| Description |
1 online resource (x, 447 pages) : illustrations |
| Bibliography |
Includes bibliographical references and index. |
| Contents |
I: Applications and foundations -- 1. Signals and systems -- 2. Mathematical prerequisites -- II: Fourier series -- 3. Fourier series: definition and properties -- 4. The fundamental theorem of Fourier series -- 5. Application of Fourier series -- III: Fourier integrals and distributions -- 6. Fourier integrals: definition and properties -- 7. The fundamental theorem of the Fourier integral -- 8. Distributions -- 9. The Fourier transform of distributions -- 10. Applications of the Fourier integral -- IV: Laplace transforms -- 11. Complex functions -- 12. The Laplace transform: definition and properties -- 13. Further properties, distributions, and the fundamental theorem -- 14. Applications of the Laplace transform -- V: Discrete transforms -- 15. Sampling of continuous-time signals -- 16. The discrete Fourier transform -- 17. The fast Fourier transform -- 18. The z-transform -- 19. Applications of discrete transforms. |
| Note |
Print version record. |
| Summary |
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. |
| Subject |
Fourier transformations.
|
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Laplace transformation.
|
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MATHEMATICS -- Functional Analysis.
|
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Fourier transformations. (OCoLC)fst00933413
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Laplace transformation. (OCoLC)fst00992599
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| Added Author |
Beerends, R. J., 1958-
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| Other Form: |
Print version: Fourier en Laplace transformaties. English. Fourier and Laplace transforms. Cambridge ; New York : Cambridge University Press, 2003 9780521806893 (DLC) 2003055187 (OCoLC)52424132 |
| ISBN |
9780511675102 (electronic bk.) |
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0511675100 (electronic bk.) |
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9780511671852 (electronic bk.) |
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0511671857 (electronic bk.) |
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9780511806834 (electronic bk.) |
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0511806833 (electronic bk.) |
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