Are There Any Qualitative Differences Between Equalizers?

[JulianW]

have a question about minimum-phase biquad equalizers in digital audio processing.





Is it theoretically possible that different “normal” minimum-phase EQ implementations (e.g., different biquad designs in various plugins or hardware DSPs) could have any meaningful difference in theoretical or audible quality, assuming they are set to the same target frequency response?





Or are they, in essence, always mathematically equivalent apart from implementation details like numerical precision, coefficient quantization, or internal processing resolution?





In other words: once we fix the magnitude response, isn’t the resulting minimum-phase system fully determined (via the Hilbert transform / causal minimum-phase relationship), making all properly implemented biquad EQs identical in theory and only differing in practical numerical errors?

 

[Sokel]

Here's an old paper addressing some of the issues:

https://firmware-developments.com/WEB/DOC/REF/ZauchaIIR_AES.pdf

And as guidelines from formal educated people are rare (they are rare themselves, so very well payed) about the proper implementation even before they touch any physical gear, the landscape is a little foggy.

Here's an example of physical implementations and some complications:

DSP Measurements and Rising Noise Floor

In several threads related to DSP platforms I've seen requests for measurements with filters engaged. I thought it unlikely that implementing filters in a DSP would have measurable effect on noise / distortion other than the obvious change in the fundamental, however @Sokel recently mentioned...

www.audiosciencereview.com

Better start measuring stuff around since is the only way to know.

 

[Waveform Fidelity]

Watch out for different definitions of Q..too!