Lossy coding of a time-limited piece of a band-limited white Gaussian source

摘要

We study the rates of source coding a T -seconds finite duration piece from a W -Hz band-limited real white Gaussian process with the mean squared error as a distortion measure. First we derive a discrete representation by projecting the signal of interest on the set of prolate spheroidal wave functions. We derive next a lower bound and an upper bound for the smallest rate that guarantees a distortion level with a probability (1 – ϵ) and we numerically evaluate these bounds. We also show that the derived bounds are asymptotically tight where they converge to Shannon’s formula.