DASP Implementation of Continuous-Time, Finite-Impulse-Response Systems
Andrzej Tarczynski, Hikmat Y. Darawsheh · 2020
Digital Alias-free Signal Processing (DASP) uses random sampling to mitigate aliasing. This paper investigates the use of DASP for realization of continuous-time, linear, time-invariant systems with finite-duration impulse response. We propose a random sampling scheme and suitable processing algorithm to produce an estimator of the target output. The estimator is unbiased, and its variance is guaranteed to converge to zero at least at O(T) rate, where T is the average distance between consecutive sampling instants. If the input signal and system impulse response are piecewise continuous and satisfy some benign conditions, the convergence rate is at least O(T^2). But if they are continuous everywhere, the rate increases to O(T^3).