A novel design of IIR multiple notch filter based on an all-pass filter by using a pole-reposition technique

Abstract

In this paper, a novel and simple method based on an all-pass filter is presented by using the benefits of a pole re-position technique. The gains at frequencies of π of each single notch filter are adjusted by adding N − 1 tuning variables. The proposed method ensures that the passband gains are uniformly flat, the notch frequencies exactly meet the specifications, and the realized 3 dB bandwidths are approximately the same as those specified. This technique is very useful for designers because there are only N − 1 tuning variables required to adjust, and it does not need a complicated mathematical calculation. Although this technique is simple and easy to implement, it requires many iterations to find a suitable parameter for making the passband gain between two notch frequencies uniformly flat. Hence in this paper, three searching algorithms have been applied to reduce the number of iterations. We obtain a faster search and a closer frequency response to the ideal one.

Design of nearly linear‐phase double notch digital filters with close notch frequencies

“…We choose to do it in 20 steps because we encountered no problems with filters of the order up to 30 (we change the slope starting from −N with step 0.2 until −N + 4). Practically, the solution would be obtained in 20 steps regardless of the all-pass filter order for i = 1: 20 (10) In the ith step, the current all-pass phase slope has the value…”

“…A simple method based on the all‐pass filter by using the benefits of pole re‐position techniques is presented in [10]. This procedure can guarantee that the passband gains are uniformly flat while the notch frequencies and the realised bandwidths meet the proposed specifications.…”

Noniterative design of IIR multiple‐notch filters with improved passband magnitude response

“…[1][2][3][4][5][6][7][8][9] Realization of notch filter using cascaded second-order sections form structures inevitable leads to uncontrollable passband gains, 2,6 while iterative design methods based on utilization of convex optimization 3,4,9 or genetic algorithms 5 exhibit high complexity especially for a greater number of notch frequencies. [1][2][3][4][5][6][7][8][9] Realization of notch filter using cascaded second-order sections form structures inevitable leads to uncontrollable passband gains, 2,6 while iterative design methods based on utilization of convex optimization 3,4,9 or genetic algorithms 5 exhibit high complexity especially for a greater number of notch frequencies.…”

“…There are several approaches to the IIR multiple-notch filter design. [1][2][3][4][5][6][7][8][9] Realization of notch filter using cascaded second-order sections form structures inevitable leads to uncontrollable passband gains, 2,6 while iterative design methods based on utilization of convex optimization 3,4,9 or genetic algorithms 5 exhibit high complexity especially for a greater number of notch frequencies. All-pass-based IIR multiple-notch filter design methods first introduced in Pei and Tseng 1 transform the specifications of multiple-notch filter magnitude response into those of the phase response of a corresponding all-pass filter.…”