Fourier and Laplace Transforms
Fourier and Laplace Transforms
H. G. ter Morsche, Technische Universiteit Eindhoven, The Netherlands
J. C. van den Berg, Agricultural University, Wageningen, The Netherlands
E. M. van de Vrie, Open Universiteit
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.
- Textbook written for self-study, complete with illustrated definitions, theorems and concepts
- Includes a rigorous treatment of distribution theory
- Solutions available to lecturers from [email protected]
Product details
August 2003Paperback
9780521534413
458 pages
252 × 163 × 21 mm
0.91kg
50 tables 125 exercises
Available
Table of Contents
- Preface
- Introduction
- 1. Signals and systems
- 2. Mathematical prerequisites
- 3. Fourier series: definition and properties
- 4. The fundamental theorem of Fourier series
- 5. Applications of Fourier series
- 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
- 11. Complex functions
- 12. The Laplace transform: definition and properties
- 13. Further properties, distributions, and the fundamental theorem
- 14. Applications of the Laplace transform
- 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.
