Impact of Thresholding on Signal Processing Performance with Applications
Abstract
In this paper the approximation behavior of the Shannon sampling series is analyzed for the Paley-Wiener space PW pi 1, if the samples are disturbed by the nonlinear threshold operator This operator sets all samples, whose absolute value is smaller than some threshold, to zero. It is shown that the peak approximation error can grow arbitrarily large, independently of how small the threshold is. However if oversampling is applied and an appropriate kernel is chosen, then the reconstructed signal converges to the original signal, uniformly on the whole real axis, as the threshold goes to zero. Furthermore, we analyze the approximation behavior if not the signal itself is to be reconstructed but the output of some stable linear time invariant system. hi particular we show for the Hilbert tran form that the peak approximation error is unbounded, even if oversampling is applied.
