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It is shown that a band-limited function f (t) is uniquely determined in terms of the samples gₖ (nT) of the responses gₖ (t) of m linear systems with input f (t), sampled at 1/m the Nyquist rate. Various known extensions of the sampling theorem follow as special cases of the resulting generalized sampling expansion of f (t).
A. Papoulis (Tue,) studied this question.