Efficient computational procedure for the design of FIR digital filters using WLS technique

The design of an FIR filter using the weighted least-squares (WLS) technique involves solving a Toeplitz matrix problem. However, if the requirement that the impulse response of the filter must be exactly symmetrical is imposed, the matrix becomes non-Toeplitz. The authors point out that it is Toeplitz-plus-Hankel, and present a method with complexity O(N²) for solving the WLS problem. As exact symmetry is imposed on the impulse response, the number of variables to be solved is reduced by about a factor of two. This results in smaller matrices and, as a consequence, the new method uses less computer time per iteration than the Toeplitz case