Second-order properties of products of clipped Gaussian processes

Closed-form expressions are derived for the partial derivatives with respect to the time delays of the fourth product momentW(t₁, t₂, t₃) = E[ Y₁(t) Y₂(t + t₁) Y₃(t + t₂) Y₄(t + t₃)]when theYᵢ(t)are infinitely clipped, zero-mean, jointly Gaussian processes. Since the output autocorrelation of systems with infinitely clipped inputs is often a sum of such fourth product moments, these partial derivatives can be used to determine second-order output properties, such as the power spectrum, when the system's inputs are correlated. In particular when the output is low-pass filtered, one numerical integration determines the variance of the smoothed process. The results are applied to study the behavior of the output variance, as a function of signal-to-noise ratio (SNR) and input bandwidth, of two systems which signal process using polarity coincidence techniques. When the normalized spectra of the independent signal and noise inputs are identical, it is shown that the output variance decreases as SNR increases, but, for SNR less than0dB and for all bandwidths considered, the output variance deviates at most-1dB relative to its value for uncorrelated, noise only, inputs.