Wavelet Theory and Its Applications

1. Front Matter

   Pages i-xiv

   PDF

2. Introduction/Background

   • Randy K. Young

   Pages 1-17

3. The Wavelet Transform

   • Randy K. Young

   Pages 19-69

4. Practical Resolution, Gain, and Processing Structures

   • Randy K. Young

   Pages 71-122

5. Wavelet Theory Extensions and Ambiguity Functions

   • Randy K. Young

   Pages 123-140

6. Linear Systems Modelling with Wavelet Theory

   • Randy K. Young

   Pages 141-187

7. Wideband Scattering and Environmental Imaging

   • Randy K. Young

   Pages 189-210

8. Back Matter

   Pages 211-223

   PDF

The continuous wavelet transform has deep mathematical roots in the work of Alberto P. Calderon. His seminal paper on complex method of interpolation and intermediate spaces provided the main tool for describing function spaces and their approximation properties. The Calderon identities allow one to give integral representations of many natural operators by using simple pieces of such operators, which are more suited for analysis. These pieces, which are essentially spectral projections, can be chosen in clever ways and have proved to be of tremendous utility in various problems of numerical analysis, multidimensional signal processing, video data compression, and reconstruction of high resolution images and high quality speech. A proliferation of research papers and a couple of books, written in English (there is an earlier book written in French), have emerged on the subject. These books, so far, are written by specialists for specialists, with a heavy mathematical flavor, which is characteristic of the Calderon-Zygmund theory and related research of Duffin-Schaeffer, Daubechies, Grossman, Meyer, Morlet, Chui, and others. Randy Young's monograph is geared more towards practitioners and even non-specialists, who want and, probably, should be cognizant of the exciting proven as well as potential benefits which have either already emerged or are likely to emerge from wavelet theory.

• Invariant
• Signal
• analog
• filtering
• filters
• function
• model
• modeling
• systems theory
• wavelets

• Pennsylvania State University, USA

  Randy K. Young

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