The authors have been beguiled and entranced by mathematics all of their lives, and both believe it is the highest expression of pure thought and an essential component-one might say the quintessence-of nature. How else can one ex­ plain the remarkable effectiveness of mathematics in describing and predicting the physical world? The projection of the mathematical method onto the subspace of human endeav­ 1 ors has long been a source of societal progress and commercial technology. The invention of the electronic digital computer (not the mechanical digital computer of Babbage) has made the role of mathematics in civilization even more central by making mathematics active in the operation of products. The writing of this book was intertwined with the development of a start-up company, Aware, Inc. Aware was founded in 1987 by one of the authors (H.L.R.), and the second author (R.O.W.) put his shoulder to the wheel as a consultant soon after.

Modulation
Signal
algorithm
algorithms
analysis
coding
communication
data compression
development
image processing
information
simulation
wavelet
information and communication, circuits

• Front Matter
• The Scalable Structure of Information
  Front Matter
• The New Mathematical Engineering
• Good Approximations
• Wavelets: A Positional Notation for Functions
• Wavelet Theory
  Front Matter
• Algebra and Geometry of Wavelet Matrices
• One-Dimensional Wavelet Systems
• Examples of One-Dimensional Wavelet Systems
• Higher-Dimensional Wavelet Systems
• Wavelet Approximation and Algorithms
  Front Matter
• The Mallat Algorithm
• Wavelet Approximation
• Wavelet Calculus and Connection Coefficients
• Multiscale Representation of Geometry
• Wavelet—Galerkin Solutions of Partial Differential Equations
• Wavelet Applications
  Front Matter
• Wavelet Data Compression
• Modulation and Channel Coding
• Back Matter

Future WAVE Inc., Boston, USA
Howard L. Resnikoff

Department of Mathematics, Rice University, Houston, USA
Raymond O. Wells

Book Title
Wavelet Analysis

Book Subtitle
The Scalable Structure of Information

Authors
Howard L. Resnikoff, Raymond O. Wells

DOI
https://doi.org/10.1007/978-1-4612-0593-7

Hardcover ISBN
978-0-387-98383-7
Published: 18 September 1998

Softcover ISBN
978-1-4612-6830-7
Published: 04 October 2012

eBook ISBN
978-1-4612-0593-7
Published: 06 December 2012

Edition Number
1

Number of Pages
XVI, 435

Topics
Applications of Mathematics, Signal, Image and Speech Processing, Fourier Analysis, Numerical Analysis, Information and Communication, Circuits, Artificial Intelligence