| n important problem in signal analysis is the representation of a given stationary process as the output of a system driven by white noise. In this thesis, we consider this problem using the truncated discrete Volterra series. Specifically, we first address the identification problem for a linear or equivalently first-order Volterra-type system given only a finite sample of its output in response to excitation by an unobservable, independent, and identically distributed (i.i.d) non-Gaussian sequence.;Parametric modeling of third-order cumulants of output sequence is also considered. New identification methods are developed for a non-Gaussian white-noise-driven linear FIR system. Recent work on NMP-LTI FIR system identification is limited to the use of second- and one-dimensional (1-D) slices of third-order cumulants. In this thesis, we show how to solve this problem using the second- and all samples of third-order cumulants in the appropriate domain of support. Identification methods that use the second-order cumulant and the diagonal slice of bispectrum are also developed. Since knowledge of the system order is of utmost important to many system identification algorithms, new procedures for determining the order of an FIR system using only output cumulants are presented.;In addition to the above, the identification problem for a class of nonlinear systems driven by white Gaussian noise is addressed. Processes generated by the second-order Volterra-type system are introduced. The second- and third-order cumulants and the power spectrum and bispectrum of such processes are derived. A least squares identification method that involves matching the second- and third-order cumulants of the output data is proposed.;Recursive and least squares methods for reconstructing the impulse response of a nonminimum phase, linear, time-invariant (NMP-LTI) system from its (k + 1)st-order spectrum... |
