Adapted wavelet analysis from theory to software.

*(English)*Zbl 0818.42011
Wellesley, MA: A. K. Peters, Ltd. xii, 486 p. (1994).

Theory and application of wavelet analysis have become a very active field of research in the last few years because they are standing at the intersection of the frontiers of mathematics, algorithmic computing, computer controlled non-algorithmic parallel computing, massively parallel photonic signal processing, digital signal processing, filter design, and remote sensing. From the mathematical point of view, the aforementioned disciplines overlap significantly. Over the years, however, the notational conventions and methodologies of the disciplines unfortunately diverged to the point that engineers and scientists working in one of the areas such as data compression, feature extraction, image processing, pattern recognition, speech signal processing, or filter design often find similar or even identical work in the other of these areas nearly unrecognizable. In spite of the widespread research activities in the various disciplines of wavelet analysis and their applications to signal processing, there have been few works devoted to bridge this gap by pointing out the interrelation of the various wavelet transforms, and to implement adapted wavelet algorithms.

The text under review carefully examines the properties of the waveforms used in adapted wavelet analysis such as sampling, Fast Fourier Transforms, orthogonal and biorthogonal wavelets, wavelet packets, local trigonometric transforms, and quadrature filters. It deals with the technicalities of algorithms primarily from the mathematical point of view and presents examples in pseudocode backed up with machine readable Standard C source code available on the optional diskette. In conjunction with the recently published monograph on “Wavelets and subband coding” by M. Vetterli and J. Kovačević (Prentice Hall, Englewood Cliffs, NJ 1995) which emphasizes the filter bank point of view, the book will help engineers and mathematicians in better understanding the concept of wavelet and in writing computer programs to analyze real data by wavelets and their discrete-time versions.

The text under review carefully examines the properties of the waveforms used in adapted wavelet analysis such as sampling, Fast Fourier Transforms, orthogonal and biorthogonal wavelets, wavelet packets, local trigonometric transforms, and quadrature filters. It deals with the technicalities of algorithms primarily from the mathematical point of view and presents examples in pseudocode backed up with machine readable Standard C source code available on the optional diskette. In conjunction with the recently published monograph on “Wavelets and subband coding” by M. Vetterli and J. Kovačević (Prentice Hall, Englewood Cliffs, NJ 1995) which emphasizes the filter bank point of view, the book will help engineers and mathematicians in better understanding the concept of wavelet and in writing computer programs to analyze real data by wavelets and their discrete-time versions.

Reviewer: W.Schempp (Siegen)

##### MSC:

42C40 | Nontrigonometric harmonic analysis involving wavelets and other special systems |

42-02 | Research exposition (monographs, survey articles) pertaining to harmonic analysis on Euclidean spaces |

65T50 | Numerical methods for discrete and fast Fourier transforms |