
Author(s)  Soize, C. 

Title  Mathematical methods in the analysis of signal 
Publisher  Masson 
Year of publication  1993 
Reviewed by  Vasile Postolica 
This is the third edition supplemented by new materials and cancelled the others in comparison with the second edition. The book contains ten chapters and an appendix each of them having a proper selected bibliography, some problems on random signals and the corresponding hints.
Chapter 1, "Fourier transform for functions  Fourier series  Discrete Fourier transform" contains some considerations on the concepts mentioned above.
Chapter 2, "Review on the analytic functions of a complex variable  Z Transform" gives elementary results on the analytic functions of a complex variable and on Z Transform, with implications in the analysis of the signals.
Chapter 3, "Laplace transform for the functions" is devoted to Laplace transfrom in <formula> and in <formula>.
Chapter 4, "Intergral transformations of signals  Linear Filters  Case of linear Differential Equations" contains some considerations on the integral transformations which are very useful in the study of the signals.
Chapter 5, "Approximation for deterministic signals  Sampling  Estimation of FT with DFT and calculation with FFT" deals with approximation for signals in Hilbert spaces, sampling and estimations.
Chapter 6, "Elementary probability theory" is a survey on fountations of stochastic modeling, random variables with values in R^n and the probability laws on R^n.
Chapter 7, "Classical stochastic processes and stochastic fields" opens the part of the book concenring with the stochastic processes.
Chapter 8, "Linear intergral transformations, linear filtering and spectral anaysis of secondorder stochastic processes and fields" explains how one applies the linear integral transformations and the spectral analysis in some secondorder stochastic processes and fields.
Chapter 9, "KarhunenLoeve expansion and integral representation of secondorder stochastic processes and fieldssampling of stationary processes" deals with the aboce concepts applied for stochastic processes and fields.
Chapter 10, "Estimation of secondorder characteristics of vectorvalued processes" contains general notions on estimation and estimators of secondorder quantities for stationary and nonstationary processes.
Appendix, "Stochastic differential equation and diffusion process" is devoted to Ito and to Stratonovich stochastic differential equations.
Finally, we find six problems sessions on random signals, hints, some linear algebraic notations and an index.
The present book is an important contribution to the analysis of signals by mathematical methods because it gives emphasis to several connections between pure mathematics and applied mathematics in this field. So, it will be bery useful to the students, research workers and engineers interested in the mathematical studies of signals.