Design of feedback-structured IIR notch filter with transient suppression using gain variation

•Feedback structure based notch filter proposed by Pei et al. [40] is analyzed for the first time with more details.•In the filter of Pei method, transient duration is a major problem, therefore, a simple time variant model to control the feedback structure gain is presented to solve it.•A new simple time-variant method to control the pole-position of the notch filter method is proposed to improve the performance of the filter in the both short transient and high quality factor aspects, simultaneously.•The performance of the proposed filter is compared with the recently reported methods as Piskorowski [44], Li [45] and Rana [48] models.•The results show that the proposed method remove the distortion of the performance, which exists in time variant filters, better than Li, Piskorowski and Rana models. It is shown that in transient parts, the performance of the proposed method is almost the same as the original signal compared to the others.•Furthermore, it is shown that in accordance with 50/60 Hz power line noise the performance of the proposed method is the best for interference removing compared to other techniques. In many applications of notch filtering, short transient response and high quality factors are very important issues. Increasing Q factor, decreases the bandwidth and improves magnitude selectivity near the notch frequency, but unfortunately increases the transient duration of the response. Recently, time-variant methods using exponential or sigmoid functions are considered to enhance the notch filter performance. In this paper, conventional and feedback-structured notch filters (following a recent work by Pei et al) are investigated in details. Using feedback structure, anyone can obtain a good narrow-band notch filter by tuning the feedback gain. However, it suffers from a long transient duration. In order to improve the performance of the filter, a new simple time-variant method to control the pole-position is introduced. Proposed method can keep the pole radius in the minimum value to decrease the transient duration more efficiently than other recently-reported ones as Piskorowski, Li and Rana methods. Also, it drives the pole to approach the unit circle or final position rapidly, normally after a few samples, while attaining a narrow bandwidth. In this paper, the performance of the proposed filter is compared with Piskorowski, Li and Rana methods. Simulation results show that the proposed algorithm can improve the performance of the feed