The Relation Between Input and Output Probability Density for Discrete-Time Linear Systems - An Approximational Approach

摘要

In spite of their growing importance the existing mathematical framework for stochastic processes and systems cannot be regarded as complete in comparison to the methods which are available for deterministic signals. This paper wants to contribute a small part to the completion of this framework: An approximational method is presented which describes the (invertible) relation between the input and output (marginal) probability density function (pdf) for a discrete-time linear time-invariant system (DT-LTI system). The method uses cumulants to consider the linear system's effect on the pdf and Hermitian polynomials for pdf approximation.