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.