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In this paper we analyze the convergence behavior of convolution-type system representations for the Paley-Wiener space PWπ1. We completely characterize all stable linear time-invariant (LTI) systems for which we have convergence in the distributional sense by giving a necessary and sufficient condition for convergence. Furthermore, we prove that there are stable LTI systems and signals in PWπ1 for...
In this paper we analyze the approximation of the outputs of stable linear time-invariant (LTI) systems T by sampling series that use only the samples of the input signal f. For our analysis we use the Paley-Wiener space of signals with absolutely integrable Fourier transform PWpi1 and consider non-uniform sampling patterns. We completely characterize all stable LTI systems T and sampling patterns...
In this paper the approximation behavior of the Shannon sampling series is analyzed for the Paley-Wiener space PWpi1, if the samples are disturbed by the non-linear 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,...
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