A new adaptive covariance symmetric algorithm and a fast initialization scheme for least squares FIR filters with symmetric impulse response

Abstract

A new fast adaptive algorithm for LS FIR filters with symmetric impulse response is developed. The algorithm has a novel structure and it evolves around symmetrical internal variables. This results in a substantial reduction in computational complexity compared to other already existing schemes. The approximate number of the required multiplications is 14.5 p and the number of additions is 16.5 p per time recursion with p being the order of the filter. The important task of the algorithm's initialization is also considered and a fast O( p) initializing scheme is developed.