Filtering and correlation of time-sequentially sampled spatiotemporal signals

With spatiotemporal signals sampled on a non-time-sequential lattice, continuous- and discrete-parameter convolution are equivalent. In many real systems, however, signals are actually sampled on a time-sequential lattice. The implementation of continuous-parameter 3D convolution with such sampled data generally requires interpolation to a non-time-sequential lattice. The exception occurs with data sampled time-sequentially according to a congruential ordering. With this data, a simple 1D convolution may be performed; and the frequency response of a desired spatiotemporal filter may be mapped directly to the frequency response of a 1D digital filter.