|Lossy coding of a time-limited piece of a band-limited white Gaussian source
|Youssef Jaffal, Ibrahim Abou-Faycal, American University of Beirut, Lebanon
|S.12: Second-order Analysis
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|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-\epsilon) and we numerically evaluate these bounds. We also show that the derived bounds are asymptotically tight where they converge to Shannon's formula.