A system identification algorithm using orthogonal functions

An adaptive filter (ADF) structure is proposed for applications in which large-order ADFs are required. It is based on modeling the impulse response of the system to be identified as a linear combination of a set of discrete Legendre orthogonal functions. The proposed adaptive filter structure has desirable stability features and a unimodal mean-square error surface as well as a modular structure that permits an easy increase of the filter order without changing the previous stages. Computer simulations in which the proposed structure is used to identify actual acoustic echo path impulse responses show that the Legendre ADF has better convergence performance than the transversal ADF when identifying systems with long impulse response