Rational Acoustics

Luciano Nelli
September 7th, 2013, 11:47 PM
Can "group delay" be read as a delay response over frequency?

There's a flat device with 0.5 ms latency in figure 1.
All frequencies take the same time to pass through the system, right?

Then, in figure 2, an eq filter at 1 kHz with 10dB cut.

The delay seems to increase at low frequencies and seems unchanged in the HF range.

But, what happens around 1000 Hz?
It is as if this range came first?


Timo Beckman
September 8th, 2013, 05:18 AM
"Can "group delay" be read as a delay response over frequency"

Yes you can . The same goes for the phase trace . But you have to read it from right to left .
( http://timobeckmangeluid.wordpress.com/2013/05/09/working-on-keynote-files-this-time-its-group-delay/ )

There was a discussion about group delay on a dutch forum some time ago where a manufacturer of a brand X posted a screenshot of the group delay of his system trying to convince people that his system was phase flat (which it was not because the system was spread over 1080dg from about 20Hz up to 18K . This is not a really big problem and the system probably sounded fine but it was not a "phase flat system").

I started thinking about group delay and did a experiment at home with a studio loudspeaker 4 processor outputs in to a mixing thing and simulated a 4 way loudspeaker with the only challenge at that time to get the phase as flat as possible to see what the group delay would do and as expected it went to nearly zero except the lower frequencies where you could see i rise of group delay (due to the wave length/period of that frequency range) .


Simply said all filters cause phase shift and thus group delay because group delay is a derivative from the phase display .
If you see the phase display of an 2nd order lp filter you see a down worth phase slope with a 90 dg of phase shift at the x-over frequency and a 180 dg of phase shift over the whole pass-band which will cause the group delay display option within smaart to show a rise in group delay on the left side of the screen meaning all frequencies on the left will be late compared to the right side of the screen (goes for every time you use a filter).
So when you use an eq filter the phase trace will change and thus your group delay value will change .
There's a really good explanation about group delay in the green bible by bob mcCarthy who does a far better job in explaining group delay then i can .

Do you also have a screen shot of the phase trace ? Not certain but you'll probably will see the phase trace going up a bit just past 900Hz then go down again and settling around 0 past +/- 1k6 or something If smaart is synchronized .


Luciano Nelli
September 8th, 2013, 11:07 AM
Thanks Timo!
I need some time to process the data , but I guess I follow you.
Meanwhile, here it is the phase traces.

Smaart is not synchronized, on purpose.
The phase screen is 0º to -720º in figure 3.


Figure 4 have a zoom in.


The blue trace (flat) shows a steady increase in the phase slope; equal time for all frequencies...
Phase changes as you predict in the filter response.

The phase goes up in the range where group delay response showed less time than propagation delay...
This confuses me.

In figure 5, Smaart is synchronized, and group delay shows negative time around 1 kHz.


I wonder what is this?

Thanks again.

Timo Beckman
September 8th, 2013, 11:43 AM
The phase goes up in the range where group delay response showed less time than propagation delay...
This confuses me.

In figure 5, Smaart is synchronized, and group delay shows negative time around 1 kHz.


I wonder what is this?

Thanks again.

It means that at that point the measured signal is in front of your synchronization point within smaart for a small section of your frequency response .

If you take a processor channel with no filters or what ever else you can think of and give it a 1ms delay then synchronize smaart to that . So smaart looks at the latency of the processor +1ms delay . If you now reduce delay to for instance 0,5ms without synchronizing Smaart the phase trace goes up instead of going down with the first wrap around at 1k and the 1st (-)360dg at 2K . It means your measured signal is ahead in time compared to the synchronization time from Smaart (which was +1ms) . As a result you should see a negative group delay value . Also your delay finder window will show the spike of the impuls on the left side of the 0 point from the delay finder .

You can use this as i did in this blog post

Try to do some impulse response measurements (linear view) on the bypassed processor channel and then with the eq point in (so no lp/hp/ap what ever) just the eq point . You'll see a very small section before the main spike (on the left side of the peak) and a ripple after the peak . All means that some of the frequencies are effected by the filter compared to the ir with all bypassed .

D*mn this hard to explain in english (being from the netherlands and all)

Luciano Nelli
September 8th, 2013, 12:22 PM
I think I understand.
Although, I will read your papers, measure IR and maybe then...

See you in a couple of days.
Thank you so much.

Timo Beckman
September 8th, 2013, 12:49 PM
More then welcome . Have fun and success .

Luciano Nelli
September 15th, 2013, 12:38 PM
Hi Timo, I'm working (slowly) on the material you posted.
Meanwhile I want to show you something from the paper “Group delay distortions in electroacoustical systems” (Blauert - Laws):


I think of what you said about the negative time related to the synchronization point of Smaart. I understand that.
But when I look at Figure 2, it is as if the filter is “reducing” system latency about 1 kHz.
The same thing happens with a band stop filter.



I'm also thinking about “group delay is a derivative from the phase display”.

There is another giant book (Handbook For Sound Engineers – Glen Ballou) where seems like this is the only thing they say about group delay.
GD is a calculation...

Don’t worry about me Timo, save yourself :confused:

Timo Beckman
September 15th, 2013, 04:00 PM
I'm also thinking about “group delay is a derivative from the phase display”.

There is another giant book (Handbook For Sound Engineers – Glen Ballou) where seems like this is the only thing they say about group delay.
GD is a calculation...

The last line (gd is a calculation) is 1 i can relate to because that's what i did in the blog post regarding group delay .
The band stop filter i have to think about because the phase display would suggest that all on the left of 1K would show a small group delay value .
Which processor did you use in the screenshot ?
Maybe 1 of the rational people has a good awnser . When and if i get a chance to look in to that i'll let you know .

Luciano Nelli
September 15th, 2013, 08:20 PM
I processed the measurement channel with an audio editor.


Maybe I could try a standard processor.

Timo Beckman
September 16th, 2013, 04:41 AM
Nice .
Did you also measure the chebichev filters ?

Luciano Nelli
September 16th, 2013, 11:49 AM
No yet; today a I will try with the processor and then the Chebychev.

Luciano Nelli
September 16th, 2013, 06:35 PM
Here are the curves with a processor.
It's a dbx DriveRack 4800.
It has notch, but not band-stop filters (the phase response is different, see figure 7).
Also put a graphic EQ curve of the same device, to compare.

More negative group delays...

I owe the Chebychev.

719 720 721 722 723

September 17th, 2013, 03:24 AM
Group delay is a poor description. It is best explained as delay of a "group" of frequencies. "Phase delay" introduced by Bob McCarthy ASFAIK is a much better description.

Mathematically it's the first derivative of phase, Bob McCarthy's phase formula calculates the difference in time expressed in cycles over frequency span. In other words dt/df which is the tangent or first derivative of phase.

Luciano Nelli
September 30th, 2013, 05:07 PM
It seems like I am temporarily entangled with group delay.
A friend of mine suggested to study calculus.

Despite negative values, there is a certainty (what Timo does in one of his posts (http://timobeckmangeluid.wordpress.com/2013/05/09/working-on-keynote-files-this-time-its-group-delay/)),
the behavior of the phase slope.

In my struggle, trying to relate the phase angles and group delay values, I thought that Bob's formula gives a representative value in the case where group delay is constant in the range analyzed.
I noticed that the LPF and HPF have a more or less uniform group delay below the cutoff frequency but, a band-pass filter can have a more irregular response, and the phase delay formula would be giving "less information"... a time value that not accurately characterize the interval analyzed.

Finally, there is a site called "DSP Related", where I found an article written by a guy named Andor Bariska, “Time Machine, Anyone? (http://www.dsprelated.com/showarticle/54.php)”, about the physical meaning of negative group delay.
Unfortunately, I did not understand the ending.

Langston Holland
October 1st, 2013, 04:47 PM
Hi Luciano:

Given that you're into stuff like the classic Blauert-Laws paper, it's obvious that your addiction is beyond the reach of professional help, so I might as well make things worse. :)

In reference to the article:

As has been mentioned, group delay is the first derivative (the rate of change) of phase, thus the study of calculus is helpful. The problem with most folks that get into deeper math or engineering or philosophy or anything else is that they take what is presented at face value, learn how to use it, but never figure out what's really going on under the hood. Thus they can't explain it to folks that don't play in their sandbox. This is my guess as to why Mr. Bariska left you wanting at the end of his article when he capitulated with the linear predictive filter "explanation".

Linear prediction is not the reason why it appears that you can get the output of a pulse to precede its input, it is more of an observation of what happens in certain circumstances. In effect, he says you can't get an output before its input occurs (causal), which is true in this world and most of the universe. Then he shows examples of how it appears that the output can precede the input using a simple peaking filter with a bunch of gain (makes the effect more obvious). Then he ruins the whole thing in what seems to imply that a simple filter has a brain and eyes and can predict what's coming and produce it in advance with a magic signal generator after studying a smaller portion of an incoming signal.

Either this guy doesn't understand what's going on himself (unlikely), or he's assuming the reader has a good background in feedback theory (the good kind) with IIR filters.


Let's stick with an analog filter analogy to keep things simple, but as you've noticed, digital implementations of IIR filters do the same thing with the addition of some latency.

Let's use the IEEE definition of group delay as "The time interval required for the crest of a group of waves to travel through a 2-port network." (Thanks Pat Brown)

Sticking with the article's example in Fig. 5, measuring the group delay between the input and output shows the crest or peak of the group of frequencies at the output preceding the group of frequencies at the input by 16ms:

Now let's define the very beginning of an electrical pulse where it just begins to move away from zero volts as the "wavefront". The wavefront (the REAL time zero) is identical in all cases. Yes Martha the kids are safe, causality is maintained.

So how did the main body of the pulse shift forward in time toward the wavefront? Simple, it was deformed by superposition of the filtered group of frequencies with the input group of frequencies. The filter shifted some of the frequencies forward in time and others backward as is clearly shown in the phase plot. Nevertheless, all frequencies remain behind the wavefront, but are shifted around due to what we call phase distortion. In the following Vin is the input group of frequencies, Vout is the magically advanced output group of frequencies and dv_in/dt is what the filter is doing to cause this "magic".

My heart-felt apologies to all those who were getting excited about creating artificial intelligence and time travel using a capacitor and an opamp.


Going further: The Cornell physics archive has a bunch of wonderful papers on negative group delay, largely applied to optics, but the fundamentals are the same. Search for a Japanese guy named Kitano and buckle your seatbelt.


Luciano Nelli
October 1st, 2013, 07:48 PM
Thank you so much for this great help Langston.


I'll have to re-read, re-think and deepen.
Thanks again!

Langston Holland
October 3rd, 2013, 02:02 PM
Hi Luciano:

Negative group delay is great fun, but it's not going to help anybody tune a PA. I'm going to try to redirect this thread at bit so folks can better appreciate the value of group delay. As a matter of fact, using the group delay plot can reduce the time required to align subs by an order of magnitude (a fancy way of saying ten times or one tenth, i.e. moving the decimal point one step).

This post does not include application, that's next, this is just additional background on group delay to get an intuitive grasp of what's going on and thus be able to spot when your measurements are questionable or flat-out wrong. In a prior life, I taught math and one thing I'd tell them is to look at the problem and get a feel for it before trying to calculate an answer. Say you were multiplying 6 x 12. If you think about it, you'll know you did something wrong if you get a single digit answer, but maybe not if you just go on autopilot and try to get it done.

For example, say you are aligning subs to mains at an event. You choose a reasonable mic position (for the majority of the audience if you're Harry, for FOH only if you're like most), and you start your acoustic measurements. Fail. :) What you should do is get out your laser distance finder and figure out how much closer the mains are to the mic position than the subs or vice-versa. Make a quick calculation in your head as to how many milliseconds you should expect to have to add to the closer boxes to get them in line with the further boxes. Due to low frequency low pass filters and possible horn length, you'll need to add a couple of milliseconds to front-loaded subs and maybe 5ms to horn-loaded subs. Now that you know approximately what the answer should be, start making acoustic measurements and align the system. Look both ways, then cross the street. :)


The group delay plot is calculated from the phase plot and is therefore another way of looking at phase.

Phase tells us (in degrees) what part of the frequency cycle is arriving at the microphone at a given snapshot in time. There is a positive half of the cycle and a negative half. If these halves line up pretty closely with the same frequency from a second source (in phase), you will get an addition in volume at that frequency (constructive superposition). If these halves do not line up well (out of phase), there will be a reduction in volume at that frequency (destructive superposition).

If you think about it, you could fix an "out of phase" situation, say at the 80Hz crossover between subs and mains, by delaying one or the other by 1/2 wavelength, or 6.25ms. This "fix" may be wrong even though it makes the 80Hz area of the crossover add together properly at that mic position. Put it this way: you could also delay one or the other by 3 times 6.25ms, or 5x, 7x, etc., and still get good addition at 80Hz, but now you are going to be causing all kinds of other problems. Thus, we not only need "in phase" addition at one crossover frequency, we need the entire group of frequencies throughout the crossover region to arrive "in phase".

Group delay can give us the right answer and get you stupid close to the exact delay (in milliseconds) to enter into the processor, which you check and fine-tune, if necessary, with the phase plot. More on this later.


I've stolen a few of your measurements to help make a connection between the phase and group delay plots. Group delay is calculated on the steepness of the slope in the phase plot. The steeper the phase trace, the greater the affect on group delay. When the steepness of the phase plots are the same between two sources in a given range of frequencies where they overlap, they are the same acoustic distance from the microphone.

If this range is our crossover range, we have achieved our goal.


GIGO reminder: if your phase measurement is garbage, so will be the group delay that is based on it. As a matter of fact, the group delay plot will be even worse because it's calculated on phase differences, which mathematically amplifies its sensitivity. Bad phase measurements happen when you have multiple arrivals from a single source (strong, nearby reflections) getting into the microphone.

Luciano Nelli
October 3rd, 2013, 08:41 PM
It’s true, people align systems despite negative group delays.
I try to do the alignment just playing with the delay and polarity buttons, most of the times.

But, I know that my brain works different with the amplitud response (and the brains of many people I know).
I see a peak and think: -ok, there is '"more sound" on that range.
And it's easy to recognize.
With the phase trace don't works the same way.
It is less tangible.

So, I tried to think about time instead of angles.
With the idea of a "less abstract quantity" (poor me).
(something like this I remember from my first approach to the phase trace.
I did not understand very well, but I knew that line was giving information related to time)
So, I ended up trying to get the phase response from the group delay, thinking that group delay could be viewed like a "time response over frequency".

Until the negative values arrived.

I'm following you very carefully, thank you very much Langston!

“Demonstration of negative group delays in a simple electronic circuit”

Langston Holland
October 4th, 2013, 01:38 AM
Hi Luciano:

The concepts of phase applied to system alignment is way easier than you think it is. You just need to experiment with real loudspeakers for a while and you'll start to wonder why you thought it was so hard. :)

My purpose in joining your thread was to address the concept of group delay that IMO has been largely overlooked, yet has much to offer. Getting comfortable with phase traces is necessary in system alignment, particularly in making the final detailed adjustments to get the summation between subs and mains just right. The group delay plot can get you very close to the right answer very quickly, thus reduce much of the time you have to spend working with the phase plot.

With that said, once you gain a great deal of experience doing alignments, you may find yourself working only with the phase traces - but even then, I think it's wise to glance at the group delay plot before considering the job done.

Generally, you have (3) tools to choose between to get the alignment close, then you use the phase trace to get things exact. The tools are; (1) your brain and a laser distance finder, (2) the leading edge (wavefront) of the IR viewed in linear mode, and (3) group delay.


Since you have questions about phase, chew on the following and I bet things will become clearer. Remember that when we work with phase, we are actually working with the phase of one sound source relative to another sound source so that they increase in volume as much as possible when played together.

Perfectly In-Phase:

90˚ Out-of-Phase:

180˚ Out-of-Phase:

360˚ Out-of-Phase:

And finally, play around with the "Phase Difference" utility on this web site for a while:


Timo Beckman
October 4th, 2013, 06:27 AM
Thanxs for the info Langston specially the bottom link on the last post .

The problem i have with group delay in relation to live tuning a pa set-up is that it's all over the place due to the acoustic environment .
I'm just thinking it might be a idea to have the coherence trace from the magnitude window visible .
Coherence blanking already takes out parts of the response in group delay mode but if coherence where visible in the group delay screen also (next to the mag display) things might be a bit more clear regarding which data to trust and what to discard (hope this is a right way of saying this in english).

Langston Holland
October 4th, 2013, 11:45 AM
The problem i have with group delay in relation to live tuning a pa set-up is that it's all over the place due to the acoustic environment .

That is a great point Timo. I only alluded to this in my "GIGO reminder" section in an earlier post, but you make an important point that the group delay plot is completely unusable at times. Like everything else in life, you need to know several ways to skin a cat if a given method isn't available.

Since group delay is a calculation of the difference between points on an unwrapped phase trace, the result will be very sensitive to abrupt phase changes. Abrupt changes occur due to strong reflections and poor S/N. These can be reduced by ground plane techniques and/or windowing the reflections out of the measurement. Since we've been talking about low frequency alignments, windowing beyond what Smaart already offers with MTW is not going to help much. Ground plane techniques won't help all that much either given the long wavelengths involved.

Still, I think that much can be learned by inspecting the group delay plot as a regular part of the system tuning process.

It would be nice if Smaart had an accelerator key to toggle between the current phase display and group delay. :)

Timo Beckman
October 4th, 2013, 04:13 PM
It would be nice if Smaart had an accelerator key to toggle between the current phase display and group delay. :)

That's a nice feature for a "code jockey" i know (his words not mine) ......... :cool:

Also most venues i have to work in are not so friendly to the phase display and there's no way to read the group delay function and make any sense out of it .
I did an experiment in getting a "as flat phase as possible system" a while back because of a discussion on a dutch forum regarding group delay vs phase display .


This was done on a studio monitor with a behri mixing thing with 4 channels of output processing routed back to that 1 monitor so it's not a real system (yet:-) . The mic was really close so almost no reflections .

During the discussion on the forum there were screen shots posted telling everybody it was a phase flat system but it was a group delay window and not the phase display . Also the screenshots were smoothed in to oblivion so they where in my eyes a bit meaningless never the less it got me thinking on how to get a "as flat phase system" as you can get and what the group delay would look like on that same system .
Also what the smoothing of the measurement would mean with regards to the phase and group delay display .
As expected the group delay went to nearly zero and in the high end the scaling within smaart is to large (?) to even see because i zoomed in and the smallest value smaart can display is 5ms .
The none smoothed screenshots are no problem to read in phase display mode but the group delay display is another story .
So in all my alignments i mostly look at the phase display but thinking about group delay got me to make a change in the way i phase correct a system to be as flat as i can get it .