Cross-correlation function of a bandpass nonlinear network

Memoryless nonlinear distortion of one of two Gaussian signals, x(t) and y(t), does not induce a change in the shape of the cross-correlation function ϕ
xy
(τ) as a function of τ (Price's theorem). A similar theorem holds for a network consisting of a cascade of three elements: a linear circuit L
1
, a memoryless nonlinear device NL, and a second linear circuit L
2
. This letter presents a proof of this property with the aim to promote a discussion on general methods by which a network of this type can be analyzed.