Expansion of the switched FIR model parameters on Laguerre bases

This paper proposes a new representation of the S-FIR model by developing its coefficients using Laguerre orthonormal functions. The resulting model, entitled S-Laguerre model, ensures a significant parameter number reduction as well as simple recursive representation. However, this reduction is strongly linked to an optimal choice of the S-Laguerre poles defining the Laguerre bases. Therefore, we propose to extended the works of Tanguy et al. (2000) by proposing an optimisation algorithm to provide the optimal values for S-Laguerre poles. The Fourier coefficients of the proposed model are identified using the classical Recursive Least Square algorithm. The performances of the proposed S-Laguerre model and the proposed identification approach are illustrated on a numerical simulation.