On the use of growing harmonic exponentials to identify static nonlinear operators

The following paper describes a method of obtaining a polynomial characteristic function for a nonlinear static system. This function,F(x) = hx + mx^{2} + dx^{3}, is obtained by the application of a growing exponentialx = exp(t)to the input of the system and the filtering of the outputh exp(t) + m exp(2t) + d exp(3t), into its separate componentsh exp(t), m exp(2t), andd exp(3t). The values of these three components att = 0are the polynomial coefficientsh, m, anddrespectively. The identification of systems not exactly describable by a cubic gives rise to an error minimization problem; the technique described in this paper minimizes the weighted mean-square error, with a weighting function1/x. This method is compared with the more widely known sinusoidal analysis of nonlinear systems. Experimental results are given.