Perfect periodic sequences for identification of even mirror fourier nonlinear filters

In this paper we consider the identification of a class of linear-in-the parameters nonlinear filters that has been recently introduced, the so-called even mirror Fourier nonlinear filters. We show that perfect periodic sequences can be derived for these filters. A periodic sequence is perfect for a nonlinear filter if all cross-correlations between two different basis functions, estimated over a period, are zero. By applying perfect periodic sequences as input signals to even mirror Fourier nonlinear filters, it is possible to model unknown nonlinear systems exploiting the cross-correlation method. Then, the most relevant basis functions, i.e., those that guarantee the most compact representation of the nonlinear system according to some information criterion, can be easily estimated. Experimental results on the identification of a real nonlinear system illustrate the effectiveness of the proposed approach.