Adaptive covariance-type internally symmetric algorithm for LS FIR filtering with linear phase

The least-squares design of linear phase filters is approached from a novel perspective to take advantage of the symmetry which is intrinsic to the problem. The structure of the proposed filter is based on an adaptive covariance-type algorithm that results in a substantial reduction in computational complexity compared to other existing schemes. The algorithm requires 12.5 multiplications and 18.5 additions per time recursion with p being the order of the filter. A fast O(p) initialization scheme is also presented.<>