4.3 Linear Time-Variant Filtering of SC Processes
4.3.1 FOT-Deterministic Linear Systems
In this section, the problem of LTV filtering of SC processes is addressed. The class of LTV systems considered here is that of the FOT-deterministic linear systems characterized in Section 6.3.8. FOT-deterministic linear systems are defined as those linear systems that transform input almost-periodic functions into output almost-periodic functions.
In Section 6.3.8 it is shown that the system transmission function of a FOT-deterministic linear system can be written as
where Ω is a countable set. The functions ϕσ(·) are assumed to be invertible and differentiable, with inverse functions ψσ(·) also differentiable and referred to as frequency mapping functions. The functions Gσ(·) and Hσ(·) are linked by the relationships
with and denoting the derivative of ψσ(·) and ...