Environmental Engineering Reference
In-Depth Information
and is the Volterra kernel. When the system
is nonlinear time-varying, the Volterra series become [44]
2.2 Multi-Frequency Network Functions
It was shown in the preceding section that a set of time-varying
Volterra kernels, are needed to characterize the
behavior of nonlinear time-varying systems in the time domain. To de-
pict the behavior of the systems in the frequency domain, we extend the
definition of the time-varying network functions for linear time-varying
systems given earlier to nonlinear time-varying systems by defining the
following multi-frequency time-varying network functions
The
Volterra kernel is obtained from the inversion transform
Substitute (3.21) into (3.17)
where is the Fourier transform of with frequency As
an example, consider a nonlinear time-varying system with the input
The response is obtained from
Search WWH ::
Custom Search