The output signals and noise from a nonlinearity with amplitude-dependent phase shift

On the assumption that each input signal represents only a small part of the total input power, the output signals and output noise spectrum are found by extending the Barrett-Lampard diagonal expansion to the case of the quadrivariate distribution of input amplitude and phase at two different times. This expansion yields a decomposition of the nonlinearity into a summation of generalized Laguerre polynomials with uncorrelated outputs, whose spectra are simply autoconvolutions of the input spectrum. A slight generalization of the notion of memoryless nonlinearity allows this result to he applied very simply to devices, such as limiters and TWT amplifiers, that cause AM-to-PM conversion.