Discussion on the -3 dB rejection bandwidth of IIR notch filters

This paper is concerned with the -3 dB rejection bandwidth of IIR notch filters. First, a general form of infinite impulse response (IIR) notch filters is presented. Then, the relationship between the bandwidths and the convergent speed of filtered signals is discussed. And, the accurate algorithm for this relationship is deduced. The conclusion is: the only factor to determine the convergent speed of filtered signals is the -3 dB rejection bandwidths of the IIR notch filters. Furthermore, an algorithm of practical IIR notch filters is given based on the previous relationship. Important statements are all verified and illustrated by simulations or applications.