Fourier and Laplace transforms

R.J. Beerends, H.G. ter Morsche, J.C. van den Berg, E.M. van de Vrie

458 pages, parution le 21/10/2003

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Résumé

This textbook presents in a unified manner the fundamentals of both continuous and discrete versions of the Fourier and Laplace transforms. These transforms play an important role in the analysis of all kinds of physical phenomena. As a link between the various applications of these transforms the authors use the theory of signals and systems, as well as the theory of ordinary and partial differential equations.

The book is divided into four major parts: periodic functions and Fourier series, non-periodic functions and the Fourier integral, switched-on signals and the Laplace transform, and finally the discrete versions of these transforms, in particular the Discrete Fourier Transform together with its fast implementation, and the z-transform.

This textbook is designed for self-study. It includes many worked examples, together with more than 120 exercises, and will be of great value to undergraduates and graduate students in applied mathematics, electrical engineering, physics and computer science.

Introduction
Applications and foundations
- Signals and systems
- Mathematical prerequisites
Fourier series
- Fourier series : definition and properties
- The fundamental theorem of Fourier series
- Applications of Fourier series
Fourier integrals and distributions
- Fourier integrals: definition and properties
- The fundamental theorem of the Fourier integral
- Distributions
- The Fourier transform of distributions
- Applications of the Fourier integral
Laplace transforms
- Complex functions
- The Laplace transform: definition and properties
- Further properties, distributions, and the fundamental theorem
- Applications of the Laplace transform
Discrete transforms
- Sampling of continuous-time signals
- The discrete Fourier transform
- The fast Fourier transform
- The z-transform
- Applications of discrete transforms
Literature
Tables of transforms and properties
Index

Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	R.J. Beerends, H.G. ter Morsche, J.C. van den Berg, E.M. van de Vrie
Parution	21/10/2003
Nb. de pages	458
Format	17,5 x 24,5
Couverture	Broché
Poids	920g
Intérieur	Noir et Blanc
EAN13	9780521534413
ISBN13	978-0-521-53441-3