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The following paper describes a method of obtaining a polynomial characteristic function for a nonlinear static system. This function, , is obtained by the application of a growing exponential to the input of the system and the filtering of the output , into its separate components , and . The values of these three components at are the polynomial coefficients , and respectively. 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 function . This method is compared with the more widely known sinusoidal analysis of nonlinear systems. Experimental results are given.