Eigenfilter approach for the design of allpass filters approximating a given phase response

摘要

We apply the eigenfilter method to design an allpass filter 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 error measures that approximate the ideal LS error are proposed. For each of these new formulations, the allpass coefficients are obtained as the 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 error solution. By employing an iterative weighting technique, the phase error can he made approximately equiripple. The design methods are illustrated with various practical examples and the results are compared to allpass filters designs reported in the literature.