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(N/sup 2/) 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.
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