Signal analysis and weighted polynomial approximation

Abstract

We present applications of Hermite polynomials in signal analysis. Among other result, we give a characterization of the so-called time-frequency window functions in terms of the Hermite--Fourier coefficients, a Bernstein-type theorem for the best approximations of window functions by Hermite-functions, time-frequency approximations. Some analogues for Hankel-transforms will also be considered.