This work is unique as it provides a uniform treatment of the Fourier theories of functions
(Fourier transforms and series z-transforms) finite measures (characteristic functions
convergence in distribution) and stochastic processes (including arma series and point
processes). It emphasises the links between these three themes. The chapter on the Fourier
theory of point processes and signals structured by point processes is a novel addition to the
literature on Fourier analysis of stochastic processes. It also connects the theory with recent
lines of research such as biological spike signals and ultrawide-band communications. Although
the treatment is mathematically rigorous the convivial style makes the book accessible to a
large audience. In particular it will be interesting to anyone working in electrical
engineering and communications biology (point process signals) and econometrics (arma models).
Each chapter has an exercise section which makes Fourier Analysis and Stochastic Processes
suitable for a graduate course in applied mathematics as well as for self-study.
