Lattice-theoretic analysis of time-sequential sampling of spatiotemporal signals. I

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 lattice theory, we develop a new unifying theory linking TS sampling with generalized multidimensional sampling. The results have a geometric nature, involving simultaneous packing of the spectral and spatial supports in their respective domains. We provide a complete characterization of TS lattice patterns, and, extending the study to temporally nonuniform patterns, analyze their minimum and average temporal sampling rates. Unlike previous studies of TS sampling, our results apply to very general multidimensional spatial and spectral supports. We present tight bounds on the temporal parameters of those TS sampling patterns that produce zero aliasing error. The use of a TS sampler for bufferless source coding of spatiotemporal signals is considered as an attractive possibility.