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Title: Frequency dependent delay or not?
Post by: Merlijn van Veen on July 20, 2017, 06:20:52 am
A while ago some colleagues and I had a vivid discussion whether group delay can be considered frequency dependent delay. Be warned though, this is a controversial topic and as far as I can tell no consensus has been achieved.

Please click here (https://www.merlijnvanveen.nl/en/miscellaneous/134-frequency-dependent-delay-or-not) to read more.

Anxious to hear what the hive-mind thinks.

(https://www.merlijnvanveen.nl/images/content/zebra.jpg)

(https://www.merlijnvanveen.nl/images/content/group_delay_equation_WEB.jpg)

EDIT: Later in this thread Frank makes me realize that the minus sign is indeed mandatory and how I wished I just took a little bit more time to think it through :-[
Title: Re: Frequency dependent delay or not?
Post by: Keith Broughton on July 20, 2017, 07:28:48 am
I read "frequency dependant" as activating the desired processing (like compression) only when a level threshold at a specified frequency (or freq band)is reached.
Under those criteria, group delay would not be "frequency dependant"
Just my POV...
Title: Re: Frequency dependent delay or not?
Post by: Stelios Mac on July 20, 2017, 08:04:07 am
I read "frequency dependant" as activating the desired processing (like compression) only when a level threshold at a specified frequency (or freq band)is reached.
Under those criteria, group delay would not be "frequency dependant"
Just my POV...

Shouldn't that be called frequency AND level dependent?

A conventional compressor is level-dependent (as the level crosses the threshold, compression starts to happen) - A multi-band compressor is that, whilst also being frequency dependent.

Frequency dependent should mean just that, "depends on the frequency" - not "depends on volume at a given frequency" or anything else.
Title: Re: Frequency dependent delay or not?
Post by: Merlijn van Veen on July 20, 2017, 08:09:49 am
"Frequency dependent delay" as in "variable delay over frequency".
Title: Re: Frequency dependent delay or not?
Post by: Keith Broughton on July 20, 2017, 11:28:16 am
"Frequency dependent delay" as in "variable delay over frequency".
So as the frequency varies, the delay varies?
I buy that.
Title: Re: Frequency dependent delay or not?
Post by: Barry Singleton on July 20, 2017, 02:02:16 pm
Oops.  Irrelevant again.

Deleted. Sorry.

Barry.
Title: Re: Frequency dependent delay or not?
Post by: Marcel de Graaf on July 20, 2017, 03:34:00 pm
Best Merlijn,

Very good subject and article written up. I always like subjects about timing.

Group delay has to be kept simple, it`s like you called a derivative of a phase plot. It is just a different view, but it is also showing the "pure" delay offset. This has to do where you set your point off reference in your analyzing tool. Group delay can help you find this offset.

In fig. 10 you could say there is a pure delay offset. I never tried this, but i am wondering what the waveform would like with an other burst signal than a pure sinewave.

Greetings,
Marcel
Title: Re: Frequency dependent delay or not?
Post by: Frank Koenig on July 21, 2017, 12:01:32 am
Group delay is -d phi/dw, where phi is phase and w is frequency. The article omits the minus sign which, while perhaps irrelevant to this philosophical discussion, is necessary to get the math right. -F
Title: Frequency dependent delay or not?
Post by: Merlijn van Veen on July 21, 2017, 02:44:08 am
Group delay is -d phi/dw, where phi is phase and w is frequency. The article omits the minus sign which, while perhaps irrelevant to this philosophical discussion, is necessary to get the math right. -F

Agreed, but I purposely omitted it. The minus sign confuses. Something that's lagging has a negative value and something that's leading has positive value. This doesn't relate to e.g. IR and the actual group delay display in Smaart where late is pos and early is neg.

EDIT: Later in this thread Frank makes me realize that the minus sign is indeed mandatory and how I wished I just took a little bit more time to think it through :-[
Title: Re: Frequency dependent delay or not?
Post by: Frank Koenig on July 21, 2017, 01:11:31 pm
Agreed, but I purposely omitted it. The minus sign confuses. Something that's lagging has a negative value and something that's leading has positive value. This doesn't relate to e.g. IR and the actual group delay display in Smaart where late is pos and early is neg.

Hi Merljin,

I think the minus sign is actually important for intuitive understanding. Causal systems have phase that lags with increasing frequency (negative slope) and have positive delay since they're causal.

Consider the "hydrogen atom" of linear systems: the first-order low-pass. It has phase = 0 at zero frequency and phase = -pi/2 at infinite frequency. In the transition region the phase has a negative slope, and the delay is positive.

A possibly useful theorem is that the center of gravity of the impulse response of a system, which we might well intuitively associate with the system's delay, is equal to the negative of the slope of the phase at the origin (zero frequency). [Papoulis, "Signal Analysis", 1977, p. 21]

Delay is difficult. I still struggle with it even as my ability to struggle with it is in decline.

Best,

--Frank
Title: Re: Frequency dependent delay or not?
Post by: Marcel de Graaf on July 21, 2017, 03:16:22 pm

Consider the "hydrogen atom" of linear systems: the first-order low-pass. It has phase = 0 at zero frequency and phase = -pi/2 at infinite frequency. In the transition region the phase has a negative slope, and the delay is positive.


Regarding absolute phase its true that you should read phase=0 at zero frequency. Systems are formed by casuality. It makes sence, because a signal can never arrive before it is emitted at the system.

Systems (we know off) always have a low pass, even at infinity high frequencys. What normally is done is that the time=zero marker is at the peak of the impulse response.
Knowing that a system has a low pass it would not be logical because we know there was energy before the peak (in very low magnitude).

Have the wright time=zero marker should keep the phase plot going negative with increasing frequency.

Delay is indeed very confusing but it can be far more. Most analyzers will show a phase plot from extracting it from the magnitude response. The plot is than at 0 degrees where the magnitude is flat. In a electronic system this is wright but acoustic can be very different. Acoustic air has impedance with a changing resistance. This changing resistance is compensated with the wright loudspeaker parameters (compensating it with the imaginairy parts) to make the magnitude response flat. It`s stil a minimum phase system BUT not having the phase plot at the 0 degrees line.

I think this is what barry mentioned in his post.

grtz. Marcel
Title: Frequency dependent delay or not?
Post by: Merlijn van Veen on July 21, 2017, 03:26:05 pm
Dear all,

As much as I appreciate your knowledgeable input, we're drifting into abstracts which is the very thing I wanted to avoid.

That's why I avoid poles, zeros and polynomials like the plague in class.

My question is about the practical physical implications. Maybe the attached illustration makes sense.

What would you say to a layman, a novice, an uninitiated, a mere mortal?
Title: Re: Frequency dependent delay or not?
Post by: Barry Singleton on July 21, 2017, 11:58:29 pm
  I don't know if that graphic really captures it Merlijn, a stretch maybe in the very most basic sense. This is a tough concept to really grasp.

  I think more about single devices that smear time like the three poles one runs across in  large format compression drivers. Yeah I had to use the P word.

  I will have to re-read Heyser again tonight.

  This is like explaining fission by saying the equal sign in E=Mc² is the bridge that if you send mass fully across and convert to energy, a piece of plutonium the size of a ChapSick can destroy a city.

 While that's functionally true, does it help anyone really understand the worlds most famous equation?

  I for one would love to see group delay made truly explainable without all the math but I am not sure how to do it.

Barry.
   

 

 

 

 
Title: Re: Frequency dependent delay or not?
Post by: Merlijn van Veen on July 22, 2017, 01:57:56 am
Thanks for proving my point. Because this is what keeps happening over and over again AFAICT. Everybody agrees that Group Delay is the first derivative of the phase response (either with or without minus sign) and that the unit must be time. But when it comes to explaining what that time entails in plain understandable language, "shit hits the fans" (pun intended).


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Title: Re: Frequency dependent delay or not?
Post by: Merlijn van Veen on July 22, 2017, 03:21:26 am
Group delay is -d phi/dw, where phi is phase and w is frequency. The article omits the minus sign which, while perhaps irrelevant to this philosophical discussion, is necessary to get the math right. -F

I stand corrected :-[

Thanks for making me think Frank!

In order to maintain causality and keep past, present and future sorted the minus sign is mandatory.

The topic swerve turns out to be serendipity :)
Title: Re: Frequency dependent delay or not?
Post by: Ivan Beaver on July 22, 2017, 08:50:38 am
Dear all,

As much as I appreciate your knowledgeable input, we're drifting into abstracts which is the very thing I wanted to avoid.

That's why I avoid poles, zeros and polynomials like the plague in class.

My question is about the practical physical implications. Maybe the attached illustration makes sense.

What would you say to a layman, a novice, an uninitiated, a mere mortal?
Your illustration is the whole idea behind the BBE sonic maximizer.

They "assumed" that all loudspeakers (or at least the ones for their target audience), had the same time offsets between woofers and mids and horns.

So the basic concept was to split the signal up into 3 bands, add some specific delay to 2 of the freq bands, and then mix them back together.

This concept DOES WORK, and I have done it.  HOWEVER, it MUST be for a SPECIFIC cabinet-and is not universal.  And it only works in a true point source/single source type cabinet-NOT one in which the lows/mids/highs are located in different places on the cabinet.

If you go to far with the delay it is just as bad as when you started.  Or if you move around in the coverage pattern, the delay times will need to change, which they can't.

I do like your illustration.

One size DOES NOT fit all in this case.
Title: Re: Frequency dependent delay or not?
Post by: Mark Wilkinson on July 22, 2017, 08:54:48 pm
But when it comes to explaining what that time entails in plain understandable language, "shit hits the fans" (pun intended).


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Yes, "shit hits the fan" and then keeps on spreading......

Don't know the simple answer with complete certainty yet, but my best guess is that time alignment means alignment at 0 degrees ...when wave forms begins to rise, and not at peak magnitude.  I'd point to stuff from Charlie Hughes.
 
I applaud your quest for simple understanding, cause i really think when something is properly defined and completely understood, it depends
gets washed away into clear simplicity
Title: Re: Frequency dependent delay or not?
Post by: Doug Fowler on July 23, 2017, 03:10:47 pm
Thanks for proving my point. Because this is what keeps happening over and over again AFAICT. Everybody agrees that Group Delay is the first derivative of the phase response (either with or without minus sign) and that the unit must be time. But when it comes to explaining what that time entails in plain understandable language, "shit hits the fans" (pun intended).


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I can tell you with great certainty that beginning measurement students absolutely do not understand that different frequencies are arriving at different times.  But you already knew that.... :-)

Are we talking science or simple field alignments?  For the overwhelming majority of FFT software users, "frequency dependent delay" gets the point across.  This is where the group delay view becomes so useful. Rather than "looking down the phase tube" just display group delay to make the point.

Now, it's quite obvious to novices that the subwoofer is 20-30ish msec behind the rest.  If you zoom in sufficiently one can see more delay present as we go lower in frequency, at least in a typical LF section of (for example) a 3 way loudspeaker. 

So for this majority of users, the biggest hurdle is the legendary sub alignment problem. I posted elsewhere in the forum about a method for using group delay to quickly get "in the neighborhood" re: delay value at crossover at the chosen alignment place.   Yes it's group delay, s/n issues can cause it to display negative time in some places, but it's a fast path to a proposed delay value which can be fine tuned with the phase display.

The user can then decide if this delay value is reasonable (no 88 msec is not reasonable:-), inspect phase which should be close at this point, and determine if it sums.  I'll leave the "how do I choose my alignment spot" to Merlijn and his excellent recent piece on this. 

This leaves (at least in my old roadie mind) the next logical step, unrelated to the alignment task but still something most want to know:

What mechanical/physical/electrical circumstances cause every loudspeaker ever constructed (thanks 6o6) to display this behavior?

If we can explain this in a way that makes sense without overloading beginners' already roasted brains, the logical conclusion is the demonstration, and in my experience group delay view is very helpful.
Title: Re: Frequency dependent delay or not?
Post by: Uwe Riemer2 on July 28, 2017, 05:22:58 pm
sorry for being late, but in July there are more important questions like getting sleep or food, also I had to create a new account, because I couldnt get the forum server to answer my request for a new password, seems my old mail adress does not work in this case.

But now back to topic:
Yes I think group delay is frequency dependant delay and Merlins nice pictures nails this.
Further I think, that Anselm Goertz in the linked article never contradicted to this view and that his explanation is equivivalent and comes from the attempt to measure Group delay directly instead of trying to derive it from the Phase response. There are some practical reasons to do this:
Measuring Phase without a reflection free envirement is already difficult and done with the help of Windowing, but still especially in Systune will often create a function ( Phase over frequency ) which is overall not differentiable ( my Math english sucks ), means the derivation of the function does not exist at certain points, therefore sometimes the stupid computer will generate negative values, which hold no meaning.

Measuring the group delay directly like described by Anselm Goertz is done with a pulse, which to me looks like a single frequency( lets call it basis frequency ) modified by a window function, which seems like an attempt to switch a single frequency smoothly on and off without creating too much new frequencies.

Personnally I hate Math so someone else should verifiy or falsify this proposition by performing a Fourier Transform on this pulse.
But if this should be true, the delay of the bulk energy of this pulse through the DUT will represent roughly the Group delay at above mentioned basis frequency

Back to sleep now
Uwe


Title: Re: Frequency dependent delay or not?
Post by: Uwe Riemer2 on July 30, 2017, 06:10:28 pm
I almost forgot
the sound of silence without any group delay,

which brings me to a question for Ivan and the BBE thingy:
how would they ( BBE ) achieve splitting the audio without creating group delay, a problem they want to cure according to you?

P.S. apologies for many spelling errors in my post above, especially the missing J

Uwe

Title: Re: Frequency dependent delay or not?
Post by: Mark Wilkinson on August 03, 2017, 08:27:42 pm
I tend to think of group delay as simply phase deviation from zero, converted into time, at a given frequency.
I don't think of  physical distances between drivers, or constant processing latency, as contributing to group delay. 
Those are simply time delays, with a linear phase slope vs freq, when freq is on linear scale.
To me group delay means some kind of non-linear phase vs freq, again when freq is on linear scale.
IOW, if group delay is a constant, it means it ain't group delay, it's time delay.
Which means to me, Yes, group delay has to vary by freq, by definition.

I also see group delay as an instantaneous value only, like any derivative, with no meaning over any larger interval.

I've played with making each pass-band in multi-way systems exhibit flat zero degree phase behavior using FIR, with a corresponding 0 sec group delay.
 
When 0 deg phase is achieved for each pass-band, time alignment is simply a function of the physical distance between the acoustic centers of the pass-bands' drivers, and the time value doesn't change as x-over freq is moved up or down within the range of each drivers ability to hold flat phase at zero.

If I go back and change FIR to traditional IIR, the group delay at x-over freq does explain most of the differences in delay finder readings in adjacent pass-bands. But that's about as much value as I can find in paying attention to group delay.

Comments or corrections to my understandings very welcome..
Title: Re: Frequency dependent delay or not?
Post by: Merlijn van Veen on August 09, 2017, 11:14:02 am
Maybe this (http://forums.prosoundweb.com/index.php/topic,164448.0.html) thread will shed some more light on the conundrum.
Title: Re: Frequency dependent delay or not?
Post by: Peter Morris on August 23, 2017, 08:47:12 am
I can tell you with great certainty that beginning measurement students absolutely do not understand that different frequencies are arriving at different times.  But you already knew that.... :-)

Are we talking science or simple field alignments?  For the overwhelming majority of FFT software users, "frequency dependent delay" gets the point across.  This is where the group delay view becomes so useful. Rather than "looking down the phase tube" just display group delay to make the point.

Now, it's quite obvious to novices that the subwoofer is 20-30ish msec behind the rest.  If you zoom in sufficiently one can see more delay present as we go lower in frequency, at least in a typical LF section of (for example) a 3 way loudspeaker.

P.S.   Merlijn ... love your Cello picture :-)


So for this majority of users, the biggest hurdle is the legendary sub alignment problem. I posted elsewhere in the forum about a method for using group delay to quickly get "in the neighborhood" re: delay value at crossover at the chosen alignment place.   Yes it's group delay, s/n issues can cause it to display negative time in some places, but it's a fast path to a proposed delay value which can be fine tuned with the phase display.

The user can then decide if this delay value is reasonable (no 88 msec is not reasonable:-), inspect phase which should be close at this point, and determine if it sums.  I'll leave the "how do I choose my alignment spot" to Merlijn and his excellent recent piece on this. 

This leaves (at least in my old roadie mind) the next logical step, unrelated to the alignment task but still something most want to know:

What mechanical/physical/electrical circumstances cause every loudspeaker ever constructed (thanks 6o6) to display this behavior?

If we can explain this in a way that makes sense without overloading beginners' already roasted brains, the logical conclusion is the demonstration, and in my experience group delay view is very helpful.

I’m a bit late to the party … I don’t know if this is useful but if you consider a speaker to a mechanical device that has:

-   Mass (cone and voice coil)
-   Spring constant (air in the box)
-   Dampening (from the suspension)
-   driving force (voice coil in the magnetic gap)

(This is a little simplistic)

Now if you watch this video https://www.youtube.com/watch?v=aZNnwQ8HJHU
and think in terms of:

-   Ball on the end of the spring = mass
-   Spring = spring constant
-   Motor / stick = driving force
-   Disk moving in the air as providing some dampening

Then you can see how phase changes with frequency and what happens at resonance with these type of systems ... you can do the same with a mass and rubber band.

@ Merlijn ... love your Cello picture
Title: Re: Frequency dependent delay or not?
Post by: Barry Singleton on August 23, 2017, 01:36:25 pm
Peter that analog doesn't hold for a loudspeaker in a couple of ways.

First this would assume that you are driving the cone with the suspension as in shaking the motor basket assembly to move the cone.

It also ignores the coil as another force, a strong force when driven by a low impedance voltage source.

The example shows uncontrolled ocillation at resonance which does not happpen when a mass is driven by a stiff force ie a strong motor being voltage driven.

It is observed by me with a positioning laser with accuracy of 0.003" at up to 100kHz with less than 10 degrees phase drift from DC to 100k that the coil-former and dust cap follow the voltage signal nearly dead on until you reach a frequency where the inductance of the voice coil gets in the way where it begins to drift in phase as any single pole low pass filter does.

Since we are discussing subs, cone breakup need not enter this discussion. :)

Barry.
 
Title: Re: Frequency dependent delay or not?
Post by: Peter Morris on August 23, 2017, 10:44:53 pm
Peter that analog doesn't hold for a loudspeaker in a couple of ways.

First this would assume that you are driving the cone with the suspension as in shaking the motor basket assembly to move the cone.

It also ignores the coil as another force, a strong force when driven by a low impedance voltage source.

The example shows uncontrolled ocillation at resonance which does not happpen when a mass is driven by a stiff force ie a strong motor being voltage driven.

It is observed by me with a positioning laser with accuracy of 0.003" at up to 100kHz with less than 10 degrees phase drift from DC to 100k that the coil-former and dust cap follow the voltage signal nearly dead on until you reach a frequency where the inductance of the voice coil gets in the way where it begins to drift in phase as any single pole low pass filter does.

Since we are discussing subs, cone breakup need not enter this discussion. :)

Barry.
 

Hi Barry,

As I said, this is simplistic ... perhaps too simplistic, but fundamentally this is what is happening. This is how all mechanical systems like this behave.
.
Yes I realize that the VC is connected directly to the cone, and this is where my analogy is a bit lose so I used the wording “think in terms of” … anyway if you write an equation that models the VC and its connection to the amplifier it starts to get complicated and the students will get completely lost.

As you know, the driving force actually comes from the BL product (the strength of the magnetic field in the gap multiplied the length of wire in this field) - this multiplied by the current in the VC gives you the driving force.
 
The problem is we are comparing the driving amplifiers’ voltage with cone movement, and driving voltage does not have to be “in phase” with the current that causes the force on the cone.

The electrical voltage / current phase relationship is in part a reflection of the systems mechanical behaviour … this is where it gets ugly and the student will get lost.

With respect to resonance here is a quote from Wikipedia … (save me typing)

https://en.wikipedia.org/wiki/Electrical_characteristics_of_dynamic_loudspeakers

“The moving system of the loudspeaker (including the cone, cone suspension, spider and the voice coil) has a certain mass and compliance. This is most commonly likened to a simple mass suspended by a spring that has a certain resonant frequency at which the system will vibrate most freely.

This frequency is known as the "free-space resonance" of the speaker and is designated by Fs. At this frequency, since the voice coil is vibrating with the maximum peak-to-peak amplitude and velocity, the back-emf generated by coil motion in a magnetic field is also at its maximum. This causes the effective electrical impedance of the speaker to be at its maximum at Fs, shown as Zmax in the graph. For frequencies just below resonance, the impedance rises rapidly as the frequency approaches Fs and is inductive in nature.”

… and it gets even more complicated when you put the speaker in a box/ horn and look at the phase of the driving voltage and compare it to the cone moment, not to mention resonate issues associated with the enclosure ???