The output properties of Volterra systems (nonlinear systems with memory) driven by harmonic and Gaussian inputs

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Abstract
Troublesome distortions often occur in communication systems. For a wide class of systems such distortions can be computed with the help of Volterra series. Results, both old and new, which will aid the reader in applying Volterra-series-type analyses to systems driven by sine waves or Gaussian noise are presented. The n-fold Fourier transform Gnof the nth Volterra kernel plays an important role in the analysis. Methods of computing Gnfrom the system equations are described and several special systems are considered. When the Gnare known, items of interest regarding the output can be obtained by substituting the Gnin general formulas derived from the Volterra series representation. These items include expressions for the output harmonics, when the input is the sum of two or three sine waves, and the power spectrum and various moments, when the input is Gaussian. Special attention is paid to the case in which the Volterra series consists of only the linear and quadratic terms.