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[Merlijn van Veen]

A while ago some colleagues and I had a vivid discussion whether group delay can be considered frequency dependent delay. Be warned though, this is a controversial topic and as far as I can tell no consensus has been achieved.

Please click here to read more.

Anxious to hear what the hive-mind thinks.





EDIT: Later in this thread Frank makes me realize that the minus sign is indeed mandatory and how I wished I just took a little bit more time to think it through

[Keith Broughton]

I read "frequency dependant" as activating the desired processing (like compression) only when a level threshold at a specified frequency (or freq band)is reached.
Under those criteria, group delay would not be "frequency dependant"
Just my POV...

[Stelios Mac]

I read "frequency dependant" as activating the desired processing (like compression) only when a level threshold at a specified frequency (or freq band)is reached.
Under those criteria, group delay would not be "frequency dependant"
Just my POV...

Shouldn't that be called frequency AND level dependent?

A conventional compressor is level-dependent (as the level crosses the threshold, compression starts to happen) - A multi-band compressor is that, whilst also being frequency dependent.

Frequency dependent should mean just that, "depends on the frequency" - not "depends on volume at a given frequency" or anything else.

[Merlijn van Veen]

"Frequency dependent delay" as in "variable delay over frequency".

[Keith Broughton]

"Frequency dependent delay" as in "variable delay over frequency".

So as the frequency varies, the delay varies?
I buy that.

[Barry Singleton]

Oops.  Irrelevant again.

Deleted. Sorry.

Barry.

[Marcel de Graaf]

Best Merlijn,

Very good subject and article written up. I always like subjects about timing.

Group delay has to be kept simple, it`s like you called a derivative of a phase plot. It is just a different view, but it is also showing the "pure" delay offset. This has to do where you set your point off reference in your analyzing tool. Group delay can help you find this offset.

In fig. 10 you could say there is a pure delay offset. I never tried this, but i am wondering what the waveform would like with an other burst signal than a pure sinewave.

Greetings,
Marcel

[Frank Koenig]

Group delay is -d phi/dw, where phi is phase and w is frequency. The article omits the minus sign which, while perhaps irrelevant to this philosophical discussion, is necessary to get the math right. -F

[Merlijn van Veen]

Group delay is -d phi/dw, where phi is phase and w is frequency. The article omits the minus sign which, while perhaps irrelevant to this philosophical discussion, is necessary to get the math right. -F

Agreed, but I purposely omitted it. The minus sign confuses. Something that's lagging has a negative value and something that's leading has positive value. This doesn't relate to e.g. IR and the actual group delay display in Smaart where late is pos and early is neg.

EDIT: Later in this thread Frank makes me realize that the minus sign is indeed mandatory and how I wished I just took a little bit more time to think it through

[Frank Koenig]

Agreed, but I purposely omitted it. The minus sign confuses. Something that's lagging has a negative value and something that's leading has positive value. This doesn't relate to e.g. IR and the actual group delay display in Smaart where late is pos and early is neg.

Hi Merljin,

I think the minus sign is actually important for intuitive understanding. Causal systems have phase that lags with increasing frequency (negative slope) and have positive delay since they're causal.

Consider the "hydrogen atom" of linear systems: the first-order low-pass. It has phase = 0 at zero frequency and phase = -pi/2 at infinite frequency. In the transition region the phase has a negative slope, and the delay is positive.

A possibly useful theorem is that the center of gravity of the impulse response of a system, which we might well intuitively associate with the system's delay, is equal to the negative of the slope of the phase at the origin (zero frequency). [Papoulis, "Signal Analysis", 1977, p. 21]

Delay is difficult. I still struggle with it even as my ability to struggle with it is in decline.

Best,

--Frank

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