, and applied mathematics will benefit from using the book and software tools.  


Introduction * Mathematical Preliminaries * Signal Representation and Frames * Continuous Wavelet and Gabor Transforms * Discrete Wavelet Transform * Overcomplete Wavelet Transform * Wavelet Signal Processing * Object-Oriented Wavelet Analysis with MATLAB 5 * References * Index

Table of Contents

1 Introduction       1.1 Motivation and Objectives   1.2 Core Material and Development   1.3 Hybrid Media Components   1.4 Signal Processing Perspective   1.4.1 Analog Signals   1.4.2 Digital Processing of Analog Signals   1.4.3 Time-Frequency Limitedness  2 Mathematical Preliminaries      2.1 Basic Symbols and Notation   2.2 Basic Concepts   2.2.1 Norm   2.2.2 Inner Product   2.2.3 Convergence   2.2.4 Hilbert Spaces   2.3 Basic Spaces   2.3.1 Bounded Functions   2.3.2 Absolutely Integrable Functions   2.3.3 Finite Energy Functions   2.3.4 Finite Energy Periodic Functions   2.3.5 Time-Frequency Concentrated Functions   2.3.6 Finite Energy Sequences   2.3.7 Bandlimited Functions   2.3.8 Hardy Spaces   2.4 Operators   2.4.1 Bounded Linear Operators   2.4.2 Properties   2.4.3 Useful Unitary Operators   2.5 Bases and Completeness in Hilbert Space   2.6 Fourier Transforms   2.6.1 Continuous Time Fourier Transform   2.6.2 Continuous Time-Periodic Fourier Transform   2.6.3 Discrete Time Fourier Transform   2.6.4 Discrete Fourier Transform   2.6.5 Fourier Dual Spaces   2.7 Linear Filters   2.7.1 Continuous Filters and Fourier Transforms   2.7.2 Discrete Filters and Z-Transforms   2.8 Analog Signals and Discretization   2.8.1 Classical Sampling Theorem   2.8.2 What Can Be Computed Exactly?   Problems  3 Signal Representation and Frames      3.1 Inner Product Representation (Atomic Decomposition)   3.2 Orthonormal Bases   3.2.1 Parseval and Plancherel   3.2.2 Reconstruction   3.2.3 Examples   3.3 Riesz Bases   3.3.1 Reconstruction   3.3.2 Examples   3.4 General Frames   3.4.1 Basic Frame Theory   3.4.2 Frame Representation   3.4.3 Frame Correlation and Pseudo-Inverse   3.4.4 Pseudo-Inverse   3.4.5 Best Frame Bounds   3.4.6 Duality   3.4.7 Iterative Reconstruction   Problems  4 Continuous Wavelet and Gabor Transforms      4.1 What is a Wavelet?   4.2 Example Wavelets   4.2.1 Haar Wavelet   4.2.2 Shannon Wavelet   4.2.3 Frequency B-spline Wavelets   4.2.4 Morlet Wavelet   4.2.5 Time-Frequency Tradeoffs   4.3 Continuous Wavelet Transform   4.3.1 Definition   4.3.2 Properties   4.4 Inverse Wavelet Transform   4.4.1 The Idea Behind the Inverse   4.4.2 Derivation for   L 2  (  R  )   4.4.3 Analytic Signals   4.4.4 Admissibility   4.5 Continuous Gabor Transform   4.5.1 Definition   4.5.2 Inverse Gabor Transform   4.6 Unified Representation and Groups   4.6.1 Groups   4.6.2 Weighted Spaces   4.6.3 Representation   4.6.4 Reproducing Kernel   4.6.5 Group Representation Transform   Problems  5 Discrete Wavelet Transform      5.1 Discretization of the CWT   5.2 Multiresolution Analysis   5.2.1 Multiresolution Design   5.2.2 Resolution and Dilation Invariance   5.2.3 Definition   5.3 Multiresolution Representation   5.3.1 Projection   5.3.2 Fourier Transforms   5.3.3 Between Scale Relations   5.3.4 Haar MRA   5.4 Orthonormal Wavelet Bases   5.4.1 Characterizing   W 0   5.4.2 Wavelet Construction   5.4.3 The Scaling Function   5.5 Compactly Supported (Daubechies) Wavelets   5.5.1 Main Idea   5.5.2 Trigonometric Half-Band Filters   5.5.3 Examples   5.6 Fast Wavelet Transform Algorithm   5.6.1 Filter Bank Decomposition of the Identity   5.6.2 Down- and Up-Sampling   5.6.3 Examples Problems  6 Overcomplete Wavelet Transform        6.1 Discretization of the CWT Revisited   6.1.1 Definition   6.1.2 Semilog Regular Time-Scale Sampling   6.1.3 Invertibility   6.1.4 Overcompleteness and Redundancy   6.2 Filter Bank Implementation   6.2.1 Analysis   6.2.2 Synthesis   6.3 Time-Frequency Localization and Wavelet Design   6.3.1 The Uncertainty Principle   6.3.2 Parametric Bandlimited Wavelets   6.4 OCWT Examples   6.5 Irregular Sampling and Frames   6.5.1 Paley-Wiener Frames   6.5.2 Wavelet Frames   6.5.3 Irregular Sampling in the Time-Scale Domain   Problems  7 Wavelet Signal Processing        7.1 Noise Suppression   7.1.1 Noise Domains   7.1.2 Problem   7.1.3 Approach   7.1.4 Coherence   7.1.5 Frame Localization and Coherence   7.1.6 Reconstruction Error from Threshold OCWTs   7.1.7 Numerical Experiment   7.1.8 Coefficient Noise and Overcompleteness   7.1.9 Measuring Noise (SNR)   7.2 Compression   7.2.1 Problem   7.2.2 Performance Measures   7.2.3 Approach   7.2.4 Numerical Experiment   7.2.5 Remarks   7.3 Digital Communication   7.3.1 Problem   7.3.2 Objectives   7.3.3 Approach   7.3.4 Performance Measures   7.3.5 Computer Implementation   7.3.6 Wavelet Communication Testbed   7.3.7 Numerical Experiments   7.3.8 Remarks   7.4 Identification   7.4.1 Approach   7.4.2 Performance Indicators   7.4.3 Numerical Experiment   7.4.4 Remarks   7.5 Conclusion   Problems  8 Object-Oriented Wavelet Analysis with MATLAB 5        8.1 Wavelet Signal Processing Workstation   8.2 MATLAB Coding   8.2.1 Object-Oriented Programming   8.2.2 Designed Classes   8.3 The sampled_signal Methods   8.3.1 Class Construction   8.3.2 sampled_signal Methods   8.4 Wavelet Transform Implementation   8.4.1 Overcomplete Wavelet Transform (OCWT)   8.4.2 GUI for Filter Bank Specification   8.5 The wavelet Object   8.5.1 Class Reconstruction   8.5.2 wavelet Methods   8.6 Processing Example   8.6.1 Forward OCWT   8.6.2 Inverse OCWT   8.7 Supporting Functions and Globals   8.7.1 Frequency and Time Units   8.7.2 Graphical   8.7.3 Wavelet  References Index

Product Details

Teolis, Anthony
Boston, MA
Engineering - Electrical & Electronic
Spectrum Analysis
Signal processing
Spectroscopy & Spectrum Analysis
Engineering / Electrical
signal precessing
Signal processing -- Mathematics.
Wavelets (mathematics)
Signal, Image and Speech Processing
Communications Engineering, Networks
Computational Mathematics and Numerical Analysis
Computational science and engineering
Fourier analysis
Electricity-General Electricity
Electronics - General
Language, literature and biography
mathematics and statistics
Computer science_xMathematics
Computer Science
Edition Number:
Edition Description:
Applied and Numerical Harmonic Analysis
Publication Date:
March 1998
235 x 155 mm 1480 gr

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Computational Signal Processing with Wavelets (Applied and Numerical Harmonic Analysis) New Hardcover
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Product details 348 pages Birkhauser Boston - English 9780817639099 Reviews:
"Synopsis" by , Introduction * Mathematical Preliminaries * Signal Representation and Frames * Continuous Wavelet and Gabor Transforms * Discrete Wavelet Transform * Overcomplete Wavelet Transform * Wavelet Signal Processing * Object-Oriented Wavelet Analysis with MATLAB 5 * References * Index
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