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by John L. Murphy

Subject:  Discussion of Group Delay in Loudspeakers

(posted around 1998  to Bass List)

Peter wrote:

> Does anyone know of demanding source material that readily demonstrates the need 
> for linear phase/flat group delay? 

ANY recorded music will reveal group delay errors if the errors are severe enough.  Take the trivial example of a 24 hour delay between the highs and lows.  The highs arrive normally but you have to wait until tomorrow to hear the lows.  Would this be audible?  I think so.  Could we all hear it in an A/B test?  YES. 

The absolute audibility of group delay is not the question.  If we make the delay severe enough anybody can hear it.  The real question is what are the thresholds where group delay becomes "just audible".  One of the most widely referenced reports of the audibility of group delay is:

Blauert, J. and Laws, P  "Group Delay Distortions in Electroacoustical Systems" 
Journal of the Acoustical Society of America
Volume 63, Number 5, pp. 1478-1483 (May 1978) 

Blauert and Laws report approximately the following thresholds for audibility:

Frequency Threshold of Audibility
8 kHz 2 msec 
4 kHz 1.5 msec
2 kHz     1 msec
1 kHz  2 msec
500 Hz  3.2 msec

The real work that needs to be done is to refine these threshold measurements and extend them further into the low frequency region (where the worst delay occurs in speakers).

In summary:  Group delay is audible.

The relevant question is:  "How much group delay is audible, at what frequency, with what program material." 

Does anybody know of more refined measurements of these thresholds that have been reported in the literature? 

Regards,

John

/////////////////////////////////////
John L. Murphy
Physicist/Audio Engineer
True Audio
http://www.trueaudio.com


(posted 20Jul98  to Bass List)

Steve wrote:

>To repeat an earlier question that got lost, if I could hear group delay
>in a system, what would it sound like? Can you describe it?

The basic equivalent circuit model of a dynamic speaker system is that of an electrical highpass filter. Such filters have the characteristic of increasing group delay at low frequencies. Thus, in general, our speaker systems tend to delay the lows while allowing the highs to arrive without delay.

Let's consider the trivial case of EXTREME delay at low frequencies. For source material imagine that we use a recording of a single snare drum hit. We know what a snare drum normally sounds like. Now, imagine introducing a delay of 5 seconds on the lows. Play the drum recording through such a delay and you hear the high frequency "snap" of the drum followed 5 seconds later by the lower frequency "thump" components. So instead of hearing one integrated "pop" sound we instead hear a "snap" followed much later (5 sec) by the "thump". We could all easily hear the delay in this exaggerated "thought experiment".

But real speakers don't add seconds of delay. They only add milliseconds or tens of milliseconds of delay. So the real question comes down to "how much delay is just audible". If we were to gradually reduce the delay in the above experiment to zero there would come a point where the delay was no longer audible as a separate distinct sound. This would probably happen above the Hass limit of 30ms or so. As the delay is reduced further there would come a point where the "delay distorted" or "time smeared" version was indistinguishable from the original recording. This delay would represent the threshold of audibility for this delay curve and source material.

Our mission as speaker designers is to keep our group delays below the threshold of audibility. In order to do this we need to first know what group delay our speakers are imparting on the music, and second, know what degrees of delay are audible.

On the subjective side I suspect that delayed bass or "late" bass is what we experience as "slow" bass. Alternately, I suspect the subjective quality of "fast bass" is likely to be associated with those systems where the bass arrives "on time" within the minimum detectable delay threshold.

For further study: Build a collection of allpass (delay only) filters and introduce stages of delay to your playback chain untill the effect is just audible in comparison with the undelayed program. Note the amount of delay that is just audible in your system. How does this compare to the delay contributed by your speaker system?

<Warning: Blatent Commercial>
Bassers, if you are speaker crazy enough to enjoy my audio ramblings then you can order my new book "Introduction to Loudspeaker Design" at either the True Audio web site or at Amazon.com. :-)

Regards,

John

/////////////////////////////////////
John L. Murphy
Physicist/Audio Engineer
True Audio
http://www.trueaudio.com


(posted 2Jun99  to Audio Engineering List)

John wrote:

> GD is NOT the delay between input and output UNLESS the delay is constant
> or zero (that special constant). A constant delay results in a linear
> change in phase with frequency, but the "relative phase" of all the
> frequency components in the input (relative to each other) remains intact
> and unaltered at the output. 

John is correct. group delay is a well defined variation on the concept of "time delay". It is NOT simply the difference in time between the input and output of a system. Rather it is the delay experienced by the signal "envelope" or "packet". Dick Heyser's works are well worth studying to explore these ideas further. 

Here is another excellent reference on this subject which discusses phase shift, phase delay, group delay, time delay and defines a "differential time delay". 

"The Differential Time-Delay Distortion and Differential Phase-Shift Distortion as Measures of Phase Linearity" by Marshall Leach, 
JAES, Vol. 37, No.9, September 1989

Leach argues that what matters is the relative delay between the signal waveform and the envelope. He further goes on to argue that bandwidths on the order of 1 Hz (yes, one Hertz) are required in order to keep "phase shift distortion above 20 Hz" below 5%. But leach is discussing amplifiers and makes no comments on audibility of such "phase shift distortion". Generous low end bandwidth is easy to achieve in an amplifier. But with our speaker systems we do not have the luxury of dialing in an extra DECADE of low end bandwidth as a safety margin. Rather, we operate at the threshold of audibility with respect to magnitude and delay anomalies. We would like to know better where the audibility thresholds fall so that we can squeak in under them as we design speakers.

John also wrote:

> I have to backhandedly agree with Phil on the point that phase is the real
> overlooked factor. It would be nice to have zero phase shift from input to
> output (zero delay), but a constant delay is just as good, since as I noted
> above, a constant delay retains the integrity of the input wave form in the
> output.

Phil, Tom and now John have expressed preferences for "viewing" the "delay" problem in terms of phase. I just wanted to point out that (for a minimum phase system) frequency response, phase response, and group delay response are simply three different views of the same physical 'delay' phenomenon. Change one of these responses an the other will change accordingly (remember, it's a minimum phase system).

For example, given only the frequency response of a system the phase response and group delay response can be calculated. This implies that the frequency response curve contains all the information concerning both phase and group delay. So frequency, phase and group delay are really just different takes on the same information. 

My current preference is to interpret this phenomenon in terms of "cycles of delay". This can be calculated from group delay by dividing the group delay by the period of the frequency at each point. I call this "normalizing" the group delay by period. If you do this the frequency dependence gets out of the way of seeing the phenomenon. For example, consider the Blauert and Laws data on audibility thresholds for group delay. Below is a table that shows the data in terms of both delay TIME in ms and normalized delay in cycles.

Frequency (Hz)  Threshold (ms)  Threshold in T 
(periods or cycles)
8k Hz  2 ms  16 T
4k Hz  1.5 ms  6 T
2k Hz  1 ms  2 T
1k Hz  2 ms  2 T
500 Hz  3.2 ms  1.6 T

Considering only the lower three data points for the moment, I see the Blauert and Laws data suggesting that group delay audibility thresholds appear to fall around 2 cycles. I find this "cycles of delay" view a much more intuitive representation of the data than either the phase or group delay views of the same data.

The essential question remains: what are human audibility thresholds for frequencies below 500 Hz.

Extrapolating the Blauert and Laws data to lower frequencies it could be that "one or two cycles" of delay continues to be the threshold as we move lower in frequency.

One comparison I did recently of a closed vs. a vented enclosure for ACI's SV-12 woofer revealed the following simulated results:

Frequency

Closed Box Delay (T) 

Vented Box Delay (T)

100  .070 cycles .074 cycles
50  .135 cycles  .149 cycles
20  .176 cycles  .338 cycles

Note that the vented system has more delay than the closed system but that both systems would appear to have delay well under my extrapolated B&L threshold of "one or two cycles". At 50 Hz the difference between these two systems is rather slight. But these two systems have very low F(3)'s (about 33 Hz for the closed, and about 23 Hz for the vented system). But a closed box speaker withe f(3) of 50 Hz and Q(tc) = .707 will still experience less than about .25 cycles (or 4.5ms) of delay at 50 Hz. This would SEEM to be well under the extrapolated B&L criteria of "one or two cycles". This would imply that the group delay of a 50 Hz closed box system would be inaudible. Leach's differential delay works out to be about .475 cycles (or 9.5 ms) for this system at 50 Hz. Using Leach's differential delay makes the delay appear worse than if you consider group delay alone. (.475 cycles for differential delay vs. .25 cycles for group delay)

But what we still don't know is: "How much bass delay is AUDIBLE?"

My current opinion would go something like this: "One cycle or so of delay in the bass range is probably just audible under controlled listening conditions (phones) and with the most challenging program material (clicks and pops). Under less well controlled listening conditions and with less difficult program material the audibility thresholds are somewhat higher."

What do you think? Is the delay (whatever flavor) of a 50 Hz, Q = .707 closed box audible?

Regards,

John

/////////////////////////////////////
John L. Murphy
Physicist/Audio Engineer
True Audio
http://www.trueaudio.com
Check out my new book "Introduction to Loudspeaker Design" at Amazon.com


(posted 3Jun99  to Audio Engineering List)

I previously wrote:

> Phil, Tom and now John have expressed preferences for "viewing" the "delay"
> problem in terms of phase. I just wanted to point out that (for a minimum
> phase system) frequency response, phase response, and group delay response
> are simply three different views of the same physical 'delay' phenomenon.
> Change one of these responses an the other will change accordingly
> (remember, it's a minimum phase system).
>
> For example, given only the frequency response of a system the phase
> response and group delay response can be calculated. This implies that the
> frequency response curve contains all the information concerning both phase
> and group delay. So Freq, Phase and Group Delay are really just different takes on
> the same information.

Tom responded (and Philip agreed):

>The statement "given only the frequency response of a system the phase
>response and group delay response can be calculated." is too often not true..

But I was careful to explicitly say that I was talking about "minimum phase systems". So I stand by my original statement as it applies to such systems. For a minimum phase system the frequency and phase responses are Hilbert Transforms of one another and can therefore be calculated from one another. However, I didn't and wouldn't claim that actual speakers are always "minimum phase systems". 

To quote Dick Heyser 
(from "Loudspeaker Phase Characteristics and Time Delay Distortion: Part 1", JAES, Jan 1969):

"If a network is minimum phase, there exists a unique relationship between 
amplitude and phase which allows a complete determination of phase from amplitude"

So there should be no question that phase response can be calculated from frequency response for a minimum phase system.

Now, the real question becomes: 'to what extent are REAL speakers minimum phase?'

If I recall correctly, Dick Heyser expressed the opinion that loudspeaker drivers are 'largely' minimum phase systems. Otherwise why would Dick have spent so much time and energy discussing the Hilbert Transform and its use in acoustic analysis. But I couldn't find a statement to this effect in my brief search of his papers. 

But I did see an AES preprint in which the author carefully measured the "excess phase" of a pair of tweeters. 

AES Preprint 2118, A Micro-Computer Program for Computing the Phase Response of Dynamic Loudspeaker Systems" 

The author measured the response of Dynaudio D-52 and D-21 dome tweeters and concluded: "It is seen that these two drivers are, very accurately, minimum phase devices."

I believe that deviation from minimum phase behavior is an exception for loudspeaker drivers under small signal conditions, and not the rule. 

Tom went on to say:

> Zero degrees phase over the entire band (with flat amplitude response) is the
> ONLY condition which a loudspeaker can faithfully reproduce (acoustically) a
> complex non repetitive signal or asymmetric signal, just as in electronics..

This is an example of the "phase view" leading to an erroneous conclusion.

Example: If an audio signal experiences a broadband delay such that all frequencies are delayed equally, the waveform is reproduced EXACTLY in spite of the fact that the delay introduced a "zillion degrees" of phase shift. The REAL requirement for faithful reproduction of a waveform is that the system have both flat frequency response and flat time delay. That is, all frequency components must arrive with the correct amplitude and time alignment. Flat phase response is just one case where the time alignment criteria is met. But what "delay" are we talking about? Phase delay? Group delay? I think the relevant delay here is Leach's "differential delay".

Does anybody have any measured data on the "excess phase" response of some of our popular drivers?

I am enjoying this "delay" discussion and appreciate that we may have differing opinions. I do hope I have convinced you that minimum phase systems really do have this characteristic that frequency, phase and group delay are just three different views of the same response phenomena.

In any event, do you think these "delay" effects are audible in our speakers?

Regards,

John

/////////////////////////////////////
John L. Murphy
Physicist/Audio Engineer
True Audio
http://www.trueaudio.com
Check out my new book "Introduction to Loudspeaker Design" at Amazon.com

 

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