LATTICE-THEORETIC ANALYSIS OF TIME-SEQUENTIAL SAMPLING OF SPATIOTEMPORAL SIGNALS .1.

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, Using the powerful techniques of la ttice, theory, we develop a new unifying theory linking TS sampling wi th generalized multidimensional sampling, The results have a geometric nature, involving simultaneous packing of the spectral and spatial su pports in their respective domains, We provide a complete characteriza tion of TS lattice patterns, and, extending the study to temporally no nuniform patterns, analyze their minimum and average temporal sampling rates, Unlike previous studies of TS sampling, our results apply to v ery general multidimensional spatial and spectral supports, We present tight bounds on the temporal parameters of those TS sampling patterns that produce zero aliasing error, Part II of this paper determines la rge space-spatial-bandwidth-product asymptotics for these bounds, The use of a TS sampler for bufferless source coding of spatiotemporal sig nals is considered as an attractive possibility.