All-Pass Filter Design Using Unimodular Interpolation

Many signal processing applications involve designing an all-pass filter with a desired phase response. Earlier methods have largely focused on approximating the desired response using an optimisation based approach, or by using numerical computations of the group delay at specific frequencies with Blaschke interpolation. The former method does not offer any guarantee to match the estimated phase response at given points, whereas the latter one matches the phases at the input points, but is sensitive to the numerical precision of the specified group delays. In this work, we present a unimodular interpolation-based method to obtain all-pass filter coefficients that match the desired phase response at the given points without the need for group delays at the interpolating points. Through detailed simulations, we show that the proposed method is more suited for obtaining all-pass filters that match the target phases when compared to earlier approaches.