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Sound Reinforcement  Forums for Live Sound Professionals  Your Displayed Name Must Be Your Real Full Name To Post In The Live Sound Forums => Audio Measurement and Testing => Topic started by: Marcel de Graaf on August 23, 2018, 01:19:32 pm

Hi All,
Maybe a somewhat offtopic question on this board, but in the end it has a link with acoustics.
Is there a way to make a frequency depending resistor (pure resistive)?
gr. Marcel

Frequencydependant? You mean resistance varies by frequency? Like a capacitor or choke but without any inductance?

Hi,
Indeed a frequency dependent restive load.
I have tought about a potmeter that will change its position with frequency, but can`t find a lot on the net about some sort of setup. I would like to build a little circuit which behave with characteristics of radiation impedance to do some test with different analyzers.
PS: maybe its more a question on a forum about electronics.

Hi,
Indeed a frequency dependent restive load.
A resistive load has impedance that is unchanging with frequency, reactive components (like inductors or capacitors) change impedance with frequency.
I have tought about a potmeter that will change its position with frequency, but can`t find a lot on the net about some sort of setup.
potentiometer? You could servo a frequency sensor to motor controlled potentiometer but that seems like an expensive and difficult way to accomplish something.
I would like to build a little circuit which behave with characteristics of radiation impedance to do some test with different analyzers.
What kind of radiation? What kind of analyzers?
PS: maybe its more a question on a forum about electronics.
Maybe its a bot?
JR

John,
Resistors does present a load that are unchanging with frequency. The analog model of the radiation impedance of a circular piston has a part which behave as a decreasing resistor with decreasing frequency.
http://www.fonema.se/mouthcorr/mouthcorr.htm (the plot from Beranek).
Its just this thing i would like to build with electronics parts.
I want to make some measurements with a changing resistive part in the circuit to see if acoustic analyzers like holmimpulse, smaart, tef etc....will measure the same. I want to do this in a electrical way so its easier to compare and under the same conditions.
marcel

Hi Marcel:
You will find more success in your quest if you clearly specify your purpose. :)
Because it's Friday night and I want to do something fun, and I'm a geek, see if the following is entertaining. Or not.
Is your goal to learn about radiation resistance with a given application in mind, or are you trying to qualify various measurement systems for that specific application, or something else?
If it's the former, you may be looking at the problem backwards. As you implied, opposition to the movement a given sized radiator changes as frequency changes. This opposition is the result of air pressure (SPL) divided by air flow (particle velocity). Electrically this is the same as voltage divided by current. In other words, impedance. The changes with frequency behave like a reactance even though the word resistance is used. That's why your linked article shows reactive components in the equivalent circuit diagram.
Since the radiator experiences a rapid loss in acoustic impedance as the wavelength of sound approaches and then exceeds its diameter, this is electrically equivalent to inductance. Again, your linked article shows inductance as the primary component of the equivalent circuit. This is your "frequency dependent resistor".
Now, if you're trying to compare and contrast acoustic measurement systems, measuring inductance isn't going to help. I'd suggest you use a test stimulus that more closely simulates acoustic behavior, such as a programmable reverb and echo effects unit. You will find all measurement systems will closely agree with fairly steady state signals, but begin to show differences as you change the stimulus over the time of acquisition. In other words, changes like you see when measuring loudspeakers and rooms. These differences you will notice are primarily due to (3) things:
1. How the measurement system selects (or allows the operator to select) the raw acoustic data (acquisition length and time domain windowing technique).
2. Whether the measurement system uses FFT or sinusoidal tracking methods (or both).
3. How the measurement system selects (or allows the operator to select) the transformed data for the purpose of displaying the impulse response or complex transfer function. This again involves data length and windowing techniques.
Almost ALL measurement systems do this stuff differently for different reasons. Thus you can get somewhat different plots on your screen with different systems using the same measurement event and each can be, and probably will be, correct! Smaart is a heck of a lot better than a scope for characterizing a sound system's correlation to human perception, but the scope is a heck of a lot better for studying oneshot events in a circuit.
It depends on your goal.
PS: If you want to get a better feel for Beranek's work on acoustic impedance as excerpted in your link, read Tom Danley and Doug Jones' chapter on Loudspeakers in the current (5th Ed) of "Handbook for Sound Engineers". Their explanation is way better. :)

Hi All,
Maybe a somewhat offtopic question on this board, but in the end it has a link with acoustics.
Is there a way to make a frequency depending resistor (pure resistive)?
gr. Marcel
Ferrite beads can be reasonably accurately modeled as frequency dependent resistors. That's what makes them useful as EMI suppressors. As frequency increases their resistance goes up without much inductance that could cause a resonance at a particular frequency. Why do you ask? F

Frequency dependent resistors are called capacitors and inductors. They have capacitance and inductance, not just pure resistance.
Components can be combined to create a purely resistive load, but only at a given frequency.
A wideband frequencydependent resistor is generally implemented as a purely resistive input to an amplifier, which hides the characteristics of the later circuit components from the source.
Eg, a graphic EQ is a uservariable frequency dependent resistor.

Langston, Frank thnx for the input.
What made me triggered is on old post of TD:
http://mailman.soundlist.org/pipermail/sound/2007January/027323.html
I find it interesting that a omni point source with flat magnitude, measures a (fixed) time difference of almost 90 degrees between a in and output signal. His explanation why this is, made me visualize this in my head.
What i want to do is to build a circuit (as simple as possible) with some resistor, cap and inductors, that measures the magnitude into that load flat, but with a (fixed) phase delay between input and output. As i see it you have to use some kind of frequency depended resistor to achieve this.
The circuit is than a good reference for me to use different analyzers, to see how they measure and see the plot, from a known load. I know a can made a compare with an acoustic measurement, but i want to do the electrically, so i can really exclude any uncertainty.
gr. marcel

What i want to do is to build a circuit (as simple as possible) with some resistor, cap and inductors, that measures the magnitude into that load flat, but with a (fixed) phase delay between input and output. As i see it you have to use some kind of frequency depended resistor to achieve this.
It sounds like what you're trying to do is to build an analog Hilbert transformer. If you hit the literature you'll likely find ways to approximate one over a limited range of frequencies. A straight integrator or differentiator will give you a 90 deg phase shift but, of course, the magnitude will vary as 6 dB / octave.
You're in the world of analog computing. Most folks doing this kind of work these days would model all this in software where everything becomes "a simple matter of programming" :) That's my first choice. F

What made me triggered is on old post of TD:
http://mailman.soundlist.org/pipermail/sound/2007January/027323.html
If nothing else came out of this thread, that link alone is worth its weight in gold. I never saw that before  thanks Marcel!
I find it interesting that a omni point source with flat magnitude, measures a (fixed) time difference of almost 90 degrees between a in and output signal.
Technically, this refers to a fixed phase shift of 90 degrees. A fixed time difference (or delay) would result in differing amounts of phase shift at each frequency. It's obvious you know this  I'm just clarifying. Also, this applies to the acoustic phase of most loudspeakers, not just omni point sources. Horn loading if done right can correct this at the cost of a minor fixed time delay. The addition of electrical high and low pass filters can mess it up again. Electrical filters (such as 2nd order all pass) if done right can also correct for the phase shift at a minor cost in fixed time delay. Audio is amazing. :)
What i want to do is to build a circuit (as simple as possible) with some resistor, cap and inductors, that measures the magnitude into that load flat, but with a (fixed) phase delay between input and output. As i see it you have to use some kind of frequency depended resistor to achieve this.
A simple inductor will simulate the current phase lag of 90 degrees throughout it's linear region (use air core), but I don't think this is the best solution.
The circuit is than a good reference for me to use different analyzers, to see how they measure and see the plot, from a known load. I know a can made a compare with an acoustic measurement, but i want to do the electrically, so i can really exclude any uncertainty.
Now for the meat of the "why" behind all this, are you mainly trying to determine the acoustic phase accuracy of different measurement systems?
Edit: if an electrically based test to determine the acoustic phase accuracy of a measurement system is your goal, click here (http://forums.prosoundweb.com/index.php?topic=105476.msg983449#msg983449). Also, there is one huge obstacle to phase accuracy with any measurement system  the organic component. :)

If nothing else came out of this thread, that link alone is worth its weight in gold. I've never saw that before  thanks Marcel!
Indeed! Tom D. is a great explainer. I've ploughed through Beranek a few times (and Thiel, Small, etc.) and while I'm somewhat conversant in electrical/mechanical/acoustic analogies and network analysis, I never came away with that. Gives credence to the notion that only folks with a deep and true understanding of a subject can explain it well to others. Required reading. Frank

Edit: if an electrically based test to determine the acoustic phase accuracy of a measurement system is your goal, click here (http://forums.prosoundweb.com/index.php?topic=105476.msg983449#msg983449). Also, there is one huge obstacle to phase accuracy with any measurement system  the organic component. :)
Indeed this is what i want to investigate and see it by myself. I have another paper, that was sent from nice fellow at the AA board, that has essentialy the same explanation as TD. The author is Richard Stroh. The paper has some graphics attached to it. If you interested in it you can contact me.
The way as i read it and i see it now is as follows (correct this if i am wrong):
What is been measured with a microphone is a pressure level of the acoustic power delivered to the air. It`s only the resistive part of the airload (radiation impedance) where this power is dissipated to.
If this power is constant over a range of frequency, while the resistive part is changing, than this is only possible with a compensation of the reactance parts. This would mean there is a phase shift (angle) and it is constant.
Its this phase shift, under that conditions, i want to see in my measurement. I think this is the real acoustic phase phase. I have a little doubt that a measurement systems with a steady state signal would show this. If measuring a electronice device this would show the correct phase, because there is no changing resistive part, but acoustics this can be different.
It sounds like what you're trying to do is to build an analog Hilbert transformer. If you hit the literature you'll likely find ways to approximate one over a limited range of frequencies. A straight integrator or differentiator will give you a 90 deg phase shift but, of course, the magnitude will vary as 6 dB / octave.
Its indeed kind of sort Hilbert Transform but than totally analog. I can`t find how this can be build with passive parts.
gr. Marcel

Hi Marcel:
You really don't need to bother with acoustics to verify the phase accuracy of a measurement system. Tom's method will work and it has the secondary benefit of teaching you how to properly remove the timeofflight (TOF) delay from a measurement so that only the behavior of the DUT remains. That is essential.
If your system measures electrical domain stuff correctly, it'll measure any other domain correctly as long as the transducer you use (measurement mic) doesn't introduce errors.
Another thing that is extremely helpful in this pursuit is to use a measurement system that can display measured phase as well as the two calculated phase plots; minimum and excess. Using Tom's approach, you will know you've removed TOF correctly when your measured phase plot is parallel to the minimum phase plot. The excess phase plot makes things simpler by subtracting the minimum phase from the measured phase to show the difference. If you end up with at flat horizontal line, there is no difference and your measured and minimum phase plots are parallel.
For those playing along at home, this only works for minimum phase devices, such as this electrical filter phase test described by Tom.

Edit: if an electrically based test to determine the acoustic phase accuracy of a measurement system is your goal, click here (http://forums.prosoundweb.com/index.php?topic=105476.msg983449#msg983449). Also, there is one huge obstacle to phase accuracy with any measurement system  the organic component. :)
Hi all,
First, Marcel thanks for the link to Tom's post about current lag and acoustic phase...it's making me realize yet again 'I know nothing'...
Before even trying to ask questions about that link,
I'd like to swerve to the link that Langston gave, which has Tom's test for checking the accuracy of phase measurements.
Hopefully, the Smaart plot below shows the test correctly. It uses a 4th order HP at 100Hz, a 2nd order LP at 10kHz, and 4ms delay.
The green trace was made with Smaart's delay manually set to 4ms, and I think? looks just like Tom says it should .
But the red trace is from clicking on Delay Finder and letting Smaart set delay to its determination 4.02ms.
This removes the HF rolloff and pretty much takes phase to flat.
My take is that Smaart's delay finder sets reference phase=0 to a frequency within the very high end of the measured spectrum.
But that kills the rolloff which I know is there....
So I guess it just comes down to, where in frequency, does phase=0 really reside ?
Seems to me, that 'phase=0 frequency' really needs to be above nyquist, because nyquist itself is a low pass filter, and anything below nyquist has already shifted in phase.....
I's almost like a little bit of time needs to be subtracted from whatever can be measured to see through to above nyquist....
Am I seeing straight??
Thanks, Mark

Mark,
The setting of the TOF a very important thing, because its the reference for the phase plot. Refering the T=0 to the highest frequency that is possible is a good thing. Usually this is around 20khz (or a little higher).
Langston has a good video about removal the TOF:
https://www.youtube.com/watch?v=LFEwxEnpcos
In the case of your example a sec. order low pass at 10khz, means a phase rotation at 180 degrees as 20khz. This would mean it would take 4.025ms before the peak of the impulse response would arrive, from the ref. 20khz. The peak in the impulse is the midband of the magnitude response, where most energy is.
Langston,
I am still a little confused with that acoustic (point source, flat magn.) measurement. In the case the above example of Mark would be that acoustic measurement, the T=0 at 20khz would be a phase plot with a point at 270deg. at 20Khz, and the midband is 90deg. I doubt if Smaart would show this.
gr. Marcel

Mark,
The setting of the TOF a very important thing, because its the reference for the phase plot. Refering the T=0 to the highest frequency that is possible is a good thing. Usually this is around 20khz (or a little higher).
Langston has a good video about removal the TOF:
https://www.youtube.com/watch?v=LFEwxEnpcos
In the case of your example a sec. order low pass at 10khz, means a phase rotation at 180 degrees as 20khz. This would mean it would take 4.025ms before the peak of the impulse response would arrive, from the ref. 20khz. The peak in the impulse is the midband of the magnitude response, where most energy is.
Langston,
I am still a little confused with that acoustic (point source, flat magn.) measurement. In the case the above example of Mark would be that acoustic measurement, the T=0 at 20khz would be a phase plot with a point at 270deg. at 20Khz, and the midband is 90deg. I doubt if Smaart would show this.
gr. Marcel
Hi Marcel, rightly or wrongly, I've come to the conclusion that correct TOF isn't determined by the impulse peak.
I think it's determined by the impulse initial rise point.....that is, t=0=initial impulse rise.
Because I think a perfect impulse is basically the first sample of all frequencies' initial rise summed together, to form the familiar dirac spike.
And that summation has to include the highest frequency, which has the finest timing and sets the stage for t=0.
So it seems to me t=0 has to be 'peak less one sample time' (or maybe less onehalf?)
This is of course no big deal timewise, peak vs initial rise, at 20kHz.
But it's big at 1kHz, and huge at 100Hz. Trying to align multiways by peak impulse was killing me...which led me to seeing initial rise times.
I don't think phase can be referenced to any part of the spectrum, other than the highest nonrotated frequency. (or perhaps more practically, referenced to the highest frequency "least rotated" by digital antialiasing filters)
Anyway, what's really blowing my mind, is what you linked about speaker movement following current, as opposed to voltage.
With only rudimentary understanding, it makes me wonder if all our phase measurements are off throughout the spectrum, by a constant 90 degrees.
But such wondering seems pretty ridiculous.....even to think that something so fundamental has been being missed...
It makes me think programs such as Smaart account for current vs voltage....
Hey, if it is true that phase follows unaccounted for current, I've just about finished a filter that simply shifts phase 90 degrees across the spectrum LoL

Anyway, what's really blowing my mind, is what you linked about speaker movement following current, as opposed to voltage.
With only rudimentary understanding, it makes me wonder if all our phase measurements are off throughout the spectrum, by a constant 90 degrees.
Hey, if it is true that phase follows unaccounted for current, I've just about finished a filter that simply shifts phase 90 degrees across the spectrum LoL
Above the speaker resonant frequency, the movement of the cone is mass dominated, and acceleration is proportional to coil force which is proportional to current. Acoustic pressure, which is what we measure with a microphone, is proportional to cone velocity (remember that (correction: specific) acoustic impedance (resistance for the radiated part) is pressure divided by particle velocity. So acceleration is proportional to current (which approximates voltage away from the resonant frequency) and pressure is proportional to velocity. Thus, a 90 degree phase shift.
Marc

acoustic impedance (resistance for the radiated part) is pressure divided by particle velocity.
Is acoustic impedance not pressure / volume velocity? Not particle velocity. F

Is acoustic impedance not pressure / volume velocity? Not particle velocity. F
You are correct. Specific acoustic impedance is pressure/velocity. My mistake.
Marc

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 21µs. 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 21µs 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 4fold by measuring at a 192kHz sample rate, but then you're only down to 5.2µs steps  still way too coarse in some cases. At 10kHz, a 5.2µs 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.

1. Smaart measures phase correctly. So does SysTune BTW. Honest.
Good to know. I believe ARTA measures phase correctly, too.
2. That 90 degree current vs. acoustic phase thing is real, but it doesn't matter.
Agree.
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, moreorless). 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 timefrequencyenergy representations, with tone bursts I know what I'm looking at (at least I think I do).
PPS: Mark is so right. I also know nothing. There's no bottom in this pool.
True indeed.
Frank

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

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 10010khz) 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

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 mictospeaker 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 subsample 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...

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 finiteorder systems whose system function is a rational function (the ratio of polynomials in s, the complex frequency variable). A lowpass system (one in which there are no zeros at the origin) has zero phase at the origin. A highpass (or bandpass) 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

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 finiteorder systems whose system function is a rational function (the ratio of polynomials in s, the complex frequency variable). A lowpass system (one in which there are no zeros at the origin) has zero phase at the origin. A highpass (or bandpass) 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

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 (upsidedown 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

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 (upsidedown 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
Sent from my Moto Z (2) using Tapatalk

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.

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...
I agree about the limited utility of absolute phase in daytoday audio work. I find the subject interesting, however, from an intellectual standpoint. It's a dark corner in a room some other parts of which I think I know pretty well.
If I understand your definition it's equivalent to taking the first arrival of the impulse response (IR) as t=0 and then applying the Fourier transform and accepting the phase as is. This seems correct in theory but in realizable measurement we don't have the luxury of integrating out to infinity on a continuous signal in the absence of noise. We're working with (uniform) samples of the IR and we need to window the IR to be able to use a finitesize discrete Fourier transform.
I recall that in some earlier experiments I did the phase at the origin appeared chaotic and at the time I didn't figure out why. I looked at it again and I think it's pretty simple (famous last words...). Ideally the IR has no DC component so H(0) = 0 + 0i (Fourier transform of the IR at zero frequency) and phi(0) = Arg{H(0)} = 0 or is undefined  more on this later. But when we truncate (window) the IR we introduce a slight DC offset. If the real part happens to be positive then phi(0) = 0 is computed as 0 . If the real part happens to be negative then phi(0) is computed as pi. The imaginary part of H(0) is always zero as Im{H(jw)} is an odd function due to the symmetry properties of the Fourier transform.
Now on the phase of zero: I'm not a mathematician by any stretch and a cursory look at my references on complex variables doesn't answer the question of whether Arg{0 + 0i} is defined. If we define Arg{H} as arctan(Im{H} / Re{H}) then it would seem not, as x / 0 is undefined. We're asking what is the direction of a vector of zero length. But if I type Arg(0) into R's interpreter it happily returns 0, so the smart folks there found it at least computationally expedient to define it this way.
In my analysis programs I've inserted code to subtract from the IR the mean (DC component) of the IR after windowing thereby removing the offset. This makes the zerofrequency element of the DFT essentially zero (there are finite precision effects). Then, knowing that H(0) should be 0, I force it to exactly 0, which will cause phi(0) always to evaluate to 0. This should get rid of the chaotic behavior.
Perhaps the best thing to do is to throw out absolute phase and talk, to the extent possible, only in terms of time. There are ways of computing group delay (GD) without unwrapping the phase and numerically differentiating. Furthermore, the GD at zero frequency is well defined and equal to the centroid of the impulse response. Once we have GD we can integrate to get relative phase with full visibility of the time reference. I'm still thinking about all this and welcome comments and guidance.
Frank
Clarification: When I say that the IR has no DC component I'm assuming a highpass system  one with infinite attenuation at DC. This is true of most acoustic measurements but not true in general. A system with H(jw) = 1 for all w clearly passes DC.