Linear time-variant transformations of generalized almost-cyclostationary signals.II. Development and applications

For pt. I see ibid., vol.50, no.12, p.2947-61 (2000). In Part I, the problem of the linear time-variant (LTV) filtering is addressed in the fraction-of-time (FOT) probability framework. The adopted approach, which is an alternative to the classical stochastic one, provides a statistical characterization of the systems in terms of functions that can be estimated by a single time-series. The analysis is carried out with reference to the wide class of the generalized almost-cyclostationary (GACS) signals, which includes, as a special case, the class of the almost-cyclostationary (ACS) signals. Examples of applications and developments of the theory introduced in Part I are presented here in Part II. Specifically, the countability of the set of the output cycle frequencies is studied with reference to linear time-variant systems for both ACS and GACS not containing any ACS component input signals. Thus, the linear almost-periodically time-variant filtering and the product modulation are considered in detail. Moreover, several Doppler channel models are analyzed. In all these examples, it is shown that the FOT probability approach allows one to characterize the system and its output in terms of statistical functions that can be measured by a single time-series. Furthermore, the usefulness of considering the linear filtering problem within the class of the GACS signals is clarified, and several pitfalls arising from continuing to adopt for the observed time-series the ACS model when an increase in the data-record length makes the GACS model more appropriate are pointed out.