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Author Topic: Frequency depending resistor  (Read 1418 times)

Langston Holland

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Re: Frequency depending resistor
« Reply #20 on: August 27, 2018, 10:01:44 pm »

Hi Everyone:

This is so much fun, but in all the excitement a few things need to be said:

1. Smaart measures phase correctly. So does SysTune BTW. Honest. See attached.

Smaart and SysTune will not be able to make the exact adjustment required to produce a perfect phase trace simply because of the 48kHz measurement granularity of 21Ás. That means adjusting TOF delay removal just right so that the phase trace nails -90 degrees at 10kHz as minimum phase dictates isn't possible unless you get really lucky with your setup's "mic to DUT" distance. Who would have ever thought that 21 millionths of a second was too coarse a resolution for anything, but a one sample step of 21Ás in your delay adjustment is a 75 degree step at 10kHz! It's not at all too coarse for our work in acoustics and aligning drivers and systems of drivers, but it is too coarse for physicists and some loudspeaker design issues.

Again, there is no error here, just a granularity issue. Breathe easily, we are just playing around - the kids are alright - our measurement analyzers are fine. :)

Of course you can increase your time resolution 4-fold by measuring at a 192kHz sample rate, but then you're only down to 5.2Ás steps - still way too coarse in some cases. At 10kHz, a 5.2Ás step is 19 degrees for example. You're probably still gonna miss an exact -90 degrees at 10kHz on your phase plot of this DUT. Now there are measurement analyzers that use math to interpolate between measured data points and that will get you there, but again - this is unnecessary for what we do.

2. That 90 degree current vs. acoustic phase thing is real, but it doesn't matter. Nor does it matter that our real analog sound source turns into trillions of numbers inside our stage racks and mixing consoles on its way to the loudspeaker. What matters is that our flat magnitude and flat phase measurement microphone converts the acoustic magnitude and phase of our loudspeaker into its electrical analog and sends that to the input of our flat magnitude and flat phase measurement analyzer. We are getting the truth regardless of the cool stuff that happens prior to the movement of air.

If you want to measure the current phase going into the loudspeaker, attach a high quality current monitor to one of the wire leads and have at it. If you want to measure the acoustic phase of the sound coming out of the loudspeakers, put a high quality measurement mic in front of it and have at it. :)

3. That TOF removal video that Marcel linked to uses this same measurement scenario, but you'll notice that I end the video with the phase trace _not_ going through -90 degrees at 10kHz! The horror! :) There's a reason for that as explained in the notes area under the video "SHOW MORE". Something to do with infinity. The bottom line is you have to decide on a TOF removal method that makes sense for your situation and your tools and stick with that method so that your measurements are comparable. Phase in our world is rarely an absolute, such as what we've been playing with in this thread. Phase as we use it for alignment is a relative thing. If your passbands at crossover sum together correctly, you measured relative phase correctly.

I have a much better way to remove TOF than what's in that video (and I bet you do too), but I wanted to lay the theory down first. Shame on me for waiting so long to produce the follow up to it. It's all scripted, just need to do it. My new measurement business did better than I expected and I'm too stinkin' cheap/chicken to hire anybody yet. :)

PS: The last time I studied it, Smaart used the peak of the log impulse response to do its automatic TOF delay removal calculation. That is a very good way to do it, though it'll be a tiny bit off in absolute terms much of the time - as is everyone else's systems. Nobody has a perfect solution yet. You have to learn how to do this yourself when absolute arrival time is important. That's what my next video will teach.

PPS: Mark is so right. I also know nothing. There's no bottom in this pool.
« Last Edit: August 28, 2018, 03:53:42 am by Langston Holland »
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Frank Koenig

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Re: Frequency depending resistor
« Reply #21 on: August 28, 2018, 02:09:18 pm »

1. Smaart measures phase correctly. So does SysTune BTW. Honest.

Good to know. I believe ARTA measures phase correctly, too.

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2. That 90 degree current vs. acoustic phase thing is real, but it doesn't matter.

Agree.

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PS: The last time I studied it, Smaart used the peak of the log impulse response to do its automatic TOF delay removal calculation.

Actually, the log of the absolute value, otherwise they'd be trying to take the log of negative numbers, which never ends well :)  One alternative would be to take the peak of the magnitude (or log mag -- doesn't matter as it's the peak) of the corresponding analytic signal, the imaginary part of which can be obtained by means of the discrete Hilbert transform (set the negative frequencies to zero and take the IDFT, more-or-less). The centroid of the impulse response is another metric of what we might call the "broadband time of flight". It has the interesting property that it is minus the slope of the phase at the origin.

In my analysis programs, after trying many things, I've come to favor a user definable "look ahead" before the peak of the impulse response to start the window and provide my delay reference. This is less problematic than trying to ferret out the start of the impulse response from the noise. It introduces an arbitrary delay in the analysis but this is of no consequence for relative phase measurements (as when working on crossovers) as I apply the same absolute delay to all measurements being compared (and don't move the measurement mic).

Slight swerve: I've found tone bursts very interesting as a way of estimating and visualizing group delay. They can be used as both physical test signals and in simulations (mostly the latter for me), are easy to understand, and, for what it's worth, resemble the waveforms produced by many musical instruments. Unlike other more abstract time-frequency-energy representations, with tone bursts I know what I'm looking at (at least I think I do).

Quote
PPS: Mark is so right. I also know nothing. There's no bottom in this pool.

True indeed.

--Frank

« Last Edit: August 28, 2018, 02:12:37 pm by Frank Koenig »
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Frank Koenig

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Re: Frequency depending resistor
« Reply #22 on: August 28, 2018, 02:14:26 pm »

Oops, missed something. Using current as the electrical reference is interesting. I've never done that but it's one more trick in the bag. Thanks. --Frank

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Marcel de Graaf

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Re: Frequency depending resistor
« Reply #23 on: August 28, 2018, 02:28:29 pm »

Hi langston,

About the TOF removal you are totally correct, its the phase trace that is the most important. I am looking forward to your new video, because i can`t think a better way to do is.

Still i am a bit confused and maybe i am totally of the record. But here`s al little example.

Lets get back to the example. Lets assume the transfer function that is shown, is the one that has been measured of a real perfect loadspeaker. A points source with the changing resistive slope in it.
In this case the midband frequency range (between 100-10khz) should shown a theoretical -90 degrees phase plot at these frequencys. I think most analyzers (without naming) will stil show a 0 degrees phase plot in this situation, but i reality this loudspeaker would not follow it`s input waveform.
Also modeling programms can show the wrong phase plot. Usually its a transformation from the magnitude response. Indeed the acoustic phase mirrors the current angle. 

But i believe aligning multiple drivers, the most important is measuring with a fixed T=0 reference. In that case its all going to be relative.

PS: I have not seen many measurements with the above spoken -90 degrees phase delay. Here
      is one of the old contrabass subwoofer.

     http://mariobon.com/Storia/pdf/1998_ContraBass.pdf

gr. Marcel
« Last Edit: August 28, 2018, 02:33:06 pm by Marcel de Graaf »
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Mark Wilkinson

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Re: Frequency depending resistor
« Reply #24 on: August 30, 2018, 11:25:57 am »

Langston, thanks for the continued explanations.

Yep, our measurement programs work just fine don't they?  I find it's 'me the measurer' that doesn't often work quite so well ;)

I read the whole All Pass Filters thread again, watching the debate about "absolute acoustic phase" and "relative phase", and came to the conclusion that everybody is right...from their own perspective.
I also think the only real difference in the perspectives comes down to what is chosen as total fixed delay (I'll just bucket it all as TOF).

It seems to me Smaart chooses a TOF that sets phase to zero at 20kHz if there is sufficient information there. (TOF = Delay Finder time)
Or if there is not sufficient magnitude at 20kHz, it seems to set phase to zero at the highest frequency that it can read, usually about 20dB down from the guts of the measurement.
I take it Smaart takes VHF to zero to make things "relatively" simpler,...... and it totally works for me.

If I understand correctly, TEF on the other other hand, does not try to take phase to zero.  It appears to use a TOF that does not vary from the actual sum of the fixed delay components.....(it does not allow phase to vary for the purpose of driving phase to zero at highest frequency available.)

My understanding is both methods would give exactly the same results if Smaart used TEF's TOF. 
I also see we are talking pretty small differences in TOF's, that really only effect the high freq end of measurements. 
What I don't see is how TEF can sort out the difference in mic-to-speaker delay from natural driver rolloff delay.  It seems like it would need to, to be assured of completely accurate TOF. How does TEF work?

Anyway, I do think there is a difference between the two (that really doesn't matter (to me at least)), other than trying know things down to the bottom.
Oh, I don't think it is just a matter of granularity.  (Granularity has come up in a few recent threads. The last one I can remember brought up that some programs like REW offer a sub-sample timing option for doing finer work, like electrical meas).

Langston, on my Smaart trace that you commented on, saying there is slightly incorrect TOF of 4.02ms causing slightly incorrect phase...... 
That curve I think you were referring to (green) did not use 4.02ms. 
It used 4.00ms....the same as in the processor..the same that I set manually thinking that's what Tom's test requires, and that 4.00ms is what TEF would use.
The flat red curve uses Smaart's 4.02ms.

I played with some higher order low passes...AFAICT Smaart always tries to take phase to zero at 20kHz, by increasing TOF as order increases.
Again, works for me.

Looking forward to your next video !
Please, you or anybody,  let me know if you see any holes in the above...




« Last Edit: August 30, 2018, 04:30:15 pm by Mark Wilkinson »
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Frank Koenig

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Re: Frequency depending resistor
« Reply #25 on: August 30, 2018, 08:52:24 pm »

Absolute phase is something I wish I understood better, but in the Internet tradition I'll say what I can, and Langston and others, please correct me where I'm wrong. Let's stick to finite-order systems whose system function is a rational function (the ratio of polynomials in s, the complex frequency variable). A low-pass system (one in which there are no zeros at the origin) has zero phase at the origin. A high-pass (or band-pass) system with m zeros at the origin has phase m * pi / 2 at the origin.

I know from playing around with discrete data that things get weird. For instance, the phase at zero frequency when applying the DFT to a numerical impulse response depends on exactly where the IR is truncated and whether the last value is positive or negative. Anyone else noticed this? This isn't the Gibb's phenomenon in its usual form, but maybe related. Bottomless pool...

--Frank
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Jay Barracato

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Re: Frequency depending resistor
« Reply #26 on: August 30, 2018, 10:45:37 pm »

Absolute phase is something I wish I understood better, but in the Internet tradition I'll say what I can, and Langston and others, please correct me where I'm wrong. Let's stick to finite-order systems whose system function is a rational function (the ratio of polynomials in s, the complex frequency variable). A low-pass system (one in which there are no zeros at the origin) has zero phase at the origin. A high-pass (or band-pass) system with m zeros at the origin has phase m * pi / 2 at the origin.

I know from playing around with discrete data that things get weird. For instance, the phase at zero frequency when applying the DFT to a numerical impulse response depends on exactly where the IR is truncated and whether the last value is positive or negative. Anyone else noticed this? This isn't the Gibb's phenomenon in its usual form, but maybe related. Bottomless pool...

--Frank
Frank, this is a totally off the cuff, impulsive (pun included) thought that I haven't had a chance to think deeply about, but...

I instantly thought of the analogy of the del (nabla) function where you need the next operator to tell which interpretation of the function you are using.

Sent from my Moto Z (2) using Tapatalk

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Frank Koenig

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Re: Frequency depending resistor
« Reply #27 on: August 31, 2018, 01:27:41 pm »

Frank, this is a totally off the cuff, impulsive (pun included) thought that I haven't had a chance to think deeply about, but...

I instantly thought of the analogy of the del (nabla) function where you need the next operator to tell which interpretation of the function you are using.

Sent from my Moto Z (2) using Tapatalk

Hey Jay, you lost me here. It's been a long time since vector fields. Are you referring to the syntactic issue of the del (upside-down capital delta) having different meanings depending on context? Is it gradient, divergence, or curl? Or something else?

I've always found math notation remarkably sloppy given that I imagine math folks being all about logical systems. As in many fields, maybe there's a hint of protectionism here -- you just gotta know.

--Frank
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Jay Barracato

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Re: Frequency depending resistor
« Reply #28 on: August 31, 2018, 01:59:46 pm »

Hey Jay, you lost me here. It's been a long time since vector fields. Are you referring to the syntactic issue of the del (upside-down capital delta) having different meanings depending on context? Is it gradient, divergence, or curl? Or something else?

I've always found math notation remarkably sloppy given that I imagine math folks being all about logical systems. As in many fields, maybe there's a hint of protectionism here -- you just gotta know.

--Frank
Frank, you got it. The analogy being the meaning of absolute phase depends on the context.

By the way, I am not sure when the notation came on to use as I don't remember it from my course work and in the 80's

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Langston Holland

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Re: Frequency depending resistor
« Reply #29 on: August 31, 2018, 09:29:30 pm »

Hi Frank:

You guys are talkin' about stuff that's over my head. :) But in reference to origins; absolute phase is always causal. Relative phase can be causal or acausal because you get to choose any t=0 you want.

In other news:

Other than the causality requirement, the meaning of absolute phase depends on who's using it! :)

Physicists say absolute phase means:

1. You are only talking about a single frequency.

2. You select t=0 arbitrarily and based on that t=0 you then define the absolute phase of the waveform.

Boring.

Also useless for what we do.

Folks that are into spectrums define absolute phase differently. BTW, never argue with a real physicist, it's an amazing experience you have just once.

In our sandbox absolute phase is determining t=0 as the zero cross of the first arriving frequency in the spectrum.* In other words, learning how to properly remove TOF from a measurement will allow you to measure absolute phase. Absolute phase is rarely a useful or necessary quantity for people aligning drivers and systems of drivers, in that case what we really care about is...

Relative phase. In this case the user selects whatever t=0 that's useful for the task at hand. Example: locking onto a phase smile of the subs at crossover, then bringing the mains back so their phase forms a parallel overlap over as broad a range as possible.

Absolute phase is about figuring out exactly when something happens, generally for the sake of loudspeaker design and room modeling. Relative phase is making stuff play together nicely and helps you predict whether a given system over a given range will preserve the waveform shapes that pass through it.

* Edit: as usual I missed something; absolute phase has yet another definition that includes TOF. Thus the t=0 reference is the zero cross from the origin of the measurement stimulus. Assuming the origin is a loudspeaker, you can end up with many thousands of degrees of phase rotation by the time the mic records the event. Like Jay said - absolute phase depends on context.
« Last Edit: September 02, 2018, 07:01:06 pm by Langston Holland »
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