An Efficient Filter Bank Structure for Adaptive Notch Filtering and Applications

Second-order IIR adaptive notch filters (ANF) andbanks (ANFB) have been extensively utilized in many applications ranging from biomedical engineering to control systems. In this paper, a new efficient ANFB is proposed that is composed of two filter banks, namely a prefilter bank with cascaded IIR notch filters and a parallel structure IIR ANFB. The second-order IIR ANFs or filter bank cells in the proposed ANFB are updated by utilizing a modified normalized gradient (ModNG) algorithm. The proposed ANFB requires the same number of cells as does a conventional parallel form ANFB. However, the filter weight initialization drawback that the conventional parallel form ANFB inherently suffers from is significantly alleviated in the proposed ANFB. Equipped with the ModNG algorithm, the proposed ANFB yields considerably improved frequency estimation performance as compared to the conventional parallel form ANFB, for a wide range of frequencies and signal-to-noise ratios (SNR). Furthermore, preliminary steady-state analysis is provided for both the proposed and conventional ANFBs, which significantly enhances our understanding of their capabilities and features. Extensive case study simulations are conducted to demonstrate the superiority of the proposed ANFB over the conventional parallel form ANFB. The proposed ANFB is also applied to real noise and vibration signals to reveal its promising analytical and practical capabilities.