Environmental Engineering Reference
In-Depth Information
The following comments are made with respect to the preceding devel-
opment:
Eq.(3.32) is a frequency-domain representation of the time-varying
Volterra series. Analogous to the time-domain representation of time-
varying Volterra series,
can be considered as
the kernel of the
order frequency-domain Volterra series.
Clearly seen is that once is known, the spectrum
of the response of nonlinear time-varying systems to the input
is defined completely.
Consider the special case where
because
we have
Eq.(3.34) provides a general means to characterize the behavior of
nonlinear time-varying system in the frequency domain. In the next
section, we will make use of these results to obtain the frequency
response of a special class of nonlinear time-varying systems, namely,
nonlinear periodically time-varying systems.
4. Frequency Response of
Nonlinear Periodically Time-Varying Systems
In this section, we make use of the results from the preceding section
to derive the frequency response of nonlinear periodically time-varying
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