Analysis of Periodic Filters with Stationary Random Inputs

A periodic filter is one whose frequency characteristic is periodic in frequency. Examples are delay-line cancellers for moving-target indication and delay-line sweep integrators.
Z-
transform techniques have proved useful in the analysis and synthesis of these filters when determinate inputs are involved. The determination of the mean square output and other statistical properties with random inputs has heretofore usually involved numerical integration, even for fairly simple cases. This paper presents formulas for computing the mean square value and other statistical properties of the output when the input is a stationary random function. The formulas involve the values of the input autocorrelation function at integral multiples of the basic delay and the sums of product pairs of the coefficients in the
Z-
transform power series. Simple algebraic forms result, making slide-rule computation feasible. The effects of internal noise are also considered by means of the same techniques. Specific formulas are derived for single and double cancellers, velocity-shaped cancellers, and sweep integrators.