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) tec hnique involves solving a Toeplitz matrix problem. However, if the req uirement that the impulse response of the filter must be exactly symme trical is imposed, the matrix becomes non-Toeplitz. The authors point out that it is Toeplitz-plus-Hankel, and present a method with complex ity 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.