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, 2022 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, 2022 at 20:23
• Digital filters frequency response is usually defined on a $\small 0-pi$-range (often labeled $\small 0-1$ for $\small 0-1\times\pi$) scale. This is a normalized frequency, the ratio $\small f/fs$. Hence, per definition, $\small fs$ determines all actual frequencies $\small f$. Magnitude and phase are affected the same way.
– mins
Apr 8, 2023 at 19:27

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.