A method for identifying the Fourier-Volterra kernels of polyperiodic
nonlinear systems by crosscorrelating the system output with prescribe
d nonlinear transformations of a prescribed random input is introduced
. A frequency-domain counterpart of this method, which can utilize a c
omputationally efficient FFT algorithm to compute cross-spectra of the
system output and prescribed nonlinear transformations of the input,
is also introduced. With complex inputs, the methods apply to infinite
-order systems with infinite memory. For real inputs, they apply only
to finite-order systems.