Overview

Presenting methods for deriving mathematical models of natural signals, this text covers the fundamentals of analysis - synthesis systems and signal representations. Some of the topics in the introduction include perfect and near-perfect reconstruction, the distinction between parametric and nonparametric methods, the role of compaction in signal modelling, basic and overcomplete signal expansions, and time-frequency resolution issues. These topics arise throughout the book as do a number of other topics such as filter banks and multi-resolution. The second chapter gives a detailed development of the sinusoidal model as a parametric extension of the short-time Fourier transform. This leads to multi-resolution sinusoidal modelling techniques in Chapter Three, where wavelet-like approaches are merged with the sinusoidal model to yield improved models. In Chapter Four, the analysis-synthesis residual is considered; for realistic synthesis, the residual must be separately modelled after coherent components (such as sinusoids) are removed. The residual modelling approach is based on psychoacoustically motivated nonuniform filter banks. Chapter Five deals with pitch-synchronous versions of both the wavelet and the Fourier transform; these allow for compact models of pseudo-periodic signals. Chapter Six discusses recent algorithms for deriving signal representations based on time-frequency atoms; primarily, the matching pursuit algorithm is reviewed and extended. The signal models discussed in the book are compact, adaptive, parametric, time-frequency representations that should be useful for analysis, coding, modification, and synthesis of natural signals such as audio.

Full Product Details

Author:   Michael M. Goodwin ,  M. Vetterli
Publisher:   Springer
Imprint:   Springer
Edition:   1998 ed.
Volume:   467
Dimensions:   Width: 15.50cm , Height: 1.70cm , Length: 23.50cm
Weight:   1.250kg
ISBN:  

9780792382911

ISBN 10:   0792382919
Pages:   248
Publication Date:   31 October 1998
Audience:   Professional and scholarly ,  General/trade ,  Professional & Vocational
Format:   Hardback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

1. Signal Models and Analysis-Synthesis.- 1.1 Analysis-Synthesis Systems.- 1.2 Compact Representations.- 1.3 Parametric Methods.- 1.4 Nonparametric Methods.- 1.5 Time-Frequency Decompositions.- 1.6 Overview.- 2. Sinusoidal Modeling.- 2.1 The Sinusoidal Signal Model.- 2.2 The Short-Time Fourier Transform.- 2.3 Sinusoidal Analysis.- 2.4 Time-Domain Synthesis.- 2.5 Frequency-Domain Synthesis.- 2.6 Reconstruction Artifacts.- 2.7 Signal Modification.- 2.8 Conclusion.- 3. Multiresolution Sinusoidal Modeling.- 3.1 Atomic Interpretation of the Sinusoidal Model.- 3.2 Multiresolution Signal Decompositions.- 3.3 Filter Bank Methods.- 3.4 Adaptive Segmentation.- 3.5 Conclusion.- 4. Residual Modeling.- 4.1 Mixed Models.- 4.2 Model of Noise Perception.- 4.3 Residual Analysis-Synthesis.- 4.4 Conclusion.- 5. Pitch-Synchronous Models.- 5.1 Pitch Estimation.- 5.2 Pitch-Synchronous Signal Representation.- 5.3 Pitch-Synchronous Sinusoidal Models.- 5.4 Pitch-Synchronous Wavelet Transforms.- 5.5 Applications.- 5.6 Conclusion.- 6. Matching Pursuit and Atomic Models.- 6.1 Atomic Decompositions.- 6.2 Matching Pursuit.- 6.3 Time-Frequency Dictionaries.- 6.4 Computation Using Recursive Filter Banks.- 6.5 Conclusion.- 7. Conclusions.- 7.1 Signal-Adaptive Parametric Representations.- 7.2 Research Directions.- Appendix A - Two-Channel Filter Banks.- Appendix B - Fourier Series Representations.- References.- References for Poetry Excerpts.

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