A General Theory Of Time-sequential Sampling
In this paper, we consider the problem of optimum sampling of spatio-temporal signals. Recently, there has been increasing interest in this topic due to the advent of next generation television systems. Time-sequential sampling is a sampling paradigm in which samples are taken from the signal, one at a time, according to a prescribed ordering which is repeated after one complete frame of data is acquired. This paper extends previous work on time-sequential sampling to include arbitrary periodic patterns, as well as sampling on lattices with arbitrary geometries. As a result, a unifying theory is developed which includes such classical field-instantaneous lattices as field-quincunx and line-quincunx, proposed for downsampling of high-definition television signals, as specific examples. Such a formulation provides a systematic way for studying the aliasing effects of the ordering in which a signal is sampled. The design and analysis of these patterns is facilitated by introducing a powerful technique from the geometry of numbers which permits these tasks to be carried out in a coordinate system where the time-sequential patterns are rectangularly periodic. The resulting anti-aliasing patterns have a congruential structure. By further extending the theory to include time-sequential sampling on selected cosets of a lattice, we can analyze sampling patterns which are not true lattices, such as the bit-reversed sampling pattern.
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