All-Pass Filter Design Using Blaschke Interpolation

Abstract

Obtaining a rational all-pass filter that matches a target phase response is a common problem in signal processing. Typical approaches have generally focused on optimizing filter coefficients while minimizing the deviation from the target phase response. However, these approaches typically do not offer a guarantee of exact match of the phase or any conditions on group delay. In this letter, we propose a Blaschke interpolation based all-pass filter design, wherein, if the phase response is known at n distinct frequencies, an all-pass filter that exactly satisfies the target values can be obtained. Moreover, the group delay at the interpolating points can be optimized or tuned to control the phase response for remaining frequencies. Simulations reveal that the design method is able to produce filters that closely match the target phase response accurately with much lower complexity than prior approaches.