A new approach to the time-sequential sampling problem

Sampling of signals that vary in time and have one or more spatial dimensions is studied for constrained sampling sets. The constraint imposed is that only one spatial sample can be taken at a given time, hence the name time-sequential sampling. J. Allebach (1984) has shown previously that the amount of aliasing error is not only a function of the sampling rates, but is also strongly dependent on the order in which spatial sample points are taken. A new design technique for finding optimal sampling patterns that minimize the sampling rates and produce zero aliasing error is developed by viewing time-sequential sampling as a specialized case of generalized two-dimensional sampling. New lower bounds for sampling rates required to produce zero aliasing error are given. These bounds are then used as stopping criteria for the aforementioned design technique. Theorems are given which state conditions under which the design problem reduces to a general two-dimensional sampling problem