EIGENFILTER APPROACH FOR THE DESIGN OF ALLPASS FILTERS APPROXIMATING A GIVEN PHASE RESPONSE

In this paper, we apply the eigenfilter method to design an allpass fi lter that approximates a given phase response in the least-squares (LS ) sense. As it is not possible to express the exact LS phase error as a quadratic form suitable for eigenfilter formulation, alternative err or measures that approximate the ideal LS error are proposed. For each of these new formulations, the allpass coefficients are obtained as t he elements of the eigenvector corresponding to the minimum eigenvalue of a real, symmetric, and positive definite matrix. We propose a fast -converging iterative technique to approximate the ideal LS phase erro r solution. By employing an iterative weighting technique, the phase e rror can be made approximately equiripple. The design methods are illu strated with various practical examples and the results are compared t o allpass filters designs reported in the literature.