TY  - BOOK
AU  - Gasquet,Claude
AU  - Witomski,Patrick
TI  - Fourier analysis and applications: filtering, numerical computation, wavelets 
T2  - Texts in applied mathematics
SN  - 0387984852
AV  - QA403.5 .G37 1999
PY  - 1999///]
CY  - New York
PB  - Springer
KW  - Fourier analysis
N1  - 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.
ER  -