Abstract:

In this talk I'm going to present a Gabor analysis point of view of stationary stochastic processes. The first part of the talk is devoted to Gabor analysis on amalgam spaces. Here I'll be interested in necessary and sufficient conditions on the analysis/synthesis windows to define bounded operators on W(L^2, l^inf) and l^inf(Z^2). In the second part, I'll analyse the optimal approximation (in the mean square, a la Karhunen-Loeve, sense) of a given stationary process for a fixed rational redundancy. Using the Zak transform, the optimal windows turn out to be generically ill-localized, similar to the Balian-Low phenomenon.