Fourier analysis and applications : filtering, numerical computation, wavelets
Author(s)
Bibliographic Information
Fourier analysis and applications : filtering, numerical computation, wavelets
（Texts in applied mathematics, 30）
Springer, c1999
- Other Title
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Analyse de Fourier et applications : filtrage, calcul numérique, ondelettes
Analyse de Fourier et applications : exercices corrigés
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Note
Translation of: Analyse de Fourier et applications : filtrage, calcul numérique, ondelette / by C. Gasquet, Patrick P. Witomski, & Analyse de Fourier et applications : exercices corrigés / by Robert Delmasso & P. Witomski
Includes bibliographical references (p. [433]-436) and index
Description and Table of Contents
Description
The object of this book is two-fold -- on the one hand it conveys to mathematical readers a rigorous presentation and exploration of the important applications of analysis leading to numerical calculations. On the other hand, it presents physics readers with a body of theory in which the well-known formulae find their justification. The basic study of fundamental notions, such as Lebesgue integration and theory of distribution, allow the establishment of the following areas: Fourier analysis and convolution Filters and signal analysis time-frequency analysis (gabor transforms and wavelets). The whole is rounded off with a large number of exercises as well as selected worked-out solutions.
Table of Contents
Signals and Systems.- Periodic Signals.- The Discrete Fourier Transform and Numerical Computations.- The Lebesgue Integral.- Spaces.- Convolution and the Fourier Transform of Functions.- Analog Filters.- Distributions.- Convolution and the Fourier Transform of Distributions.- Filters and Distributions.- Sampling and Discrete Filters.- Current Trends: Time-Frequency Analysis.- References.
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