High-quality factor, double notch, IIR digital filter design using optimal pole re-position technique with controllable passband gains

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

“…The technique relies on solving for filter coefficients to satisfy the table of gains at specific frequencies. The optimal pole reposition algorithm 5 works only for double notch filters, but the modified version of this algorithm 6 shows that this technique also works well in the general multiple notch filter case, i.e., the case of more than two notch frequencies. This algorithm yields an acceptable result.…”

“…For the wide bandwidth case, let ω 01 = 0.3π, ω 02 = 0.5π, BW 1 = 0.1π, BW 2 = 0.15π. The transfer functions of the narrow bandwidth case and the wide bandwidth case can be directly derived from (6), where the magnitude responses are shown in Fig. 1.…”

“…They can also be designed in several ways, such as transforming analogue notch filter [1][2][3] , the pole-reposition technique [4][5][6] , and implementation based on all-pass filters [7][8][9] which is considered in this paper.…”

A generalized design framework for IIR digital multiple notch filters

“…Several approaches exist to design IIR multiple notch filters [1][2][3][21][22][23][35][36][37][38][39][40]. The cascading method is a popular direct design technique that realizes a multiple notch filter by cascading several well-designed secondorder IIR single-notch filters [36].…”

“…The optimal design method requires computations for pole placement that results in a better frequency characteristic [2,3,37,38], but highly complex search-based or iterative algorithms are required even for a notch filter with two frequencies [2,38]. For a greater number of notch frequencies, a two-stage approach has been proposed to generate a stable optimal multiple notch filter, but the design procedure involves quadratic programming via an iterative scheme [3].…”