A GENERALIZATION OF NONUNIFORM BANDPASS SAMPLING

Nth-order nonuniform sampling is described for generalized bandpass si gnal 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 ord ers of nonuniform sampling tend to zero as N tends to infinity. Bandpa ss interpolants based on the sine function are derived for the general ized Nth-order sampled bandpass signals. It is shown that, for minimum (Nyquist) rate sampling, these interpolants are comprised of N bandpa ss filters, each with independent phase. The number of bandpass filter s comprising the interpolant is found to decrease as the sample rate i ncreases. The advantage of describing Nth-order sampling as the Nth re plication and uniform sampling of a signal is demonstrated. Finally, d igital 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 rat e, where the interpolation is to be performed digitally.