Optimal filtering of periodic pulse-modulated time series

The present study concerns the optimal filtering of a class of input time series in which the amplitude is modulated by uniformly-pulsed periodic functions. A uniform sampling of the output at a period equal to the pulsing period displays the property of time invariance. The consequent usage of bilateral Fourier-Laplace transformations and the separability of terms implicit in the time-invariant nature of the processing effectively inverts the Wiener-Hopf equation and solves the problem. The weighting function is shown to be the sum of the Wiener-Zadeh-Ragazzini solution for the unmodulated case and set of appropriately-weighted delta-function-derivative terms occurring at each end point of the pulsing intervals.