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Wavelets and Their Applications: Case Studies

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Mei Kobayashi, Editor


1998 / xvi + 142 pages / Softcover / ISBN: 978-0-898714-16-6 / List Price $64.00 / SIAM Member Price $44.80 / Order Code OT62

This collection of independent case studies demonstrates how wavelet techniques have been used to solve open problems and develop insight into the nature of the systems under study. Each case begins with a description of the problem and points to the specific properties of wavelets and techniques used for determining a solution.

The cases range from a very simple wavelet-based technique for reducing noise in laboratory data to complex work on two-dimensional geographical data display conducted at the Earthquake Research Institute in Japan. One case study shows how wavelet analysis is used in the development of a Japanese text-to-speech system for personal computers and another presents new wavelet techniques developed for and applied to the study of atmospheric wind, turbulent fluid, and seismic acceleration data.

Although calculus and some junior and senior mathematics courses for scientists and engineers will suffice, a solid background in undergraduate mathematics, particularly analysis and numerical analysis, and some familiarity with the basics of wavelets are helpful for reading this book.

Preface; Chapter 1: Wavelet-Based Multiresolution Display of Coastline Data, Sumiko Hiyama and Mei Kobayashi; Introduction; Properties of Scaling Functions and Wavelets; Approximation of Curves Using Mallat's Algorithm; Conclusion; Chapter 2: A Wavelet-Based Technique for Reducing Noise in Laboratory Data, Susumu Sakakibara; Introduction; Wavelets and a Data Smoothing Method; Two Examples; Conclusion; Chapter 3: A Wavelet-Based Conjugate Gradient Method for Solving Poisson Equations, Nobuatsu Tanaka; Introduction; The Incomplete Discrete Wavelet Transform; Numerical Examples; Conclusion; Appendix 1: Conjugate Gradient Methods; Appendix 2: Preconditioned Conjugate Gradient Methods; Appendix 3: Successive Over-Relaxation Methods;Chapter 4: Wavelet Analysis for a Text-to-Speech (TTS) System, Mei Kobayashi, Masaharu Sakamoto, Takashi Saito, Yasuhide Hashimoto, Masafumi Nisroduction; Wavelets and Speech Signal Processing; TTS Conversion; Conclusion; Appendix 1: Selection of Synthesis Units; Appendix 2: Overlap-Add Methods; Chapter 5: Wavelet Analysis of Atmospheric Wind, Turbulent Fluid, and Seismic Acceleration Data, Michio Yamada and Fumio Sasaki; Introduction; Extraction of Events from Time-Series; Spatial Distribution of Fourier Components; Correction of Seismic Data; Index.

ISBN: 9780898714166

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