Design of IIR Notch Filter with Approximately Linear Phase

Abstract

A method for design of linear phase notch IIR filters is presented in this paper. The filter is realized in the form of a parallel connection of two all-pass sub-filters. In order to achieve the resulting filter with an approximately linear phase in the pass-band, the applied all-pass sub-filters should be also with a linear phase. The desired amplitude characteristic of a resulting filter is obtained by all-pass sub-filter phase approximation. It can be achieved by applying either a pure delay or an IIR all-pass filter in one branch. If a pure delay is positioned in one branch, equiripple phase of all-pass sub-filter from the other branch is guaranteed for an equiripple amplitude characteristic of the resulting filter. Efficiency of the proposed algorithm is demonstrated on a few examples. The algorithm exhibits a fast convergence and an easy determination of initial values. In the case where IIR all-pass sub-filters are placed in both branches, the resulting amplitude characteristic satisfies all the prescribed demands, but the amplitude characteristic is not equiripple even when both all-pass sub-filters have equiripple phase.