Artifacts in Wiener Kernels Estimated Using Gaussian White Noise

Wiener's nonlinear system identification theory characterizes a system function with a set of kernels of integrals. One method of determining these Wiener kernels is the cross-correlation technique proposed by Lee and Schetzen, which uses Gaussian white noise as the input to the unknown system. Because a test stimulus is only an approximation of infinitely long Gaussian white noise, it is possible that artifacts are generated during the estimation of the kernels. To help identify and characterize these artifacts, Wiener kernel estimates for two simple nonlinear model systems were made using a pseudorandom Gaussian white noise sequence. The results showed that because of the approximation of a Gaussian distribution, artifacts appear in the estimated kernels due to a form of aliasing. These artifacts can be reduced by increasing the sequence length of the input noise.