Higher-order characterization of linear time-variant systems operating on generalized almost-cyclostationary signals

In this paper, the higher-order characterization of linear time-variant systems in the time domain is introduced in the fraction-of-time probability framework. Specifically, the Nth-order system temporal moment function is defined as the operator that transforms the almost-periodic component of the input Nth-order lag product into the almost-periodic component of the output Nth-order lag product. The proposed characterization turns out to be useful to analyze systems operating on almost-cyclostationary or, more generally, on generalized almost-cyclostationary signals since their lag products can be decomposed into can almost-periodic component and a residual term.