# How to apply two notch filters simultaneously

I have a sound file that I need to apply a notch filter to in Matlab.

comparing to original file I have two frequencies which are the noise. Applying a notch filter like this one:

wo = 1750/(44100/2);  bw = wo/35;
[b,a] = iirnotch(wo,bw);
fvtool(b,a);
f1 = filter(b, a, f);


This will atenuate the frequency at 1750 Hz. However there is one more frequency that is causing trouble at 820Hz. What I can do is reapply the same notch to the "new" version:

wo = 820/(44100/2);  bw = wo/35;
[b,a] = iirnotch(wo,bw);
fvtool(b,a);
f2 = filter(b, a, f1);


and f2 will be my clean file. However I need to have one vector "b" and one vector "a" that will clean all the noise at one go. Can I apply two notches simultaneously? I am very new to this kind of stuff. Thanks

You want to concatenate the two filters, which is equivalent to convolving the $$a$$ and $$b$$ coefficients of the individual notch filters to obtain the coefficients of the resulting filter with two notches.