Design of allpass filters for phase approximation and equalization using LSEE error criterion

Abstract

Considers a simple scheme for the design of allpass filters for approximation of a given phase function using a least-squares equation-error criterion. Assuming that the desired phase response is prescribed in a discrete set of frequency points, the authors formulate a general least-squares solution with a possible weight function. Based on the general formulation and analysis of the introduced error, a new design algorithm is developed for phase approximation. In addition to the iterative weighting of the equation error, the nominal value of the desired group delay was also adjusted iteratively to minimize the total phase error measure. This new feature essentially eliminates the difficult choice of the nominal group delay value which is known to have a profound effect on the stability of the designed allpass filter. The performance of the algorithm is analyzed with examples, showing that this simple and easy-to-use design method yields excellent phase equalizers for practical use. >