Analysis of Best Linear Approximation of a Wiener–Hammerstein System for Arbitrary Amplitude Distributions

For a nonlinear system with an input signal having a Gaussian probability distribution (this includes random-phase multisines), the best linear approximation (BLA) is proportional to the frequency response of the overall system. However, this is not the case for non-Gaussian input signals, for which the frequency response is biased with respect to the Gaussian BLA. In this paper, theoretical expressions for determining this bias for Wiener-Hammerstein systems are developed both for binary input signals and for white noise inputs with arbitrary probability distribution. Cubic and quintic nonlinearities are considered, but the methods can be extended to other forms of polynomial nonlinearity. Simple measures for quantifying the bias are also developed. It is shown that the bias decays rapidly to zero for a growing length of the impulse response.