Bandpass sampling and bandpass analogues of prolate spheroidal functions

We use the bandpass form of sampling theorem to construct a set of finite support functions that have highest energy concentration in bands of frequencies centered on a given carrier-frequency. These functions form an orthogonal set similar to the angular prolate spheroidal functions of order zero and hence we refer to them as “bandpass analogues of prolate spheroidal functions” (BPSF). Numerical examples are provided to illustrate the computation of BPSF and their potential application to efficient representation of carrier-frequency type signals.