Fourier analysis and applications : filtering, numerical computation, wavelets / C. Gasquet, P. Witomski ; translated by R. Ryan

Includes bibliographical references (pages [433]-436) and index

Translator's Preface. Preface to the French Edition. Ch. I. Signals and Systems. Lesson 1. Signals and Systems. Lesson 2. Filters and Transfer Functions. Ch. II. Periodic Signals. Lesson 3. Trigonometric Signals. Lesson 4. Periodic Signals and Fourier Series. Lesson 5. Pointwise Representation. Lesson 6. Expanding a Function in an Orthogonal Basis. Lesson 7. Frequencies, Spectra, and Scales. Ch. III. The Discrete Fourier Transform and Numerical Computations. Lesson 8. The Discrete Fourier Transform. Lesson 9. A Famous, Lightning-Fast Algorithm. Lesson 10. Using the FFT for Numerical Computations. Ch. IV. The Lebesgue Integral. Lesson 11. From Riemann to Lebesgue. Lesson 12. Measuring Sets. Lesson 13. Integrating Measurable Functions. Lesson 14. Integral Calculus. Ch. V. Spaces. Lesson 15. Function Spaces. Lesson 16. Hilbert Spaces. Ch. VI. Convolution and the Fourier Transform of Functions. Lesson 17. The Fourier Transform of Integrable Functions. Lesson 18. The Inverse Fourier Transform. Lesson 19. The Space [actual symbol not reproducible] (R). Lesson 20. The Convolution of Functions. Lesson 21. Convolution, Derivation, and Regularization. Lesson 22. The Fourier Transform on L[superscript 2](R). Lesson 23. Convolution and the Fourier Transform. Ch. VII. Analog Filters. Lesson 24. Analog Filters Governed by a Differential Equation. Lesson 25. Examples of Analog Filters. Ch. VIII. Distributions. Lesson 26. Where Functions Prove to Be Inadequate. Lesson 27. What Is a Distribution?. Lesson 28. Elementary Operations on Distributions. Lesson 29. Convergence of a Sequence of Distributions. Lesson 30. Primitives of a Distribution. Ch. IX. Convolution and the Fourier Transform of Distributions. Lesson 31. The Fourier Transform of Distributions. Lesson 32. Convolution of Distributions. Lesson 33. Convolution and the Fourier Transform of Distributions. Ch. X. Filters and Distributions. Lesson 34. Filters, Differential Equations, and Distributions. Lesson 35. Realizable Filters and Differential Equations. Ch. XI. Sampling and Discrete Filters. Lesson 36. Periodic Distributions. Lesson 37. Sampling Signals and Poisson's Formula. Lesson 38. The Sampling Theorem and Shannon's Formula. Lesson 39. Discrete Filters and Convolution. Lesson 40. The z-Transform and Discrete Filters. Ch. XII. Current Trends: Time-Frequency Analysis. Lesson 41. The Windowed Fourier Transform. Lesson 42. Wavelet Analysis. References. Index.