Mathematical Principles of Signal Processing

Fourier and Wavelet Analysis

Pierre Brémaud

270 pages, parution le 31/05/2002

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Résumé

Fourier analysis is one of the most useful tools in many applied sciences. The recent developments of wavelet analysis indicates that in spite of its long history and well-established applications, the field is still one of active research.

This text bridges the gap between engineering and mathematics, providing a rigorously mathematical introduction of Fourier analysis, wavelet analysis and related mathematical methods, while emphasizing their uses in signal processing and other applications in communications engineering. The interplay between Fourier series and Fourier transforms is at the heart of signal processing, which is couched most naturally in terms of the Dirac delta function and Lebesgue integrals.

The exposition is organized into four parts. The first is a discussion of one-dimensional Fourier theory, including the classical results on convergence and the Poisson sum formula. The second part is devoted to the mathematical foundations of signal processing - sampling, filtering, digital signal processing. Fourier analysis in Hilbert spaces is the focus of the third part, and the last part provides an introduction to wavelet analysis, time-frequency issues, and multiresolution analysis.

An appendix provides the necessary background on Lebesgue integrals.

Contents

Fourier Analysis in L1
Fourier Transforms of Stable Signals
Fourier Series of Locally Stable Periodic Signals
Pointwise Convergence of Fourier Series

Signal Processing
Filtering
Sampling
Digital Signal Processing
Subband Coding

Fourier Analysis in l2
Hilbert Spaces
Complete Orthonormal Systems
Fourier Transforms of Finite Energy Signals
Fourier Series of Finite Power Periodic Signals

Wavelet Analysis
The Windowed Fourier Transform
The Wavelet Transform
Wavelet Orthonormal Expansions
Construction of a MRA
Smooth Multiresolution Analysis

L'auteur - Pierre Brémaud

CNRS/ESE, Gif-sur-Yvette, France

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Springer
Auteur(s)	Pierre Brémaud
Parution	31/05/2002
Nb. de pages	270
Format	16 x 24
Couverture	Relié
Poids	539g
Intérieur	Noir et Blanc
EAN13	9780387953380
ISBN13	978-0-387-95338-0