1. Fourier Series -- 2. Laplace Transforms -- 3. Fourier Transform -- 4. Discrete-Time Fourier Transform, One- and Two-Dimensional -- 5. Distributions, Delta Function -- 6. The Z-Transform -- 7. Windows -- 8. Two-Dimensional Z-Transform -- 9. Analytical Methods -- 10. Signals and Their Characterization -- 11. Discrete Fourier Transform -- 12. Analog Filter Approximations -- 13. Sine and Cosine Transforms -- 14. The Hartley Transform -- 15. The Hilbert Transform -- 16. The Radon and Abel Transform -- 17. The Hankel Transform -- 18. The Mellin Transform -- 19. Time-Frequency Transformations -- 20. Complex Variable Analysis -- 21. Legendre Polynomials -- 22. Hermite Polynomials -- 23. Laguere Polynomials -- 24. Chebyshev Polynomials -- 25. Bessell Functions -- 26. Zernike Polynomials -- 27. Special Functions -- 28. Asymptotic Expansions -- 29. Non-Recursive Filters -- 30. Recursive Filters -- 31. Recursive Filters Satisfying Prescribed Specifications -- 32. Statistics. 33. Matrices -- 34. Random Variables and Stochastic Processes -- 35. Random Digital Signal Processing -- 36. Spectral Estimation of Random Discrete Signals -- 37. Adaptive Filters -- 38. Band-Limited Functions and Sampling Theorem -- 39. Higher-Order Statistical Analysis -- 40. Stochastic Simulations -- 41. Nonlinear Digital Filtering -- 42. Wavelet Transforms -- 43. Trigonometric and Hyperbolic Functions -- 44. Algebra -- 45. Calculus.
This book serves as an essential reference for all engineers involved in signal and image processing. It examines the theories and applications of signal processing in filtering, coding, transmitting, estimating, detecting, analysing, recognising, and reproducing signals.