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The World According to Wavelets : The Story of a Mathematical Technique in the Making, Second Edition - Barbara Burke Hubbard

The World According to Wavelets

The Story of a Mathematical Technique in the Making, Second Edition

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The World According to Wavelets, 2nd Edition introduces a broad audience including scientists and engineers working in a variety of fields as well as mathematicians from other subspecialties to one of the most active new areas of applied mathematics and the story of its discovery and development. Organized in "hypertext fashion," the book tells a story of scientific discovery with separate brief entries for technical terms and explicit appendices in a section called "Beyond Plain English".

To the Reader
Fourier Analysis: A Poem Transforms Our Worldp. 5
Seeking New Toolsp. 21
A New Language Acquires a Grammarp. 39
Applicationsp. 57
Beyond Waveletsp. 91
The Fourier Transformp. 117
The Convergence of Fourier Series and the Stability of the Solar Systemp. 125
Computing Fourier Coefficients with Integralsp. 137
The Fast Fourier Transformp. 141
The Continuous Wavelet Transformp. 149
Orthogonality and Scalar Productsp. 153
Multiresolutionp. 165
The Fast Wavelet Transformp. 183
Wavelets in Two Dimensionsp. 193
Pyramid Algorithms of Burt and Adelsonp. 199
Multiwaveletsp. 201
The Heisenberg Uncertainty Principle and Time-Frequency Decompositionsp. 203
Probability, Heisenberg, and Quantum Mechanicsp. 209
Traveling from One Function Space to Another: Wavelets and Pure Mathematicsp. 223
Wavelets and Vision: Another Perspectivep. 231
Which Wavelet?p. 239
Different Transforms: A Summaryp. 249
Wavelets, Music, and Speechp. 253
The Lifting Schemep. 257
Best Basisp. 259
Appendicesp. 263
Mathematical Symbolsp. 265
A Review of Some Elementary Trigonometryp. 267
Integralsp. 271
The Fourier Transform: The Different Conventionsp. 275
The Sampling Theorem: A Proofp. 277
The Heisenberg Uncertainty Principle: A Proofp. 281
The Fourier Transform of a Periodic Functionp. 285
An Example of an Orthonormal Basis and a Proof of Fourier's Resultp. 291
Further Readingp. 295
Wavelet Software and Electronic Resourcesp. 299
Referencesp. 305
Indexp. 319
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9781568810720
ISBN-10: 1568810725
Series: Ak Peters Ser.
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 286
Published: 1st April 1998
Country of Publication: US
Dimensions (cm): 24.13 x 16.51  x 1.91
Weight (kg): 0.59
Edition Number: 2
Edition Type: New edition