Identification and Sampling of Stochastic Operators

The classical Shannon-Nyquist theorem allows regular sampling of bandlimited signals. Recently, this result was generalized to sampling of channels with delay-Doppler occupancy pattern of area less than one, resolving Bello’s conjecture in positive. In this paper, it is shown that stochastic channels possess a similar property, namely, that we can characterize the channel as long as the support of its scattering function has area less than one. This holds for rectangular as well as nonrectangular regions, allowing sampling of channels classically considered overspread. Keywords— stochastic, sampling, identification, operators, spreading function, scattering function, estimation.