What is group delay?

[ernestcarl]

audible pre-ringing is a single phase correction filter with a modest Q, say 5

Well, someone claimed before more than 1 was already enough to to cause audible ringing. I find it incredibly hard to believe myself, but 4 and above is much more plausible to me, for sure... I suppose esp. if without any pre-ringing compensation.

 

[thorvat]

Well, someone claimed before more than 1 was already enough to to cause audible ringing. I find it incredibly hard to believe myself, but 4 and above is much more plausible to me, for sure... I suppose esp. if without any pre-ringing compensation.

Using filters with Q=2..3 will leave noticeable "waves" in front of IR response but they will hardly be audible. The more filters you use things are getting worse. But I really see no reason to risk audible pre-ringing with phase correction as all it needs to be done is passive XO compensation and eventually some mild phase adjustment in LF between channels (when difference is caused by speaker positioning) to avoid phase cancellations in summed LF response. Apart from that phase should just be left as it is.

Simple explanation why pre-ringing is much more audible than GD variations is that pre-ringing is artificial phenomena which normally doesn't happen in world around us so we are mcuh more sensitive to it. Contrary to that, GD variations are normal thing caused by reflections etc, but we are much more toleratnt to it as it is quite common.

 

[dasdoing]

in my experience audibility of preringing depends heavily on the frequency and the shape/band. a single too early midrange spike in the excess group delay is audible even when only a few ms. a whole subwoofer can be too early for a 1 ms or 2 on the other hand and you wont hear it.
at the end you want to be in the middle, where you neither hear pre-delay nor pos-delay. people who claim any predelay is audible generaly ignore totaly the a minimum phase filter creates an audible effect on the transients, too. a kick-drum over a system with 10ms group delay in the bass will never sound like the real thing. It will loose the "punch"

 

[JohnPM]

Can someone explain why it is the group delay but not phase delay that is more important to human hearing?

Part of the process of hearing involves detecting the envelope of the sound pressure at the eardrum. If group delay is not constant the shape of the envelope changes, which may affect perception.

 

[KSTR]

Part of the process of hearing involves detecting the envelope of the sound pressure at the eardrum. If group delay is not constant the shape of the envelope changes, which may affect perception.

To illustrate this, I've used a 5-periods shaped sine burst (aka blip) and fed it through two filter functions, both of which had negative group delay at the test frequency.
Negative Group Delay appears to be sort of counter-intuitive as it seems to imply true negative time delay, a non-causal behavior. But the envelope of the filtered signal (bottom trace in plots) indeed looks like it has been shifted to the left in time though actually it just has been deformed by the filter. The phase may or may not be deformed as well.

Example 1:
A peaking bell filter, f = 4x test frequency, +12dB, Q=2.

The envelope appears as shifted to the left by the negative group delay. The phase is different also, and as it happens we see that the filtered waveform again is pretty much symmetrical wrt the new envelope center which makes the deformation even more resembling a true negative time shift.
I've truncated the last 3/4th period of the generator pulse to highlight that the filter of course still is causal, minimum phase. The ringing tail from the step change oscillates at the filter's resonance frequency, post-ringing only.


Example 2:
A dipping bell filter, f = test frequency, -12dB, Q=2 (output trace with +12dB make-up gain applied for easier visual comparison).

Again the envelope appears as to be shifted to the left, giving the impression of arriving before the input signal, exactly what the negative group delay should associate to. This time the phase is not altered, though, as defined by the filter's zero phase response at resonance.

When listened to this in stereo, I note a position shift to the right in both cases, the right channel preceeding. It is a bit weaker with the second example as there is no phase difference, just enevelope difference. Even a bit of level reduction on the right channel (as it appears to be somewhat too hot after the 12dB make-up boost) does not change that impression so it really must be envelope difference that triggers the perceived position change.

----------

Bottom line: Both envelope "shift" by group delay (deformation, actually) and phase shift contribute to the time perception individually. They can add constructively or desctructively (trading) in perceived phantom center shift for the stereo case, according to the ITD/ILD relationships.

 

[dualazmak]

I recently did the same "time alignment" measurements and adjustments in 1 msec precision and also in 0.1 msec precision;

- Precision measurement and adjustment of time alignment for speaker (SP) units: Part-1_ Precision pulse wave matching method: #493
- Precision measurement and adjustment of time alignment for speaker (SP) units: Part-2_ Energy peak matching method: #494
- Precision measurement and adjustment of time alignment for speaker (SP) units: Part-3_ Precision single sine wave matching method in 0.1 msec accuracy: #504, #507

 

[Astrozombie]

Next thread -

Harmonic distortion
Intermodulation distortion
Dynamic compression

 

[Rottmannash]

Next thread -

Harmonic distortion
Intermodulation distortion
Dynamic compression

please no...

 

[zergxia]

I recently did the same "time alignment" measurements and adjustments in 1 msec precision and also in 0.1 msec precision;

- Precision measurement and adjustment of time alignment for speaker (SP) units: Part-1_ Precision pulse wave matching method: #493
- Precision measurement and adjustment of time alignment for speaker (SP) units: Part-2_ Energy peak matching method: #494
- Precision measurement and adjustment of time alignment for speaker (SP) units: Part-3_ Precision single sine wave matching method in 0.1 msec accuracy: #504, #507

Hello friend
I read the method you presented. It's ingenious!
Um~ I have a question... Where can I find the download link for the test audio file?
Looking forward to your sharing~
Thank you very much！

 

[dualazmak]

Hello @zergxia,

Thank you for your interests on my unique time alignment tuning methods.
I will soon contact you by the PM personal contact system of this forum for sharing info on my test tone signals.

 

[srkbear]

I too became curious about this topic, to help me greater understand and apply Amir’s principles of headphone measurements. And once I saw the OP pose the most earnest plea for an introductory and basic explanation of what “group delay” means, I had the highest hopes of learning a new fundamental concept of audio science—as well as the rush of confidence and self-efficacy that I would surely enjoy as a result!

The first answer was a bit inscrutable. But not to worry, the conversation got started and I was determined to maintain my hopeful, innocent curiosity. I love to learn! And after all, I was in the good company of the OP, who seemed equally resolved to prevail over his struggles. We’ll figure this out together!

Then the next few comments added a bit of doctoral thesis level differential equations and some pithy time-solved quantum electronics.

No matter, I’m sure I’m capable of acquiring at least a rudimentary understanding of this pragmatic group delay concept. Progress, not perfection! Sure enough, an opposing theory came to the rescue, adding a bit of audiometric string theory and chromodynamics to bring things into much greater focus.

Yes, yes—I think there was one sentence that whizzed by there that was within my grasp! This was surely going to wrap up with a cogent explanation, I just had to keep going. It was only a nine page thread, piece of cake.

And boy, did my persistence pay off! The inevitable rejoinder and metaphysical debate that followed was a journey of breathtaking suspense, that rose to an almost unbearable climax until around page seven or so. Then, as a reward for my tenacity I was regaled with a topic of even greater fascination and practical utility—the esoterica of wave theory matching methods.

Thanks to all of you for generously offering your insights to those of us on the quest for greater knowledge! What an invaluable discussion, I’ll be reaping its rewards in incalculable ways for years to come.

PS: I just have one more question, if I may? Is there anyone who wouldn’t mind explaining what group delay means again? My ears want to know. Thanks again!

 

[DonH56]

For phase p and frequency f group delay GD is the negative of the derivative of the change in phase with respect to the change in frequency: GD = -dp/df. In general phase is a function of frequency p(f); that is, phase changes with frequency. That's the math behind it.

A change in phase is equivalent to a time shift, for example a 180-degree phase shift is like shifting the time by one-half cycle of the signal. The derivative is a fancy expression for the slope of a line, so it is a measure of phase linearity. A straight (linear) line has the form y = mx+b where every point x is multiplied by the slope m and added to offset b to produce a y value. For a straight line, m is constant (just a number, not a function of something else), and hopefully we remember this formula from school. Now replace m with GD so to get a straight line, that means the change in phase divided by the change in frequency must be constant, meaning group delay is a constant, and every frequency is delayed by the same amount of time. What goes in, comes out again, exactly as it was but just a little later in time.

Now, a pulse, or musical signal, includes many frequencies. If we send the signal through a component like an amplifier or speaker with constant group delay, then every frequency is delayed the same amount, and the output is just like the input except delayed in time. If the group delay is not constant, that means different frequencies have different delays through the component, so at the other end the signal will be "smeared" in time with different frequencies arriving at different times. Things like transient attacks from drums or instruments will not be as clean. There are various studies discussing just how far off the delay can be at different frequencies before we notice it, some referenced in the Wikipedia article mentioned previously (https://en.wikipedia.org/wiki/Group_delay_and_phase_delay).

HTH - Don

 

[srkbear]

For phase p and frequency f group delay GD is the negative of the derivative of the change in phase with respect to the change in frequency: GD = -dp/df. In general phase is a function of frequency p(f); that is, phase changes with frequency. That's the math behind it.

A change in phase is equivalent to a time shift, for example a 180-degree phase shift is like shifting the time by one-half cycle of the signal. The derivative is a fancy expression for the slope of a line, so it is a measure of phase linearity. A straight (linear) line has the form y = mx+b where every point x is multiplied by the slope m and added to offset b to produce a y value. For a straight line, m is constant (just a number, not a function of something else), and hopefully we remember this formula from school. Now replace m with GD so to get a straight line, that means the change in phase divided by the change in frequency must be constant, meaning group delay is a constant, and every frequency is delayed by the same amount of time. What goes in, comes out again, exactly as it was but just a little later in time.

Now, a pulse, or musical signal, includes many frequencies. If we send the signal through a component like an amplifier or speaker with constant group delay, then every frequency is delayed the same amount, and the output is just like the input except delayed in time. If the group delay is not constant, that means different frequencies have different delays through the component, so at the other end the signal will be "smeared" in time with different frequencies arriving at different times. Things like transient attacks from drums or instruments will not be as clean. There are various studies discussing just how far off the delay can be at different frequencies before we notice it, some referenced in the Wikipedia article mentioned previously (https://en.wikipedia.org/wiki/Group_delay_and_phase_delay).

HTH - Don

Seriously? Maybe you missed the tone of my post?

 

[Jimbob54]

Seriously? Maybe you missed the tone of my post?

I don't know. Suspect the last paragraph of Don's is going to be as clear an answer as us laymen will get.

 

[ernestcarl]

My ears want to know.

Try to A/B the ff. filters using a music player that can do convolution (e.g. foobar2000) and listen carefully if you can hear the additional GD increase:

Alternatively, if you can't hear a difference with your speakers, try it with headphones as well.


Here's how it looks in the wavelet spectrogram view in REW:

Peak energy time is "smeared" or spread out in time. Suppose you can't hear a difference... still, objectively, this negatively affects accurate transient reproduction.

 

[srkbear]

Try to A/B the ff. filters using a music player that can do convolution (e.g. foobar2000) and listen carefully if you can hear the additional GD increase:

View attachment 244554

Alternatively, if you can't hear a difference with your speakers, try it with headphones as well.


Here's how it looks in the wavelet spectrogram view in REW:
View attachment 244556

Peak energy time is "smeared" or spread out in time. Suppose you can't hear a difference... still, objectively, this negatively affects accurate transient reproduction.

Wow. Or someone could just offer a simple explanation in layman terms for the benefit of those of us without engineering degrees! Do they not teach irony in EE programs? I give up.

 

[srkbear]

I don't know. Suspect the last paragraph of Don's is going to be as clear an answer as us laymen will get.

I guess my English Major training went right over some heads.

 

[Plcamp]

I had always thought of group delay as being a measure of stored (but not dissipated) energy in a speaker system, which leads to phase response differences in affected frequency ranges.

 

[ernestcarl]

Not an engineer nor english major myself...

Just imagine that for a solo kickdrum track/clip the bass frequencies are delayed by several milliseconds. In effect, you hear higher frequencies first before the lower frequencies. Ideally, everything starts at the same time -- and nothing continues play for too long i.e. rings excessively or energy continues to linger in time.

 

[Berlin]

So, if I understand correctly the term "group" in this context refers to a group of frequencies i.e. low versus high frequencies. Is this correct?