Designing allpass filters using the eigenfilter method

The eigenfilter method is used in the design of allpass functions that approximate a given phase response. For a prescribed phase response, it is not possible to express the ideal least-squares error in a quadratic form. Several alternative least-squares error measures are introduced as means to approximate the ideal least-squares error. For each of these alternative errors, a quadratic error is formulated and the allpass coefficients are the elements of the eigenvector corresponding to the minimum eigenvalue of a real, symmetric, and positive definite matrix. Using iterative weighting functions, both the true least-squares and the equiripple phase error solutions can be approximated very fast and accurately with 15-20 iteration steps. Design examples are analysed. Consideration is given to the design of phase equalizers and the approximately linear-phase IIR (infinite impulse response) filter using the allpass eigenfilter method.<>