What is group delay?

[pkane]

Sir, I’m a physician and epidemiologist, I understand linearity. I’ll do as you suggested and try to read it through more than once, although there surely must be some way to explain the basics of how group delay translates to an audible result that doesn’t require this level of esoterica and detail.

I did not mean to single you out personally. I just think that some folks on here are like myself—hobbyists seeking fundamentals that will allow them to interpret measurements in practical terms. And I’ve learned can incalculable amount of useful info from the many generous, patient folks on here who are eager to teach.

However this particular thread seemed to be a bit of a grandstanding exercise, a show of academic oneupmanship on the part of some highly didactic folks who were not paying attention to the struggles of others involved. The question was basic; the explanation dove right into the deep end before some folks learned to swim.

That is one of the most uninformed and insensitive posts I’ve seen here. Not only is @DonH56 one of the more technical, hands-on experts in ASR, but he’s also the one that’s always willing to jump in and explain complex subjects to any level of detail, spending a lot of his personal time to document and illustrate difficult concepts for others - do some searching. Just because this content went over your head is no reason to attack Don: you owe him an apology.

And perhaps, just perhaps, you may want to use less sarcasm and show off less of your English-major skills when asking for help the next time.

 

[srkbear]

That is one of the most uninformed and insensitive posts I’ve seen here. Not only is @DonH56 one of the more technical, hands-on experts in ASR, but he’s also the one that’s always willing to jump in and explain complex subjects to any level of detail, spending a lot of his personal time to document and illustrate difficult concepts for others - do some searching. Just because this content went over your head is no reason to attack Don: you owe him an apology.

And perhaps, just perhaps, you may want to use less sarcasm and show off less of your English-major skills when asking for help the next time.

I expressly told him I wasn’t targeting him specifically. I have great respect for him and appreciate the many times he has helped me on here, And I posted an additional response thanking those (including him) who have attempted to help since.

Yes, my original post was apparently a failed attempt at humor, but it wasn’t intended viciously. I’ll go ahead and delete it—but my original intent was to defend the OP (and myself) who was in my view intending to find a simple explanation, several times, but was met with an escalating debate that eventually excluded him from the conversation altogether. It was a call to acknowledge that there are a considerable number of folks on here without an audio engineering background who are eager to learn—and as a teacher myself, I am inclined towards championing those seeking knowledge.

@DonH56 , if my response appeared directed towards you and you were offended, please accept my sincere apology.

 

[DonH56]

@pkane -- Thank you very much for the kind words and defense! I too took the comments personally at first reading.

@srkbear -- Not sure I was ever able to answer your quest to understand group delay, but I understood and appreciated your response.

 

[srkbear]

@pkane -- Thank you very much for the kind words and defense! I too took the comments personally at first reading.

@srkbear -- Not sure I was ever able to answer your quest to understand group delay, but I understood and appreciated your response.

Don, please don’t give up on my yet. I’m in Germany attending my mother-in-law’s funeral—I fully plan to focus my energies on this when I return, and to respond to your generous explanations. I hope you have a happy holiday! —Steve

 

[budje]

This thread is still the first result in Google for "headphone group delay" so I think it's still significant to have an actual ELI5 answer. This thread is hilarious to stumble across. Once you understand group delay, it's funny to go back through the thread and see where people are technically correct, and where they add obviously unnecessary detail. Some of the below is copied from the YouTube video already mentioned in this thread, but I couldn't find anyone posting an ELI5 explanation as easy to understand as the video.

Group delay refers to different frequencies being delayed different amounts.

If you send an audio signal through a device, and the bass frequencies are played with 1ms of delay and the high frequencies are played with a 2ms delay, that's an example of group delay. Each "group" of frequencies is "delayed" a certain amount. When different frequencies in the same signal have different delays, that's group delay.

If you send an audio signal through a device, like a wire, and you get the same signal out the other side, there is no group delay in that device. If some frequencies come out the other side at the different times, that's group delay.

The critical thing is to tie this back to headphones. Everyone keeps coming to this thread to understand headphone measurements. Headphone group delay doesn't really make sense on the surface: You're saying that a headphone driver, a few centimeters away from your ear, is producing an audio signal where the frequencies coming out of the driver have variable frequency timings, different from the signal going into the driver? That the driver itself is making a waveform where the bass notes hit your eardrum milliseconds sooner than the high notes? No!

Amir's post is a little dense and terse, but makes sense now that we know what group delay is. He's saying that audio bouncing around inside the cups getting combined with the original signal can make it sound like that part of the signal is delayed. In a device like an amplifier, group delay might be from electrical signal processing. In a headphone, Amir is measuring the audio reflections in the cups combining with the original signal, not from the driver itself. At least, I haven't seen any of the reviews cite the driver as the reason for group delay, it's always reflections.

Group delay might* affect the soundstage/imaging of headphones. Your ears determine where things are in the world by the phase at which signals hit each ear. Your ears are very sensitive to this. If different frequencies in a signal have different delays, it affects your ability to perceive/imagine where the sounds sources are in space. I haven't seen any data on what level of group delay has a perceivable effect on soundstage (and soundstage may be impossible to objectively measure anyway).

* the group delay measured on ASR is the same for both cups of a headphone. If the group delay is the same for both ears, does it actually affect soundstage? Now that's a good question!

Once you understand this, it's a lot easier to see where other posters start to explain it and then get lost in the details of digital signal processing, because they're trying to be more accurate with their details of the explanation. I find it entertaining and fascinating that the more technical details people add, the more muddied their explanations become.

 

[witwald]

Headphone group delay doesn't really make sense on the surface: You're saying that a headphone driver, a few centimeters away from your ear, is producing an audio signal where the frequencies coming out of the driver have variable frequency timings, different from the signal going into the driver? That the driver itself is making a waveform where the bass notes hit your eardrum milliseconds sooner than the high notes? No!

I've used VituixCAD to simulate a "perfect" loudspeaker. In this example, the bass frequencies have a 2nd-order Butterworth high-pass response with a –3 dB point of 20 Hz. The high frequencies have a 2nd-order Butterworth low-pass response with a –3 dB point of 20 kHz.

The frequency response of this dynamical system is shown below. This could be the response of an amplifier, a loudspeaker (a very good one!), or the driver in a headphone.

VituixCAD also computes the group delay curve, which is shown below.

The above plot shows the presence of approximately 11 milliseconds of group delay at 20 Hz. It reduces quickly as frequency increases, and by 50 Hz the group delay is approximately 2 milliseconds.

 

[Holmz]

…
Group delay might* affect the soundstage/imaging of headphones. Your ears determine where things are in the world by the phase at which signals hit each ear. Your ears are very sensitive to this. If different frequencies in a signal have different delays, it affects your ability to perceive/imagine where the sounds sources are in space. I haven't seen any data on what level of group delay has a perceivable effect on soundstage (and soundstage may be impossible to objectively measure anyway).
…

Ah.. no…
It is not the cups.

 

[dasdoing]

a "perfect" loudspeaker.

perfect in what sense? minimum phase?
perfect would be linear phase even the roll-off must be there in the real world

 

[NTK]

perfect in what sense? minimum phase?
perfect would be linear phase even the roll-off must be there in the real world

Unfortunately, one cannot realize a linear phase response from a bandwidth limited real physical device such as a headphone/loudspeaker driver.

source

 

[dasdoing]

Unfortunately, one cannot realize a linear phase response from a bandwidth limited real physical device such as a headphone/loudspeaker driver.
View attachment 332308
source

well, I include digital processing into "the perfect loudspeaker". I see you don't

 

[egellings]

As long as they're all showing up at the same time, should not make a difference, n'est pas?

It would be the time the party was scheduled to start and the time the guests, as a group, arrived--group delay.

 

[fpitas]

Practically speaking, a sine wave that started in the infinite past and never ends can only show a phase delay of a period, maximum. As soon as you modulate it, then group delay is applicable. Somebody linked it earlier, but here it is again: https://en.wikipedia.org/wiki/Group_delay_and_phase_delay

 

[witwald]

perfect in what sense? minimum phase?
perfect would be linear phase even the roll-off must be there in the real world

Here I was thinking of a non-DSPed electrodynamic system, consisting of components that have mass, stiffness, and damping. This would be a minimum-phase system. Of course, DSP could be used to modify the minimum-phase behavior of the frequency response function to produce linear-phase behavior.

 

[budje]

perfect in what sense? minimum phase?
perfect would be linear phase even the roll-off must be there in the real world

Perfect as in "made up". Here's Focal Celestee on this forum measured with 0ms group delay at 50hz https://www.audiosciencereview.com/forum/index.php?threads/focal-celestee-review-headphone.21917/

Ah.. no…
It is not the cups.

Amir calls out the cups as a source of group delay here: https://www.audiosciencereview.com/forum/index.php?threads/focal-utopia-review-headphone.22103/

 

[daverosenthal]

This thread was fascinating to read through. So many confused people (and some not!). Here's my humble attempt to explain group delay, as well as to explain why it tends to confuse:

What it is (conceptually):

At the simplest level, group delay is the amount of delay (measured in seconds) that some device/filter imparts, as a function of frequency.

OK, give me more detail:

Say we have a signal (a song, say) that is going to pass through some component (headphones, amplifier, etc.). I think we can all agree that the song can be thought of as certain frequencies sounding at certain times with certain amplitudes. All good? Good. Those individual mini sounds that make up the song are called "wavelets" in math terms. Thinking about wavelets makes understanding group delay easy. First let's talk about a concept we all understand, frequency response. What frequency response measures is how much each wavelet's amplitude is modified, as a function of frequency. Group delay is exactly the same, but it measures how each wavelet's time is modified (delayed) as a function of frequency. Just like frequency response, the ideal that how things are modified shouldn't vary with frequency. If a bass drum and a piccolo hit the downbeat at the same time, you want to hear them together. If there is big enough group delay in the bass relative to the treble they will be out of sync. There, that's all it is.

Finally, why does Amir show this graph for headphones? Well, partly because it's useful as is, and partly because it helps see if the headphone is 'well behaved' with how the sound bounces around inside it. (In the same spirit as we might look for wrinkles in a speaker's impedance graph to see cabinet resonances.)

Why it confuses people:

The pedagogy of signal processing encourages thinking about things in frequency-domain terms (that is, as a bunch of summed sine waves with frequencies and phases.) When you think about things in these terms some things are easy (simple crossover filters, etc.) but some things are hard. For example, a simple "delay one second" in this frequency world becomes a "linear phase shift with a slope k". Why? Well, let's not get into it, but this kind of math is why you get people saying "duh, group delay is simply the derivative of the phase delay of the system". True, but confusing. It's also why people get wrapped around the axle when you say: "OK, so group delay is just how much a frequency is delayed". Even though this is essentially correct, people will say 'no!'. That's because in frequency world, a pure frequency passing through a system has no beginning and end so the concept of delay doesn't exist--only phase shift. This is why phase shift kept coming up in conversations even though it's not really relevant.

 

[budje]

Here's my humble attempt to explain group delay

Pretty good example of the more detail you add, the muddier your explanation gets.

 

[daverosenthal]

Pretty good example of the more detail you add, the muddier your explanation gets.

Well, I did say "humble" What part did you find muddy/confusing?

 

[Holmz]

…
Amir calls out the cups as a source of group delay here: https://www.audiosciencereview.com/forum/index.php?threads/focal-utopia-review-headphone.22103/

I am not sure how the group delay was determined, but it is mostly measurement or processing noise there in that upper mid band.

One does not get +/- 3 milliseconds of error.
That is like +/- 3 feet… and one cannot get that instantaneously as the frequency moves up and down a small amount.

He calls it out with the question mark at the end, sort of implying a question of it being a possibility… it does not read as a statement of fact… at least in that way that I read it.

 

[cavedriver]

So how much group delay does it take to be perceptible? The reason I ask is that as a footnote the following review of the newish Purifi 8" woofers mentions that when tested in a vented box of an appropriate size one of the trade-offs is "increased group delay" and the accompanying graph shows a peak delay of 17.4 mS at 18 Hz versus 5.5 mS at 32 Hz for the same driver in a sealed box. So can this delay be perceived? I see that Amir does not include group delay measurements in the reviews for speakers even though it would seem possible to measure and report it. Is this because it's too difficult to perceive for most people, or because the room contributions overwhelm it, or what?

The graphs are at the end of the article:

Purifi PTT8.0X04-NAB-02 8" Alu midwoofer | HiFiCompass

What is on the test bench? On March 30, 2022, the Danish company PURIFI announced a long-awaited novelty - a long-stroke 8" aluminum cone midwoofer PTT8.0X04-NAB-01. If we draw an analogy with boxing, then this next vertical expansion of their lineup corresponds to the moving from middleweight...

hificompass.com

 

[NTK]

So how much group delay does it take to be perceptible? The reason I ask is that as a footnote the following review of the newish Purifi 8" woofers mentions that when tested in a vented box of an appropriate size one of the trade-offs is "increased group delay" and the accompanying graph shows a peak delay of 17.4 mS at 18 Hz versus 5.5 mS at 32 Hz for the same driver in a sealed box. So can this delay be perceived? I see that Amir does not include group delay measurements in the reviews for speakers even though it would seem possible to measure and report it. Is this because it's too difficult to perceive for most people, or because the room contributions overwhelm it, or what?

The graphs are at the end of the article:

Purifi PTT8.0X04-NAB-02 8" Alu midwoofer | HiFiCompass

What is on the test bench? On March 30, 2022, the Danish company PURIFI announced a long-awaited novelty - a long-stroke 8" aluminum cone midwoofer PTT8.0X04-NAB-01. If we draw an analogy with boxing, then this next vertical expansion of their lineup corresponds to the moving from middleweight...

hificompass.com

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.