Perfect periodic sequences for Legendre nonlinear filters

The paper shows that perfect periodic sequences can be developed and used for the identification of Legendre nonlinear filters, a sub-class of linear-in-the-parameters nonlinear filters recently introduced in the literature. A periodic sequence is perfect for the identification of a nonlinear filter if all cross-correlations between two different basis functions, estimated over a period, are zero. Using perfect periodic sequences as input signals, the unknown nonlinear system and its most relevant basis functions can be identified with the cross-correlation method. The effectiveness and efficiency of this approach is illustrated with experimental results involving a real nonlinear system.