Theoretical Bounds on the Performance of Sampled Data Communications Systems

Abstract

A general derivation is given for the minimum mean squared error in the smoothed output of a sampled data communication system. The message which is to be sampled and transmitted is assumed to be a stationary random function of time and is not strictly bandlimited. The results presented here are more general than previous calculations because the message spectrum has an arbitrary cut-off rate, the sampling duration can be finite, and "white" noise is assumed introduced into the system by transmission. Filtering of the message before sampling is shown to allow a smaller minimum error than without such filtering, even though the error is determined with respect to the original unfiltered message. The transfer function of the optimum presampling filter is derived as well as the corresponding optimum smoothing filter.