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EnglishThe paper discusses a novel sub-class of linear-in-the-parameters nonlinear filters, the Legendre nonlinear filters. The novel sub-class combines the best characteristics of truncated Volterra filters and of the recently introduced even mirror Fourier nonlinear filters, in particular: (i) Legendre nonlinear filters can arbitrarily well approximate any causal, time-invariant, finite-memory, continuous, nonlinear system; (ii) their basis functions are polynomials, specifically, products of Legendre polynomial expansions of the input signal samples; (iii) the basis functions are also mutually orthogonal for white uniform input signals and thus, in adaptive applications, gradient descent algorithms with fast convergence speed can be devised; (iv) perfect periodic sequences can be developed for the identification of Legendre nonlinear filters. A periodic sequence is perfect for a certain nonlinear filter if all cross-correlations between two different basis functions, estimated over a period, are zero. Using perfect periodic sequences as input signals permits the identification of the most relevant basis functions of an unknown nonlinear system by means of the cross-correlation method. Experimental results involving identification of real nonlinear systems illustrate the effectiveness and efficiency of this approach and the potentialities of Legendre nonlinear filters.
| Titolo: | Nonlinear system identification using quasi-perfect periodic sequences |
| Autori: | |
| Data di pubblicazione: | 2016 |
| Stato di pubblicazione: | Pubblicato |
| Rivista: | |
| Abstract: | The paper discusses a novel sub-class of linear-in-the-parameters nonlinear filters, the Legendre nonlinear filters. The novel sub-class combines the best characteristics of truncated Volterra filters and of the recently introduced even mirror Fourier nonlinear filters, in particular: (i) Legendre nonlinear filters can arbitrarily well approximate any causal, time-invariant, finite-memory, continuous, nonlinear system; (ii) their basis functions are polynomials, specifically, products of Legendre polynomial expansions of the input signal samples; (iii) the basis functions are also mutually orthogonal for white uniform input signals and thus, in adaptive applications, gradient descent algorithms with fast convergence speed can be devised; (iv) perfect periodic sequences can be developed for the identification of Legendre nonlinear filters. A periodic sequence is perfect for a certain nonlinear filter if all cross-correlations between two different basis functions, estimated over a period, are zero. Using perfect periodic sequences as input signals permits the identification of the most relevant basis functions of an unknown nonlinear system by means of the cross-correlation method. Experimental results involving identification of real nonlinear systems illustrate the effectiveness and efficiency of this approach and the potentialities of Legendre nonlinear filters. |
| Handle: | http://hdl.handle.net/11368/2933857 |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1016/j.sigpro.2015.08.018 |
| URL: | http://dx.doi.org/10.1016/j.sigpro.2014.10.037 |
| Appare nelle tipologie: | 1.1 Articolo in Rivista |
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