Perfect periodic sequences for even mirror Fourier nonlinear filters

• The paper deals with the identification of even mirror Fourier nonlinear filters.
• It shows that perfect periodic sequences (PPSs) can be developed for these filters.
• Nonlinear systems can be efficiently modeled with cross-correlation method using PPSs.
• The most relevant basis functions can be estimated using an information criterion.
• Experimental results on real nonlinear systems illustrate the proposed approach.

The paper deals with the identification of a class of nonlinear filters recently introduced in the literature, the even mirror Fourier nonlinear filters, and shows that perfect periodic sequences can be developed 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 using the cross-correlation method. Moreover, 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 real nonlinear systems illustrate the main advantage of the proposed method which is the remarkable reduction in the computational complexity.