I am reading up about notch filters. I understand the closer the pole is to the zero, the narrower the width gets and thus the bandwidth gets smaller. Is there an equation that links the bandwidth to the location of a pole? I have tried searching for so long and I couldn't get any useful answers.
I want to be able to determine the position of the pole given the required bandwidth and sampling rate and the frequency of the noise. I do not want to do it via trial and error