Characterization of abrupt nonlinearity by the Volterra-Fourier method (Q1106791)

A new method based on the combination of the Volterra series and Fourier series to identify the system of abrupt nonlinearity has been developed and the results are more accurate and easier to compute than those of existing methods. Equations are derived for the Nth and Kth orders of the truncated Volterra-Fourier repeated series. Additional accuracy can be obtained by using Fejér's method to eliminate the Gibbs phenomenon at discontinuity. Convergence of the repeated series of the double series is established and the radius of acceptable convergence is derived by the d'Alembert criterion. An example for the nonlinear element of dead zone plus jump is given to illustrate this method. Two additional examples, an on-off clipper and a full-wave rectifier is presented and compared with the Hermite polynomial series approximation. It is found that the Volterra-Fourier method gives a far more accurate approximation near the point of expansion and also within a relatively large part of period of the Fourier series. It also admits a wider class of nonlinear functions, including abruptly nonlinear ones.