Tq. Nguyen et al., EIGENFILTER APPROACH FOR THE DESIGN OF ALLPASS FILTERS APPROXIMATING A GIVEN PHASE RESPONSE, IEEE transactions on signal processing, 42(9), 1994, pp. 2257-2263
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.