What is group delay?

[Raindog123]

The delay is between input and output however defined

As was pointed out, this is a “delay” not “group delay”:

[Phase] delay = φ/f,
Group delay = δφ/δf

I deal with group delays - at RF, calculate them and compensate for - every day, so “you can safely sleep at night”. And so far no complaints. So, pardon me, but I do know what I am talking about... But it’s ok.

 

[EdTice]

I've done a lot of Googling and searching... And I still don't understand what it is or what it does!

Can anyone ELI5 what it is, assuming minimal technical knowledge?

This thread has gone nuts. What is your interest in group delay? We can probably answer better if we know that.

There are two concerns you have to deal with in terms of delay and I'll let others comment on the exact terminology usage.

The first is that, even with a single driver, two different frequencies will arrive at slightly different times. This can be exacerbated with a two-way or three-way speaker. That's something the speaker designer has to take care of. It's a physical property of the speaker and something you can't really change. One could imagine a DAC that tries to add delay to compensate for this but I'm not aware of any that do so because it really isn't necessary. Some speakers are designed with "time aligned" drivers so that, as you transition the crossover point, there isn't a risk of the same frequency arriving at slightly different times when being partially played by both drivers. Is that helpful? Maybe for some people in some situations. In actual listening, you are going to get not just the direct sound from the speaker arriving at your ears but "early reflections" as sound bounces off the walls and floor and ceiling and such. And those bounced sounds will take trivially longer to reach your ears. That's why speakers here are given a "predicted in-room response."

The other context in which this is used is when you have multiple speakers as part of the same system. In addition to L/R, many people use subwoofers. Most subwoofers these days use Class D amplifiers with DSP. As a result, the sound from the subwoofer comes out about 1ms later than the sound from the mains. You can compensate for this two ways. You can move the subwoofer about a foot closer to the listening position or, if using a digital source, the DAC can delay the output to the mains by about 1ms to make the reproduction more accurate. If no compensating action is taken, some people can hear this difference. I can't. I use AVRs that do compensate for this in my house. In my gym, I have two-channel DACs and the subwoofer is delayed by a millisecond. Since I walk around the gym I can't move the subwoofer to a closer position (since then it would be further away when standing near the walls). I also don't hear a difference.

Again this is not a strict definition of group delay and I'm sure that will be pointed out, but I'm hoping this gets you closer to solving whatever problem you have.

In some cases you need to be careful to not introduce too much or too little delay. If you are using wireless transmitters, using multiple speakers in a large venue, et cetera. Of all the issues we have to worry about setting up audio at home, group delay is nowhere near the top of the list, which brings me back to why you have interest in this?

 

[TurtlePaul]

For a laymen: group delay is the measure of time between input and output and you will encounter it in two realms:

1. Some DSPs allow you to adjust group delay. This adds a fixed time delay across all frequencies. This is different from phase delay where the delay time varies as a function of frequency. This can be useful to adjust crossover to make sure the drivers are in phase at the crossover frequency. This can also be used if one speaker is physically farther than another to make sure the music information arrives at the same time to form a more coherent soundstage.

2. We also measure group delay to form the charts used in many reviews. Speakers are given an electrical signal to convert to audio. The inductance in speaker drivers, the inductance and capacitance in crossover components and the internal box pressurization in ported speakers are energy storage devices, so this energy is often released as music after the input impulse and we can measure this delay in time at various frequencies.

 

[dc655321]

Please stop saying, “group delay is the delay between input and output”.

It is not.

 

[witwald]

The first is that, even with a single driver, two different frequencies will arrive at slightly different times.

Can you provide an example of time-domain signal, from onset to steady state? Say with frequencies at 50 Hz, 80 Hz and 125 Hz (approximate centre frequencies of the ANSI 1/3-octave frequency bands, spaced approximately 2/3 of an octave apart). The "two frequencies will arrive at slightly different times" refers to the delay in their steady state waveforms. The transient response, which is triggered when the signals begin, has died away by then.

The other context in which this is used is when you have multiple speakers as part of the same system. In addition to L/R, many people use subwoofers. Most subwoofers these days use Class D amplifiers with DSP. As a result, the sound from the subwoofer comes out about 1ms later than the sound from the mains.

I've heard that DSP latency can be around 5–6 ms. It's a quite significant delay, distance wise, as sound travels at approximately 1 foot/ms (0.34 m/ms).

 

[witwald]

Please stop saying, “group delay is the delay between input and output”. It is not.

It is if the group delay is constant with frequency, isn't it?

 

[FrantzM]

Can you provide an example of time-domain signal, from onset to steady state? Say with frequencies at 50 Hz, 80 Hz and 125 Hz (approximate centre frequencies of the ANSI 1/3-octave frequency bands, spaced approximately 2/3 of an octave apart). The "two frequencies will arrive at slightly different times" refers to the delay in their steady state waveforms. The transient response, which is triggered when the signals begin, has died away by then.

I've heard that DSP latency can be around 5–6 ms. It's a quite significant delay, distance wise, as sound travels at approximately 1 foot/ms (0.34 m/ms).

Things is it take us a really long time for our hearing apparatus to even recognize the presence of a 50 Hz tone; according to some studies, upward of 50 ms, which is enough for the wave to have hit some of the of the walls in a not-palatial home, several times.. creating all kinfd of room room modes, in the process... To have an idea 50 ms is enough for a wave to travel 6 meters, about 20 feet, 3 times ... (360 x o.05 sec= 18 ).

We are moving further from defining "Group Delay"... Which is NOT the delay between input and output of a Signal Processor. This particular is rather called processing delay.. for good reasons...

 

[dc655321]

It is if the group delay is constant with frequency, isn't it?

No. GD can be a component of that though.

 

[Holmz]

This thread has gone nuts. What is your interest in group delay? We can probably answer better if we know that.
..,
… which brings me back to why you have interest in this?

^That^ is more of an engineering answer of how one may use it.
Thetre is no dishonour in knowing what it is scientifically, as then the person may also know when and why they would want to use it.

As was pointed out, this is a “delay” not “group delay”:

[Phase] delay = φ/f,
Group delay = δφ/δf

I deal with group delays - at RF, calculate them and compensate for - every day, so “you can safely sleep at night”. And so far no complaints. So, pardon me, but I do know what I am talking about... But it’s ok.

It is apparent you understand it.

Almost every cell phone, telephone line modem, etc… is doing some channel calibration to unhose the channel back to get back to the intended signal. In digitial this is easy as once it is good enough, then the ones and zeros are correct.

it could be that some fields of study, and languages could have the terms a bit mixed up, which could possibly be a source of disagreement?

 

[MRC01]

One of the interesting aspects of group delay is how it can affect impulse and step response.

An impulse or step has lots of high frequencies. The mathematically perfect reconstruction of a bandwidth-limited impulse or step has flat phase response / group delay. This creates high frequency ripples that are symmetric both before and after the impulse or step. These ripples are at or near Nyquist (22,050 Hertz for CD).

Here are some measurements I've made using some of my own audio equipment, showing how group delay affects step and impulse response.

Step response - you can see a bit of ripple before and after each step transition.

Impulse response - you can see ripple before and after the impulse - it's symmetric (more or less).

A reconstruction that uses a filter having non-flat phase response, or non-flat group delay, delays some frequencies more than others. A filter that delays high frequencies in just the right way can slide them to the right so there is no ripple before a step or impulse -- all the ripple is delayed to after the impulse.

The step response looks like this - there is no pre-ripple, but there's more post-ripple. The high frequencies have been delayed, or shifted right, relative to lower frequencies.

The impulse response then looks like this - the high frequencies have been delayed, so there's no pre-ripple but there is more post-ripple.

 

[retroflex]

Group delay is a tricky thing. On my first graduate level acoustics and vibration course, the professor explicitly said that we were not expected to fully grasp it yet, so I wouldn't blame anyone who struggles with it. But to the best of my understanding, this is how it works:

Group delay is the derivative of phase with respect to frequency. Nothing more, nothing less. This must be contrasted to the phase delay, which is the phase divided by the frequency, or, in other words, the time (in seconds) that each individual frequency is delayed by a filter (I use filter in a very general sense here. Could be a standard low/high-pass filter, could be a very long (km) transmission line, could be a speaker, a plate reverb, could be a digital device, could be whatever).

What you might ask yourself, then, is why the fuck should I care about the derivative of phase with respect to frequency (group delay)? Well, it's an interesting quantity because it describes the delay of energy, as it turns out.

One might think that the delay of energy should be some kind of average of the delay of each individual frequency (phase delay), but strangely this is not actually the case. Well, it is the case for some filters; for a pure time delay -- let's say some device that records a signal and then outputs it one second later -- the phase delay is the same as the group delay. They would both be 1 second. But in general, one should consider the delay that a filter puts on each individual frequency as a separate (but highly related) quantity to the delay of energy.

As to what a group delay plot might tell you about a piece of hi-fi equipment, I don't know. Someone else would have to elaborate on that. I wouldn't read too much into it.

 

[MRC01]

PS: to tie this back to the OP question, here are the group delay curves for the 2 different response filters I measured above:

Flat phase / group delay (symmetric impulse/step response):

Non-flat phase / group delay (asymmetric impulse/step response):

You can see that in this case, the only difference is in the high frequencies.

 

[Digital Mastering System]

PS: to tie this back to the OP question, here are the group delay curves for the 2 different response filters I measured above:

Flat phase / group delay (symmetric impulse/step response):

Non-flat phase / group delay (asymmetric impulse/step response):

You can see that in this case, the only difference is in the high frequencies.

The first plot's filter can be said to have 'linear phase', implying the group delay is constant across the bandwidth.
And the second plot is likely to be 'minimum phase', which typically concentrates delay near the HF cut-off frequency.
As side note: It's called 'minimum phase' because this is the filter with the given amplitude response which transfers the signal in the minimum amount of phase shift, hence, the minimum time. Minimum phase systems typically have only one path from input to output. Also minimum phase systems exhibit phase response which is the Hilbert transform of the amplitude response, so if you have only a magnitude transfer function you can find the phase response via the Hilbert T (and you assume minimum phase).
The 'ringing' is technically called the "Gibbs phenomena".
Group delay is very important in the performance of IF filters in FM broadcast reception. Only with the introduction of software defined IF filters (with their perfect group delay) has the ultimate audio performance of FM broadcast been realized. Group delay linearity is also very important in digital data transmission and reception.

 

[MRC01]

The first plot's filter can be said to have 'linear phase', implying the group delay is constant across the bandwidth.
And the second plot is likely to be 'minimum phase', which typically concentrates delay near the HF cut-off frequency.
...

Yep. I've also seen them called "a-causal" and "causal". Why?

The Whittaker-Shannon reconstruction formula requires looking ahead at samples in the future. More specifically, the amplitude for each sample is the sum of an infinite series involving all samples both past & future. This violates our intuitive notion of cause and effect: how can the value for this moment depend on what happens in the future? That's OK mathematically but doesn't make intuitive sense.

Minimum phase filters can be computed without looking ahead at future samples, which makes them "causal", or consistent with our intuition of cause and effect.

By analogy, if I smack a drum with a stick (the cause), sound (the effect) necessarily happens afterward. The universe doesn't anticipate the stick hitting the drum and start vibrating the air beforehand. There can't be any pre-ripple in real-world sounds or music. For this reason, some people consider minimum phase filters to be more natural or realistic. Yet they are not more "correct"... in fact they are less correct, as the Whittaker-Shannon formula is the mathematically correct and perfect reconstruction.

To summarize and simplify, we want linear phase filters when reconstructing the analog wave from the digital samples, yet minimum phase filters when applying EQ to correct for room or headphone response.

 

[pozz]

Would it be accurate to say that GD measures the impact to the amplitude envelope per frequency?

 

[KTN46]

I apologise for my delayed reply. Trying to understand all the replies here has left me a bit more confused than I started off. It seems people are disagreeing with the definition of the group delay, which confuses me greatly because I am struggling to even process the difference between people's definitions.

To clarify the reason why I asked, I've been trying to better understand headphone measurements, and there seems to be a bit of discussion on the group delay measurements and what they audibly mean. I am trying to understand this better for myself, so that I can understand how it would sound (and whether or not I would be able to perceive it).

An interim question while I try to digest your comments, if two different headphones have very similar frequency response, but vastly different group delay measurements, would they sound different? If so, how?

 

[thorvat]

I've done a lot of Googling and searching... And I still don't understand what it is or what it does!

Can anyone ELI5 what it is, assuming minimal technical knowledge?

To understand what group delay is you have to be familiar with the meaning of term "derivation" in mathematical context. So, derivation, mathematics, is defined as "the rate of change of a function with respect to a variable". Let's try with the example, if you travelling in the car, than in each point of time the distance you travelled so far can be expressed as a function of time, time being the variable and distance is the function of time. Commonly this is expressed as s=f(t), meaning distance (s) is a function of t (time).

Now, if you derive the function of distance over the time you will get another function, which will also be function of time and this function will show the rate of change of the distance function. Rate of change of the distance over time is more commonly called "speed", and it is also function of time as speed changes in every moment of your travel. So far so good?

Let's return to the group delay now. Group delay is defined as derivation of phase over frequency range, so it is a function which shows the rate of phase change for each frequency point. So, in this case frequency is a variable and phase angle is a function dependent on the frequency. Group delay is nothing but derivation of that function showing its rate of change.

 

[Habu]

To make it easy, one explanation in French

https://www.petoindominique.fr/pdf/group_delay.pdf

And below the google traduction.

 

[TurtlePaul]

I don’t get why there cant be an explanation of group delay in time domain that is intuitive. Everyone insists that there can only be a frequency domain explanation. Can we all agree it measures delay?

I thing it should be more intuitive to explain in the time domain, in fact the units of measure for group delay are time. The previous poster said the derivative of frequency vs phase angle. Well we frequency is 1/period where period is time. Phase angle is delay/period mod period where again all units are time.

I am pretty sure that group delay can be intuitively explained in time domain, but can anyone tell me why this cannot?

 

[pkane]

I don’t get why there cant be an explanation of group delay in time domain that is intuitive. Everyone insists that there can only be a frequency domain explanation. Can we all agree it measures delay?

I thing it should be more intuitive to explain in the time domain, in fact the units of measure for group delay are time. The previous poster said the derivative of frequency vs phase angle. Well we frequency is 1/period where period is time. Phase angle is delay/period mod period where again all units are time.

I am pretty sure that group delay can be intuitively explained in time domain, but can anyone tell me why this cannot?

Constant group delay can be intuitively explained in time domain as a simple delay, easy to visualize and to measure. Variable group delay that affects different frequencies differently isn't very intuitive in the time domain (at least to me), nor is it easy to measure without first transforming the signal into the frequency domain.