Designing a Notch filter for Digital Audio to be able to work with all audio sampling frequencies

I am currently designing an FIR notch filter using Matlab Filter Design & Analysis tool. I created a notch filter at desired notch frequency (lets say f0) with sampling frequency of 44.1kHz. But I found that the same notch filter is not able to filter-out/attenuate the desired frequency in other audio signals with different sampling rates.

Is it possible to design a single notch filter that works for all audio sampling frequencies.

FYI, I have tried with designing a notch filter with highest sampling frequency, but it is not working for audio with sampling rate other than what it is designed for?

Can somebody help me/provide me a lead in designing such a notch filter?

• Can you please clarify what does this "it doesn't work at different sample rates" means? If its centre frequency appears to "shift" with a varying sampling frequency then that is expected. – A_A Sep 20 '16 at 11:18

What you want is impossible. The notch frequency is always relative to the sampling frequency, so you design a notch filter with a given ratio $f_{notch}/f_s$. What you need to do is design different notch filters for different sampling frequencies. The same is of course true for cut-off frequencies of frequency selective filters, center frequencies, etc.