Periodically nonuniform bandpass sampling as a tapped-delay-line filtering problem

We consider systems for demodulation/modulation which use periodically nonuniform sampling (of arbitrary order) of the bandpass signal to circumvent the carrier-frequency restrictions of uniform sampling. The design of a particular tapped-delay-line (demodulation) or piecewise-constant-impulse-response (modulation) equivalent filter determines both the actual implementation filters and system performance. The tap spacing of the former and the transition times of the latter are periodically nonuniform. Following a characterization of the equivalent filter response, the special case of second-order sampling is examined for insight into the choice of sampling offset. A set of example designs demonstrates that, while nonuniform sampling permits carrier frequencies not allowed with uniform sampling, the resulting system performance is limited by the choice of carrier frequency