Fourier and Laplace transforms
Fourier transformations Laplace transformation e-böcker
Cambridge University Press
2003
EISBN 9780511671852
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.
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.
