Open AccessUnconstrained linear combination of even mirror Fourier non‐linear filters
Author(s) -
Sicuranza Giovanni L.,
Carini Alberto
Publication year - 2014
Publication title -
iet signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.384
H-Index - 42
eISSN - 1751-9683
pISSN - 1751-9675
DOI - 10.1049/iet-spr.2013.0256
Subject(s) - linear filter , linear system , mathematics , fourier transform , trigonometric functions , fourier series , invariant (physics) , filter (signal processing) , basis function , algorithm , basis (linear algebra) , computer science , mathematical analysis , geometry , mathematical physics , computer vision
In this study, the unconstrained linear combination of the outputs of even mirror Fourier non‐linear filters is considered. These filters are new members of the class of causal, shift‐invariant, finite‐memory and linear‐in‐the parameters non‐linear filters. Their name derives from the even symmetry of their trigonometric basis functions. Even mirror Fourier non‐linear filters are universal approximators for causal, time invariant, finite‐memory and continuous non‐linear systems. Moreover, their basis functions are mutually orthogonal for white uniform input signals in the interval [−1, +1]. The authors show in this study how to exploit these characteristics, in the framework of the unconstrained linear combination of non‐linear filters, for modelling unknown non‐linear systems. In particular, they show that the filters whose outputs are combined can be adapted avoiding the choice of the step sizes, by using a simple algorithm presented in this study. The analysis of the proposed structures is accompanied by a set of simulation results that confirm the good performance obtained in different situations.