A generalization of nonuniform bandpass sampling

Nth-order nonuniform sampling is described for generalized bandpass signal frequency position, bandwidth, sampling rate, frequency-shift and phase-shift. A bandpass extension to the Nyquist criterion is derived, showing that restrictions on bandpass frequency position for odd orders of nonuniform sampling tend to zero as N tends to infinity. Bandpass interpolants based on the sinc function are derived for the generalized Nth-order sampled bandpass signals. It is shown that, for minimum (Nyquist) rate sampling, these interpolants are comprised of N bandpass filters, each with independent phase. The number of bandpass filters comprising the interpolant is found to decrease as the sample rate increases. The advantage of describing Nth-order sampling as the Nth replication and uniform sampling of a signal is demonstrated. Finally, digital implementation of the Nth-order bandpass sampling interpolants is discussed. It is established that it is not practicable to attempt to perform nonuniform bandpass sampling at the theoretical minimum rate, where the interpolation is to be performed digitally