Modeling Nonlinear Stochastic Filter by Volterra Transfer Functions

The Volterra series are widely employed to represent the input-output relationship of a nonlinear system. This representation is based on the Volterra transfer functions. The Volterra transfer functions are evaluated by a so-called harmonic probing method. In this paper the simulation of a stochastic resonance effect using a nonlinear device is discussed. Three cases are under consideration: harmonic input, Gaussian noise input, and sine wave plus Gaussian noise input. The output signal is determined by the Runge-Kutta method and in terms of the Volterra series. Expressions for the output harmonics were derived. If the Volterra transfer functions are known, the items of interest regarding the output signal can be obtained by substituting them into the general formulas derived from the Volterra series representation. These items include expressions for the output power spectrum. Frequency dependences of the output power spectral density of a non-linear stochastic filter, as well as amplitude characteristics are calculated and analyzed for the case of different parameter values of the filter. Numerical calculations of the output signal by the Runge-Kutta method were carried out to estimate the accuracy and reliability of results obtained. The comparative analysis has shown that the dependences of output signal power spectrum densities, obtained using the numerical calculation and Volterra series, are of the same character.