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Should I be concerned with the group phase delay which a filter produces? Especially in an audio application? Should I aim at using a linear phase delay filter for example?

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    $\begingroup$ this really depends a lot on your specific application, requirements, and your constraints. If you need a highpass at 40Hz, a linear phase filter is going to be REALLY expensive. $\endgroup$ – Hilmar Nov 19 at 21:50
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i will agree with Hilmar that it can depend on the specific application.

if the application is to essentially losslessly store or transmit audio to later retrieve or receive that audio, including conversions of format (and this includes the A/D and D/A and SRC) then i would say that there is no good reason for a process to not be linear phase (which is constant group delay, constant phase delay, and the two constants are the same number). there are audio format conversion processes (like a lossy codec) that are meant for storage or streaming that, for the sake of data reduction, have non-constant phase delay or non-constant group delay.

so if the application is to change the audio in some manner, it might not be possible to have the entire transfer function to be linear phase because of feedback.

enter image description here

if there is never any feedback and the audio is passed from one process to another, in cascade similar to the figure above, and all processes are meant to not change the perceived sound, then each process can have constant delay and there will be no waveform distortion due to non-constant phase delay or non-constant group delay (non-constant delay would not be a linear phase filter). so in this non-feedback case, there is no necessity to ever make different frequency components have different delays, and i would suggest to normally make that application linear phase.

sometimes, there are audio application in which a the process is one of several in a feedback loop, such as a feedback exterminator or maybe some reverberation control, it might be in this application that you might be tuning for a specific non-constant phase or group delay.

there are also applications like musical effects where a non-linear phase shift might not be perceptually relevant, but we know that linear phase shift is perceptually irrelevant when the processed sound is not compared directly with the input sound, so that the delay is detected.

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  • $\begingroup$ Thank you both for your comments! Much appreciated. $\endgroup$ – Luke Galea Nov 20 at 6:20
  • $\begingroup$ You are right, it does depend a lot on the application at hand which I did not specify. My main interest is musical/sound effects and so my main concern was perhaps - is that group delay heard? Well when the output is straight from the filter a micro second delay might not be an issue (not sure). However how about blending the filter output and original signal? That might result in some non-ideal behaviour since the frequencies aren't summed at the same point in time. And so if none of the processes use feedback, one should aim for a linear phase right? $\endgroup$ – Luke Galea Nov 20 at 6:27
  • $\begingroup$ With regards to aiming for a linear phase, the magnitude response is going to suffer then usually. Isn't that undesirable in audio ? $\endgroup$ – Luke Galea Nov 20 at 6:28
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    $\begingroup$ The magnitude doesn't inherently suffer – you might (usually: will) have to design a higher-latency / longer / more resource-intense filter if you want the same steepness or flatness of filtering, though. If your system has no feedback, then it's often a system where processing latency doesn't matter, and then your statement isn't true: you can at least approximate that nonlinear-phase filter's magnitude response with a (potentially) longer linear-phase filter. $\endgroup$ – Marcus Müller Nov 20 at 9:46
  • $\begingroup$ of course, in blending the processed sound with the original sound, delay and phase (of just the processed sound) will affect the audible sound of the blended result. that's how phase shifters and flangers work. but that is not the illustration i had meant to show above with the simple cascade of processes. $\endgroup$ – robert bristow-johnson Nov 21 at 6:49

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