The evaluation of the response of single-valued non-linearities to several inputs

The transform method for evaluating the coefficients of the various terms in the output autocorrelation function of a non-linearity with an input consisting of a sinusoidal signal and Gaussian noise is considered. Solutions, all of which involve confluent hypergeometric functions, are given for a few analytically defined non-linear characteristics. A short table of these functions is also given to facilitate computation. A new expression for evaluating the coefficients, a double integral involving the non-linear characteristic and the moments of the sinusoidal and Gaussian input signals, is derived. A graphical method of solution applicable to any single-valued non-linearity is given, and a comparison made, with experimental and theoretical results. Extension of the technique to several uncorrelated input signals of any known amplitude probability density distribution is shown to be possible.