##
**Wavelets and subband coding.**
*(English)*
Zbl 0885.94002

Prentice Hall Signal Processing Series. Hemel Hempstead: Prentice Hall. xvi, 488 p. (1995).

Since the implementation of the fast Fourier transform (FFT) algorithm and its variants, transform analysis plays an important role in signal processing and therefore has witnessed a great deal of activity, with a wide range of electrical engineering applications. From the signal processing point of view, transform analysis represents a hierarchy of transforms ascending from square transforms to wavelet transforms and filter banks, and finally to linear transforms. The final objective of linear transform analysis is the signal decomposition in order to decorrelate a signal prior to quantization. Combined decomposition and quantization should optimize the coding gain, minimize the output square error, and minimize the coding artifacts at a given rate.

The book under review presents an introduction to filter banks and their applications from the electrical engineering point of view. It provides a unified approach to affine wavelets and subband coding, including quadrature mirror filters and perfect reconstruction filter banks [P. P. Vaidyanathan, Multirate systems and filter banks, Prentice Hall, Englewood Cliffs, NJ (1993; Zbl 0784.93096)]. The level of the book is that of a first year graduate engineering text. All what the reader needs is some knowledge of elementary Fourier analysis, the elements of functional analysis, and basic linear systems theory in terms of discrete-time signals.

The book under review presents an introduction to filter banks and their applications from the electrical engineering point of view. It provides a unified approach to affine wavelets and subband coding, including quadrature mirror filters and perfect reconstruction filter banks [P. P. Vaidyanathan, Multirate systems and filter banks, Prentice Hall, Englewood Cliffs, NJ (1993; Zbl 0784.93096)]. The level of the book is that of a first year graduate engineering text. All what the reader needs is some knowledge of elementary Fourier analysis, the elements of functional analysis, and basic linear systems theory in terms of discrete-time signals.

Reviewer: W.Schempp (Siegen)

### MSC:

94-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to information and communication theory |

94A12 | Signal theory (characterization, reconstruction, filtering, etc.) |

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

93E11 | Filtering in stochastic control theory |

65Txx | Numerical methods in Fourier analysis |