Pre-envelope covariances and spectral moments for filtered input processes

摘要

The paper deals with the evaluation of the pre-envelope output process of linear systems subjected to filtered stationary and non-stationary pre-envelope input process. The pre-envelope covariances are evaluated by means of two approaches: i) in the first, the input process is defined by its autocorrelation function, while ii) in the second the input is solution of a set of differential equations (filter equations) subjected to a white input. In the latter approach, the pre-envelope differential equations are determined by an extension to the complex field of the stochastic differential calculus.