An efficient weighted least-squares design of linear-phase nonrecursive filters

An accelerated procedure for the design of linear-phase nonrecursive filters using a weighted least-squares technique is described. This procedure is based on formulating the error reflecting the difference between the desired amplitude response and the amplitude response of the practical filter in a quadratic form. The coefficients of the filter are obtained by solving a system of linear equations involving a Toeplitz-plus-Hankel matrix. Such a system of linear equations can be solved by computationally efficient algorithms having only O(N²) complexity. By choosing the appropriate frequency-dependent weighting function, a filter with either a least-squares or an equiripple error variation can be designed