# Scaling of a notch filter

Let's say I have an IIR filter that is a notch type with a peak at -20db. How do I modify the coefficients of the filter so that the peak is at -10 db for example?

I know I can scale the denominator coefficients so that the global peak amplitude can be set, but it affects the whole filter, which I don't want.

Here is what I want :

• There is no way to just change the depth of the notch without affecting the frequency response at all frequencies. The question is how much of a change in the response at other frequencies you can tolerate. If the answer is None then there is no answer. – Dilip Sarwate Oct 14 '13 at 21:01
• You should provide an explanation of how you derived your filter coefficients, or at least what your coefficients are. – PAK-9 Oct 15 '13 at 10:46
• okay . follow me here : suppose i mix two signals : one is a full allpass with magnitude = 1 on all frequencies . If i mix it with the notch filter : (a+b)/2. the bottom frequency (-20db) is 0.1. It will become : (1+0.1)/2=0.55. so the notch is affected. Ins't there a way to report that on the coefficients? – IonOne Oct 15 '13 at 10:54
• There is a way to achieve the same result by changing the filter coefficients - however you need to change to process by which you obtained the coefficients, there is no one 'thing you do to filter coefficients to increase the notch amplitude in notch filters'. – PAK-9 Oct 15 '13 at 13:38
• Note that it's hard to go in the direction that you want, as you essentially need to redesign the filter. However, if you wanted to go the other way (turn a -10 dB notch into a -20 dB notch), a simple approach that is worth considering is just applying the filter twice in cascade. This will also have the effect of doubling any passband ripple, however (you'll get an effective squaring of the frequency response). – Jason R Oct 15 '13 at 15:11