Lattice-theoretic analysis of time-sequential sampling of spatiotemporal signals - part II: Large space-bandwidth product asymptotics

We consider the sampling of bandlimited spatiotemporal signals subject to the time-sequential (TS) constraint that only one spatial position can be sampled at any given time. Part I of this paper developed a new unifying theory linking TS sampling with generalized multidimensional sampling. It provided a complete characterization of time-sequential lattice patterns, including tight bounds on the temporal parameters of those time-sequential sampling patterns that produce zero aliasing error. In this paper we present large space-spatial-bandwidth product asymptotics for these bounds. One of the surprising results is that in many cases, there exist optimal patterns, for which, asymptotically, there is no extra penalty for lattice sampling subject to the time-sequential constraint, as compared to unconstrained multidimensional sampling. The implication to source coding is that an optimum encoder for spatiotemporal signals can be implemented with no buffering or other processing using a time-sequential sampler. The results apply to very general multidimensional spatial and spectral supports (star shaped, or at most convex).