Optimal Stochastic Approximations and Encoding Schemes Using Weyl-Heisenberg Sets

R. Balan

Siemens Corporate Research, 755 College Road East, Princeton, NJ 08540, USA
email: rvbalan@scr.siemens.com

I. Daubechies

Department of Mathematics and Program in Applied and Computational Mathematics, Princeton University, Fine Hall, Washington Road, Princeton, NJ 08544-1000, USA
email: ingrid@math.princeton.edu

In this chapter we study two classes of optimization problems concerning the interaction between stochastic processes and coherent Weyl--Heisenberg sets. One class involves approximation of stochastic signals, the other class refers to signal encoding for transmission in noisy channels. Both problems are studied in continuous and discrete time setting. Explicit solutions are found in Zak transform domain. The optimizers turn out to be generically ill-localized similar to the no-go Balian--Low theorem.