# Can sampling rate impact filter output?

I am noticing that the behavior of equalizers in music softwares varies depending on the sampling rate.

If we apply a filter (IIR or FIR) to a digital signal, in what situations does the sampling rate impact the filter output ?

My current understanding is : filter coefficients are linked to the frequency rate but the phase stays the same.

• There are all kind of implementations in music software so without source code it's hard to comment why behavior would change by sample-rate (actually, what do you mean by that comment). Yes, coefficients are sample-rate specific. If we stay in human hearing range then, higher sample-rate can improve certain type of filters (low pass, peaking, ...) which has issues at close the Nyquist frequency (fs/2) ... but, also may lead to issues at lower frequencies if the sample-rate is high enough and corner frequency low enough. May 30 at 21:33
• Do you mean keep all the coefficients the same and change the sampling frequency? Or change the sampling frequency and redesign the filters to the same specifciations? May 31 at 20:23

Yes. More specifically, for digital filters this is a result of the relationship between the cutoff frequency $$f_c$$ and sampling rate $$f_s$$.

Have a look at this question and this corresponding answer for the illustration.

Here's illustration for my comment:

Above plots shows how higher sample-rate improves filter magnitude response at higher frequency area.

When you use coefficients calculated for 44.1kHz with higher sample-rates, cut-off frequency follows behind to same direction as where Nyquist frequency (sample-rate / 2) moves to:

Base sample-rate is 44.1kHz (blue), other sample-rates are 88.2kHz (red) and 176.4kHz (black). Q = 1/sqrt(2) (0.707...) and cut-off frequency 10kHz.

IIR filters are generally converted from their analog implementation by using the bilinear transform. The bilinear transform causes so-called frequency warping that makes the digital filters steeper compared to their analog counterparts when getting closer to the Nyquist frequency. So a typical graphical equalizer with xdb/octave steepness and regularly spaced sliders on an octave pattern (namely logarithmically) will not end up similarly regular when transformed into the digital domain.

So a typical graphical EQ arrangement across the audible range will end up more regular when implemented with 96kHz sampling frequency than with 48kHz.