Estimation of Higher Moments of a Transfer Function Using Input and Output Data

This paper demonstrates a novel method for identifying the higher moments of an arbitrary linear-time-invariant system. By combining the method introduced in this paper and current available methods for reconstructing a function from its moments, it is possible to reconstruct a system from its input and output data. As a result, the paper introduces a new approach in system identification. Moreover, a relationship between the upper and lower limits for the time delay and the first two moments of a specific class of linear systems is derived.