Abstract. Shannon's sampling theorem is one of the most powerful results in signal analysis. The aim of this overview is to show that one of its roots is a basic paper of de la Vall6e Poussin of 1908. The historical development of sampling theory from 1908 to the present, especially the matter dealing with not necessarily band-limited functions (which includes the duration-limited case actually studied in 1908), is sketched. Emphasis is put on the study of error estimates, as well as on the delicate point-wise behavior of sampling sums at discontinuity points of the signal to be reconstructed.

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The Whittaker-Shannon-Kotel'nikov sampling theorem enables one to reconstruct signals f bandlimited to [−πW, πW ] from its sampled values f (k/W ), k ∈ Z, in terms of