Time-limited sampling theorems for band-limited signals (Corresp.)

A procedure is given for the recovery of a band-limited signal from any set of samples by which it is uniquely determined. Containing, as a special case, Shannon's sampling theorem, it applies even to situations, such as time-limited sampling, for which no sampling basis exists, and extends to those eases the essential features of the Shannon representation needed for approximation from finite data. A second reconstruction, based on sequences of time-limited equispaced sample values, is also presented, and the extension to stochastic processes is discussed.