Environmental Engineering Reference
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For linear time-invariant systems, phasors are defined at the input
frequency only. For linear periodically time-varying systems, they are
defined at both the input frequency and the sideband frequencies
This is a distinct characteristic of these systems.
2. Transfer Functions of Nonlinear Time-Varying
Systems
2.1 Volterra Functional Series
Nonlinear time-invariant systems are most often analyzed using power
series [42] where the response of the system, denoted by
is repre-
sented as the power series of the excitation
where are constants. It is seen that the response is related to the
inputs at the present time only. Because it does not take into account the
effect of the past states of elements with memory, such as capacitors and
inductors, power series approach is only valid for circuits consisting of
memoryless elements or circuits with memory elements but operated at
sufficiently low frequencies such that the contribution of the past states
of elements with memory is negligible. For high-frequency applications,
the effect of past states must be considered. In this case, the coefficients
of the power series become frequency-dependent. The response in this
case is characterized by Volterra functional series, also known as power
series with memory [43]
where
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