Generalizations of Cyclostationary Signal Processing: Spectral Analysis and Applications

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

(4.77a)

(4.77b)

where Ω is a countable set. The functions ϕ_σ(·) are assumed to be invertible and differentiable, with inverse functions ψ_σ(·) also differentiable and referred to as frequency mapping functions. The functions G_σ(·) and H_σ(·) are linked by the relationships

(4.78)

(4.79)

with and denoting the derivative of ψ_σ(·) and ...