LATTICE-THEORETIC ANALYSIS OF TIME-SEQUENTIAL SAMPLING OF SPATIOTEMPORAL SIGNALS .2. 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 ne w unifying theory linking TS sampling with generalized multidimensiona l sampling, It provided a complete characterization of time-sequential lattice patterns, including tight bounds on the temporal parameters o f those time-sequential sampling patterns that produce zero aliasing e rror, In this paper we present large space-spatial-bandwidth product a symptotics for these bounds, One of the surprising results is that in many cases, there exist optimal patterns, for which, asymptotically, t here is no extra penalty for lattice sampling subject to the time-sequ ential constraint, as compared to unconstrained multidimensional sampl ing, The implication to source coding is that an optimum encoder for s patiotemporal signals can be implemented with no buffering or other pr ocessing using a time-sequential sampler, The results apply to very ge neral multidimensional spatial and spectral supports (star shaped, or at most convex).