What is group delay?

[DonH56]

Note a constant group delay means every frequency is delayed equally so the effect is the same as moving the speaker. A constant 1 ms delay is about the same as moving a speaker about 1 foot (13.524 inches using 1127 ft/s for the speed of sound). What matters is the difference in group delay over frequency, which results from the phase changing non-linearly over frequency. That is, the phase is not a straight line with constant slope. The yellow highlighted section in the post above by @NTK makes that clear (compare low to high frequency delay to check audibility). How audible the delay difference depends upon frequency since longer wavelengths (lower frequencies) mean more delay can be tolerated without significantly changing the waveform we hear. Also note that, if the delay results in some multiple of the wavelength, it will not be heard for a steady-state signal, since one wave is the same as another when delayed by a full cycle. The speaker's crossover design, or DSP (room correction), can help correct nonlinear phase and achieve (near) constant group delay.

 

[cavedriver]

From: https://acris.aalto.fi/ws/portalfil...udspeaker_Group_Delay_Characteristics_AAM.pdf
Note that the tests were done with the most sensitive/revealing signals known to the authors, and we are probably less sensitive with real life materials.

Wow, so by that article it appears that there are speaker responses in production speakers that we can perceive (namely, group delays in frequencies over 300 Hz), and that should get measured and reported if present. Question then is, why doesn't Amir measure and report them?

Also, the graphs don't report what the peak group delay below 200 Hz was that they created and at what presumably large delay it is perceptible. Subwoofer folks report group delays in the 30-100 mS range iirc, while the graphs in the article stop at 10 mS and the measurement is off the scale.

 

[cavedriver]

Note a constant group delay means every frequency is delayed equally so the effect is the same as moving the speaker. A constant 1 ms delay is about the same as moving a speaker about 1 foot (13.524 inches using 1127 ft/s for the speed of sound). What matters is the difference in group delay over frequency, which results from the phase changing non-linearly over frequency. That is, the phase is not a straight line with constant slope. The yellow highlighted section in the post above by @NTK makes that clear (compare low to high frequency delay to check audibility). How audible the delay difference depends upon frequency since longer wavelengths (lower frequencies) mean more delay can be tolerated without significantly changing the waveform we hear. Also note that, if the delay results in some multiple of the wavelength, it will not be heard for a steady-state signal, since one wave is the same as another when delayed by a full cycle. The speaker's crossover design, or DSP (room correction), can help correct nonlinear phase and achieve (near) constant group delay.

yes, I wasn't among the people that didn't understand what group delay is, only trying now to suss out when it matters, and particularly in the case of the driver I was reading about, when does it matter for low frequency reproduction less than 200 Hz. How much time until our ears can perceive the difference? Clearly this is frequency dependent. Recently demoed a speaker (a Revel F328Be) that felt extremely "tight" in the bass. I have the impression (from statements on this forum mostly) but no data that my perception of this tightness is mostly based on room reflections or a lack thereof, however I want to know to what degree the speaker's design can contribute to (or destroy) good bass reproduction, and why we aren't measuring for it. Perhaps I should have posted in another thread.

 

[NTK]

Wow, so by that article it appears that there are speaker responses in production speakers that we can perceive (namely, group delays in frequencies over 300 Hz), and that should get measured and reported if present. Question then is, why doesn't Amir measure and report them?

Also, the graphs don't report what the peak group delay below 200 Hz was that they created and at what presumably large delay it is perceptible. Subwoofer folks report group delays in the 30-100 mS range iirc, while the graphs in the article stop at 10 mS and the measurement is off the scale.

Using Erin's recent measurement of the JBL Studio 630 as an example, group delay is hardly a problem. Note that the vertical axis should be shifted so that group delay reads zero at the high frequencies. A constant vertical shift makes no difference, it is just a time delay.

JBL Studio 630 Bookshelf Speaker Review

JBL Studio 630 2-Way Bookshelf Speaker Review

www.erinsaudiocorner.com

 

[cavedriver]

Using Erin's recent measurement of the JBL Studio 630 as an example, group delay is hardly a problem. Note that the vertical axis should be shifted so that group delay reads zero at the high frequencies. A constant vertical shift makes no difference, it is just a time delay.

JBL Studio 630 Bookshelf Speaker Review

JBL Studio 630 2-Way Bookshelf Speaker Review

www.erinsaudiocorner.com

Yes, looking through some more of Erin's reviews where he has reported group delays there do not appear to be any speakers with groups above ~20 mS below 200 Hz, nor any with group delays above ~1 mS above 300 Hz. So not likely to be a measurable factor that could correspond to my perception of "tightness" in bass reproduction. Darn.

 

[Thomas savage]

My English class when I was 12 .

 

[Holmz]

Yes, looking through some more of Erin's reviews where he has reported group delays there do not appear to be any speakers with groups above ~20 mS below 200 Hz, nor any with group delays above ~1 mS above 300 Hz. So not likely to be a measurable factor that could correspond to my perception of "tightness" in bass reproduction. Darn.

1msec is about 1 foot… so there is some tightness above 300 Hz, that would “spatial tightness.”

The impulse response would show you what is happening generally and transient response is aligned with most peoples description of “bass tightness” and/or muddiness as the TR gets worse.

 

[cavedriver]

1msec is about 1 foot… so there is some tightness above 300 Hz, that would “spatial tightness.”

The impulse response would show you what is happening generally and transient response is aligned with most peoples description of “bass tightness” and/or muddiness as the TR gets worse.

Got a link to a review or two where a good or bad transient response is measured?

 

[Holmz]

Got a link to a review or two where a good or bad transient response is measured?

Maybe Erin has one, but generally 1st order is lower than 2nd order… which is lower than 3rd, etc.
The bandpass boxes really get TR and GD values that are quite poor or large.

If you like Rap then get a ported or bandpass box
If you like tight bass then get an infinite baffle or sealed.

 

[cavedriver]

From: https://acris.aalto.fi/ws/portalfil...udspeaker_Group_Delay_Characteristics_AAM.pdf
Note that the tests were done with the most sensitive/revealing signals known to the authors, and we are probably less sensitive with real life materials.

View attachment 339385

btw, came across this study (here on ASR in a thread on blind testing) on the threshold of human's ability to detect group delay and they reported it to be around 0.6 mS in the 500Hz to 4 kHz range, which makes some of the variations in group delay readings in speaker reviews come close to being detectable.

Audibility of Group-Delay Equalization

This paper discusses the audibility of group-delay variations. Previous research has found limits of audibility as a function of frequency for different test signals, but extracting the tolerance for group delay to help audio reproduction system designers is hard. This study considers four...

ieeexplore.ieee.org

 

[ctrl]

btw, came across this study (here on ASR in a thread on blind testing) on the threshold of human's ability to detect group delay and they reported it to be around 0.6 mS in the 500Hz to 4 kHz range, which makes some of the variations in group delay readings in speaker reviews come close to being detectable.

Not really. Even if you take the hearing thresholds of group delay with artificial signals such as pink impulse as a reference, the hearing thresholds with typical filters are not reached with two and three-way loudspeakers.

Even if you take the lowest individual hearing thresholds with artificial signals of all test participants (see red mark above), these group delay thresholds are not reached with typical two- and three-way loudspeakers (the best individual hearing thresholds with artificial signals are just above the typical GD of loudspeakers, but have nothing in common with normal music).
With real musical instruments, such as castanets, the GD of typical loudspeakers is 6-15 times lower than the average hearing thresholds in the range above 500Hz.


Example 1, typical 2-Way speaker (dark grey curve in right diagram is the GD):

Example 2, typical 3-Way speaker (dark grey curve in right diagram is the GD):

Example 3, real 3-Way speaker (dark grey curve in right diagram is the GD):

Now some will object that even here in the ASR forum there are reports from people who have perceived sound changes above 500Hz after phase linearization.
As things stand at present, this is either a figment of the imagination or is due to slight changes in the frequency response caused by phase linearization.

As example the real 3-way speaker once without phase linearization and with.

GD without and with phase linearization:


FR without and with phase linearization:

The slight changes in the frequency responses in the crossover frequency range are easy to recognize. If such deviations are not checked and compensated for by measurements, differences are audible that are not due to GD differences.

 

[cavedriver]

Not really. Even if you take the hearing thresholds of group delay with artificial signals such as pink impulse as a reference, the hearing thresholds with typical filters are not reached with two and three-way loudspeakers.

View attachment 342282

Even if you take the lowest individual hearing thresholds with artificial signals of all test participants (see red mark above), these group delay thresholds are not reached with typical two- and three-way loudspeakers (the best individual hearing thresholds with artificial signals are just above the typical GD of loudspeakers, but have nothing in common with normal music).
With real musical instruments, such as castanets, the GD of typical loudspeakers is 6-15 times lower than the average hearing thresholds in the range above 500Hz.


Example 1, typical 2-Way speaker (dark grey curve in right diagram is the GD):
View attachment 342320


Example 2, typical 3-Way speaker (dark grey curve in right diagram is the GD):
View attachment 342321


Example 3, real 3-Way speaker (dark grey curve in right diagram is the GD):
View attachment 342322


Now some will object that even here in the ASR forum there are reports from people who have perceived sound changes above 500Hz after phase linearization.
As things stand at present, this is either a figment of the imagination or is due to slight changes in the frequency response caused by phase linearization.

As example the real 3-way speaker once without phase linearization and with.

GD without and with phase linearization:
View attachment 342328 View attachment 342329

FR without and with phase linearization:
View attachment 342330 View attachment 342331
The slight changes in the frequency responses in the crossover frequency range are easy to recognize. If such deviations are not checked and compensated for by measurements, differences are audible that are not due to GD differences.

Ok, so looking at this graph of the group delay measurements of the JBL Studio 698, the "baseline" delay at 5 kHz is around 4.5 mS, while the delay at 500 Hz is over 5.6 mS for a differrence of +1.1 mS. This should put it above the threshold for the average pink noise detectability, no? Granted most of the speakers I looked at data for show less than this. For example, the Wharfedale Linton has a worst difference of right around +0.5 mS. Perhaps I'm reading this wrong as I do not see how you could have a negative group delay in the speaker measurement. Also, I did not read the entire paper so maybe I missed why vocals couldn't be one of the more sensitive tests for group delay since the harmonics cover a reasonably wide frequency range and the human ear is so used to listening to voices?

And to be clear, I'm not saying group delay is that important, plenty of other issues can be found that would appear to be more important, just that it seems like it can't be wholly ignored in speaker design and testing because there are some speakers where it could be an issue, especially if a less than professional designer screws it up, like a DIY'er perhaps.

 

[ctrl]

Ok, so looking at this graph of the group delay measurements of the JBL Studio 698, the "baseline" delay at 5 kHz is around 4.5 mS, while the delay at 500 Hz is over 5.6 mS for a differrence of +1.1 mS. This should put it above the threshold for the average pink noise detectability, no? ... Perhaps I'm reading this wrong...

You always do a relative comparison of the drivers. So in case of the JBL Studio 698 the 0 ms baseline is as shown in the modified GD diagram from Erins website (The approximately 4ms GD that always appear in Erin's measurements are probably caused by a delay in the measurement system).

So the pink impulse threshold at 500Hz is 1.1 ms (according to the listening tests in the paper), Erin's measurement show about 1.2ms. So you don't need to worry at all about possible audibility. Threshold for real instrument at 500Hz is 3.2 ms.

 

[cavedriver]

a bit quick on my response there, deleted for clarity

 

[ctrl]

yes, that IS how I read it, and so if you set the zero baseline at ~4.5 mS from his graph, then at 500 Hz we're at >+1.1 mS. With the lines you've drawn it looks like ~1.3 mS actually

You're way too quick with your answer, before I've made my correction, you've already replied

 

[ernestcarl]

FR without and with phase linearization:

The slight changes in the frequency responses in the crossover frequency range are easy to recognize. If such deviations are not checked and compensated for by measurements, differences are audible that are not due to GD differences.

Is that kind of loss in magnitude level typical of phase linearization? With a phase inversed all pass filter, I would have thought otherwise — at least on-axis I haven’t noted such.

 

[ctrl]

Is that kind of loss in magnitude level typical of phase linearization? With a phase inversed all pass filter, I would have thought otherwise — at least on-axis I haven’t noted such.

I don't know if it's typical, depends how you set up the FIR filter. In VCAD I did the "inverted FIR" (e.g. LR4@200Hz) filter for each crossover IIR filter used. But the resulting IIR filter at the crossover frequency is not perfect, since the driver isn't. And this is the reason (I think) why in this case there are small FR changes - the FIR filter is "perfect", the IIR filter is influenced by the driver, cabinet,...

I wanted to use an example to show what reasons there could be (other than imagination) that people believe they can hear a difference in the GD above 500Hz (normal speaker versus speaker with phase linearization) when the current state of research rules this out - with typical speaker concepts shown in post#231.
Another reason would be when phase linearization is done with the measured data at the listening position (without gate). In this case one does primarily "phase linearizes" the room reflections (which will definitely influence the sound).

 

[ernestcarl]

And this is the reason (I think) why in this case there are small FR changes - the FIR filter is "perfect", the IIR filter is influenced by the driver, cabinet,...

Someone said to me some years back that even if you don’t see changes in the magnitude response after applying a phase linearizing all pass filter, slight magnitude changes in the windowed response curve counts as a FR change. I think it’s a bit of a cop out since that sort of phase linearization EQ does flatten the group delay as well, and, it’s not easy/possible separate the two.

 

[Sal1950]

I agree with your claim here that Amir might be a liar.

Liar !!!?
Excuse me sir, anyone can make a mistake or be in error.
But to call someone a liar without any substantiation is going a bit too far.

 

[KSTR]

Someone said to me some years back that even if you don’t see changes in the magnitude response after applying a phase linearizing all pass filter, slight magnitude changes in the windowed response curve counts as a FR change. I think it’s a bit of a cop out since that sort of phase linearization EQ does flatten the group delay as well, and, it’s not easy/possible separate the two.

Apparently different FR with different phase response but by definition identical magnitude response (from an upstream phase-only modifier) is a measurement issue and yes, it's the windowing. The lower the frequency the stronger the potential error. Most measurement systems cannot automatically cope with a linear-phase bass roll-off, for example, where the signal starts quite a while before the actual HF peak.

Windowing, especially types with variable width vs. frequency (FDW-types) is basically forbidden when you want to have identical conditions.