A generalized shaping filter method for higher order statistics

The shaping filter method has been a valuable tool for computing the stochastic response of linear dynamical systems to Gaussian stochastic inputs that are not delta-correlated. A straightforward extension of this method to the non-Gaussian case involves determining shaping filters that “match” higher order cumulant functions of the stochastic noise input. However it is easy to find simple examples of input signals for which this will not work because their cumulant functions cannot be realized as cumulant functions of the output of a linear system with delta-correlated input. This paper proposes an alternative shaping filter and it shows that it is applicable to an entire class of input signals for which the original shaping filter method fails.A further extension of the shaping filter method is suggested, that involves the introduction of the concept of generalized moments that includes as particular cases both the moments and the cumulants.