Spectral Response of a Quadratic Device to Non-Gaussian Noise

Abstract

In order to compute the spectral response of a quadratic device to noise, a fourth-order moment P of the input noise is sufficient, P being a function of three independent time delays. The function P1 by which this fourth moment for a non-Gaussian noise differs from the corresponding moment for a Gaussian noise having the same spectrum is examined. The Fourier transform of this function is Q1, a function of three frequencies. Q1 is capable of an interpretation in terms of nonlinear correlations between noise components at different frequencies. A specialization of Q1 leads to E, a function of two frequencies which is a measure of the correlation between the squares of the envelopes associated with those frequencies. Several networks involving quadratic nonlinear elements are examined to illustrate the theory. It is shown that while the function P makes it possible to compute the complete spectral response of the network, the function E (together with the spectrum of the input) is sufficient in order to find the spectral density at zero frequency. Finally, for three examples of non-Gaussian processes, the corresponding P1, Q1 and E functions are computed.