IIR Multiple Notch Filters Design with Optimum Pole Position

Abstract

The following article introduces the new design and implementation of IIR multiple notch filters by the application of suitable pole placement technique. The initial step is to design the two IIR single notch filters with difference notch frequency to find suitable pole that can control the pass-band gain at 3 frequencies such as DC, yT and frequency between the notch frequency. After that, connect the IIR single notch filters with difference notch frequency in cascade to create IIR multiple notch filters which can control the pass-band gains at DC and yz frequency especially the frequency between the notch frequencies.

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 resulting system is characterized by a canonical structure for software and hardware realization. The main drawback is that it is restricted to few notch frequencies and very narrow *Correspondence: wangqiusheng@buaa.edu.cn 1 School of Automation Science and Electrical Engineering, Beihang University, Xueyuan Road No.37, Haidian District, 100191 Beijing, China Full list of author information is available at the end of the article bandwidths otherwise leading to non-unity pass-band gains [37].…”

“…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].…”

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

“…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.…”

“…In general, multiple notch filters are designed to have not-too-narrow bandwidths for stability reasons. There are two techniques for solving the overlapping problem, which are the optimal pole position technique 5 , and the all-pass filter of order 2N technique 8 . The optimal pole position technique 5 is simple and practical, since it does not require any complicated calculation.…”