A General Theory Of Time-sequential Sampling

Conference PaperinSignal Processing 28(3):3.1-3.1 · October 1991with6 Reads
Impact Factor: 2.21 · DOI: 10.1109/MDSP.1991.639321 · Source: IEEE Xplore
Conference: Multidimensional Signal Processing, 1991., Proceedings of the Seventh Workshop on

    Abstract

    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.