This textbook describes in detail the various Fourier and Laplace transforms that are used to analyze problems in mathematics, the natural sciences and engineering. These transforms decompose complicated signals into elementary signals, and are widely used across the spectrum of science and engineering. Applications include electrical and mechanical networks, heat conduction and filters. In contrast with other books, continuous and discrete transforms are given equal coverage.
This textbook describes in detail the various Fourier and Laplace transforms that are used to analyze problems in mathematics, the natural sciences and engineering. These transforms decompose complicated signals into elementary signals, and are widely used across the spectrum of science and engineering. Applications include electrical and mechanical networks, heat conduction and filters. In contrast with other books, continuous and discrete transforms are given equal coverage.
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.
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.
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