Fourier and Laplace Transforms

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.

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