Some new results in sampling deterministic signals

Abstract

Whittaker's (or Shannon 's) Sampling Theorem is a well-known interpolation formula that has been extended in many directions. In this paper, we introduce two new formulations: -The first follows Papoulis' Generalized Sampling Expansion for reconstructing a signal from regular samples of N(linear, time-invariant) functionals of it, taking the samples at 1/N the Nyquist rate; but generalizing it for including linear T- periodically time-varying systems. This way is in close relation with works that extend sampling in other directions. -The second generalizes Linden's proof of Kohlenberg's sampling for a bandpass signal, in order to maintain the minimum sampling rate (in the average) and to obtain a separate interpolation of the in-phase and quadrature components of the signal. This follows Grace- Pitt-Brown's theory of bandpass sampling.