Statistical Design and Evaluation of Filters for the Restoration of Sampled Data

A new analysis of the problem of continuously recovering periodically sampled data is given which starts with the assumption that the waveform being sampled is a stationary random function of time. The popular idealization of a band-limited frequency spectrum is not made; results obtained apply to all types of spectra and for any sampling frequency. In addition to such things as telemetering, radar, and data storage systems, for which the solution of this problem is of direct interest, the analytic techniques used may also be applied in the design and analysis of closed-loop control systems which utilize some digital elements.