Optimum recovery of a continuous signal from two discrete channels

Abstract

This paper deals with the recovery of a continuous signal from received discrete data. Very often, two sets of discrete data, obtained independently, are available for the recovery of a continuous signal. The two sets of discrete data have, in general, different data-rates. A better signal recovery will be achieved if both sets of data are employed in an optimum way, rather than when only one of the two sets is used. Optimum systems using both sets of discrete data are, in general, time-varying as opposed to the time-invariant property of the systems using only one set of discrete data, even though the signals and noise are stationary. A procedure for the optimum recovery of a continuous signal using two sets of discrete input-data will be developed, and methods for evaluating the mean square-error will be shown. An example will also be given to illustrate the method, and the quality, of the double-input system as compared with that of the single-input system.