Dear All,
Anybody who ever measured a loudspeaker driver using MLS or ESS measurement systems faced a problem with placement of FFT window. In order to obtain true minimum-phase phase response, the FFT window must be located where it should be.
I have produced two papers describing the method of dealing with this issue.
In the first paper, I introduce Inverse Hilbert-Bode Transform and it’s application.
https://www.bodziosoftware.com.au/IHBT_White_Paper.pdf
The second paper describes an automated method for extracting minimum-phase phase response and more.
https://www.bodziosoftware.com.au/Automated_IHBT.pdf
If you have any questions, please contact me on
bohdan@bodziosoftware.com.au
Best Regards,
Bohdan
Anybody who ever measured a loudspeaker driver using MLS or ESS measurement systems faced a problem with placement of FFT window. In order to obtain true minimum-phase phase response, the FFT window must be located where it should be.
I have produced two papers describing the method of dealing with this issue.
In the first paper, I introduce Inverse Hilbert-Bode Transform and it’s application.
https://www.bodziosoftware.com.au/IHBT_White_Paper.pdf
The second paper describes an automated method for extracting minimum-phase phase response and more.
https://www.bodziosoftware.com.au/Automated_IHBT.pdf
If you have any questions, please contact me on
bohdan@bodziosoftware.com.au
Best Regards,
Bohdan
I really do not understand this but i do have some problems with phase responses when doing on and many off-axis measurements to be used for crossover simulation. I must first find the nearest driver and angle to set the time window start and then use this start setting for all drivers and measurements. I guess there would be to much errors and very time consuming if i had to set new time window for each driver/measurement
Hi Jim, the discussion was via PMs so can't provide a link.
And really, it was a bit of one way...me being an advocate of the kind of thing Bohdan is doing, with the other saying it's not real world relevant.
I don't have the AES paper i referred to in the PM discussion because it has a fee, but AES provides an entire anthology collection from the author Dick Heyser for free. (which makes no sense why they would charge for an article within it.)
Anyway, here's the full Heyser collection.
https://www.aes.org/technical/documents/openaccess/AES_TimeDelaySpectrometry.pdf
These are the articles in the collection i was discussing with the other party.
Determining the Acoustic Position for Proper Phase Response of Transducers.
(JAES, vol. 32, no. 1/2, pp. 23-25, 1984 January/February) ................................ 182
Comments on “Determining the Acoustic Position for Proper Phase Response of
Transducers.” Stanley P. Lipshitz and John Vanderkooy. (JAES, vol. 33, no. 6,
pp. 463-465, 1985 June) ....................................................................................... 185
Author’s Reply. Richard C. Heyser. (JAES, vol. 33, no. 6, pp. 465-466, 1985
June)......................................................................................................................... 187
And really, it was a bit of one way...me being an advocate of the kind of thing Bohdan is doing, with the other saying it's not real world relevant.
I don't have the AES paper i referred to in the PM discussion because it has a fee, but AES provides an entire anthology collection from the author Dick Heyser for free. (which makes no sense why they would charge for an article within it.)
Anyway, here's the full Heyser collection.
https://www.aes.org/technical/documents/openaccess/AES_TimeDelaySpectrometry.pdf
These are the articles in the collection i was discussing with the other party.
Determining the Acoustic Position for Proper Phase Response of Transducers.
(JAES, vol. 32, no. 1/2, pp. 23-25, 1984 January/February) ................................ 182
Comments on “Determining the Acoustic Position for Proper Phase Response of
Transducers.” Stanley P. Lipshitz and John Vanderkooy. (JAES, vol. 33, no. 6,
pp. 463-465, 1985 June) ....................................................................................... 185
Author’s Reply. Richard C. Heyser. (JAES, vol. 33, no. 6, pp. 465-466, 1985
June)......................................................................................................................... 187
Sure,
the gentlemen (who knows filters very very well imo) talked about that it is difficult to locate an acoustic center , because the acoustic center changes with frequency, whether in a horn or a direct radiator.
And he felt the exchange by Heyser, Lipschitz, and Vanderkooy is purely academic, bearing little relevance to the real world.
My reply to that point-of-view was:
"Yep, my understanding is acoustic phase moves (lags) by 90 degrees, and is frequency dependent, making acoustic center location practically impossible.
I think linear phase can remove that frequency dependent phase lag, and thereby make a stable acoustic center.
The trick i'm finding, is nailing exactly what TOF to phase linearize. TOF found via Hilbert transform, or TOF found more in line with Heyser's paper ?
Which makes it all very real world to me."
I also attached an old Tom Danley forum post, with parts i think that fit that discussion......
Here it is...it's quite a good read on several topics
> > Hi all
> >
> > I am not sure how many Joes are in the "its all magic" camp and how many
> > are interested in how things really work but so far as how a woofer
> > really works, this has been known for some time. Authors like Benson,
> > Heyser have written very good books and papers on the subject.
> > At least from being able to model / predict the performance of a real
> > speaker from its electroacoustic equivalent circuit, there are no
> > missing links or mysteries, just a few things mfr.'s chose not to
> > explain and or things some choose not to look at..
> > Perhaps this explanation will help.
> >
> > The number one misconception about woofers is that moving mass has
> > something to do with "speed" of response or its high frequency limit.
> > It does not, at least directly.
> > What mass effects is efficiency and also the shape of the low frequency
> > roll off.
> >
> > A radiator that is small compared to the wavelength it is producing,
> > experiences an increasing acoustic load with increasing frequency (one
> > of the few places on sees a frequency dependent resistance with out a
> > reactance). That radiator in an infinite baffle, driven at a constant
> > velocity
> > will produce a +6 dB oct rising response because its radiation
> > efficiency increases with frequency.
> > To make a driver like this have "flat response", we must roll off the
> > voltage response 6 dB per octave, one pole.
> > This is done by having a much larger amount of mass or weaker motor such
> > that above some point velocity control is lost and then with increasing
> > frequency, the velocity falls 6 dB oct. It is this range, where the
> > velocity falls 6 dB /oct that one has flat response.
> > Electrically, this speaker looks like and acts like an R/C filter, the R
> > is the coil R+the amplifier source R and the C is the moving mass of the
> > speaker reflected through the motor, which looks /acts like a capacitor.
> >
> > Since the moving part is the C, it is the voltage across it (the voltage
> > /velocity output) which falls 6 dB /oct, which is canceled out by the
> > changing radiation resistance and now gives flat response. The -90
> > degree phase shift of the slope is not canceled out as the radiation
> > resistance is pure resistance. Changing the size of the C (moving mass)
> > has no effect on the slope angle, just its level and starting point.
> >
> > 99% of the people do not realize that when a point source has flat
> > response, its mid band acoustic phase lags behind the input signal by
> > about -90 degrees (once all fixed time delays are accounted for). This
> > broad band lag is equal to a time delay who's amount increases with
> > decreasing frequency. This -90 degree operation is how some of the
> > simpler measuring systems "determine" acoustic phase, it is a Hilbert
> > transform of the amplitude and at low frequencies for a simple piston,
> > this is a safe assumption.
> >
> > Consider how a normal "perfect" speaker spreads out a signal in time.
> > Make an imaginary signal that has equal amplitude content from 100 Hz to
> > 25 Hz, a specific waveshape which has this property.
> > Take an imaginary perfect flat response speaker who's upper and lower
> > cutoffs are way past our needed bandwidth.
> > This mass controlled "flat" response speaker has a -90 degree lag or
> > delay, at 100 Hz the phase shift is equal to a source 2.83 feet behind
> > the speaker cone, at 50 Hz, the delay is equal to 5.66 feet, at 25 Hz is
> > equal to 11.32 feet and so on.
> > This test signal's wave shape defines the input "time" of each frequency
> > component.
> > When reproduced, the highest frequency component at 100 Hz emerges from
> > the radiator 2.5 ms AFTER the signal arrived at the driver terminals.
> > At 50 Hz, this component emerges 5 ms AFTER the signal hit the terminals
> > and at 25 Hz, the signal emerges after 10 ms and so on.
> > With the driver spreading the signals frequency components out in time,
> > it is simply not possible to retain the same waveshape as the input
> > signal, lower frequencies arrive progressively later in time than the
> > original signal.. Any signal reproduced is done so with the spectrum
> > rearranged in time by the drivers acoustic phase response.
> >
> >
> > If one had a driver which had a very strong motor or a normal motor but
> > very low moving mass, one gets an "over damped" response.
> > This term is from filter design meaning that it is not optimally flat,
> > excessively damped, rolling off too soon and gradually
> > Should the slope of the response reach 6 dB per octave, the driver is
> > operating in the Velocity controlled mode, while the response is not
> > flat, the acoustic phase DOES track the input signal (zero degrees) and
> > the different frequency components are not spread out in time.
> > The waveshape of the input signal is more closely replicated as the
> > frequency components are in the original "time" although the amplitudes
> > are off 6 dB/oct. Each 3 dB /oct change in the slope produces a 45
> > degree change in phase.
> >
> > An over damped response more closely retains the time information where
> > a flat amplitude response cannot.
> >
> > A proper LF horn can have flat acoustic response AND roughly zero degree
> > acoustic phase.
> >
> > For a person more sensitive to "time errors", they will likely find an
> > over damped system more realistic.
> > For a person more sensitive to "amplitude errors" the traditional "flat
> > response" system will be more satisfying.
> > For the person lucky enough to have heard a proper lf horn system, you
> > have heard that one can have "lightning fast" sounding bass and still
> > make your pant legs flap.
> >
> > A normal "flat" response point source speaker HAS this kind of delay
> > built right in and it is unavoidable (currently).
> > All conventionally driven point source speakers MUST have the phase
> > shift / delay if they are to have flat frequency response (dictated by
> > the falling velocity, acceleration controlled response needed to offset
> > the changing radiation resistance with frequency).
> >
> > Additional reactance's can alter this phase relationship.
> > For example above midband at the point in the impedance called Rmin, the
> > electrical series "L" is equal but opposite the reflected moving mass
> > (capacitive reactance) of the driver thus canceling each out and being
> > resistive (no phase shift).
> > Above that frequency, the series Inductance dominates and produces a
> > roll off with an inductive reactance.
> > At the bottom end ot the response, for a simple sealed box, there is a
> > point where the parallel spring or "compliance" of the box and driver
> > are equal but opposite the moving mass and this point is also resistive
> > (at box resonance). Below that frequency, the spring constant dominates
> > (an inductive reactance) and the acoustic phase leads
> >
> > More complications from non perfect drivers and alignments..
> >
> > In pro sound it is a common practice to evaluate subwoofers with a kick
> > drum signal.
> > Such a signal has a wide spectrum however it makes a bad test signal for
> > a subwoofer alone.
> > Nearly always, the subwoofer with the best "snap" or attack is the one
> > with the greatest distortion and or the highest low cutoff.
> > Clearly, the ear hears the added hf content and judges it to be more
> > lifelike.
> > In actual operation, the subwoofer is mated with midbass speakers who's
> > job it is to produce the spectrum above the subwoofer.
> > Now, with the actual drum signal being produced in the upper ranges, the
> > subwoofers formerly desirable distortion spectrum interferes with the
> > real drum signal. Now, the subwoofer with the least distortion will
> > often have the best subjective sound.
> >
> > A subwoofer can be made with a under damped low frequency corner, this
> > puts a bump in the response right before roll off.
> > Subjectively, this can make a woofer sound even slower and the "decay"
> > of the too high Q takes more time.
> >
> > Remember that it is acceleration which produces sound, it is the
> > amplifier current which produces the force which produces the
> > acceleration.
> > While few of you may have a TEF machine or are able to measure real
> > acoustic phase, most of you can plot the current phase angle with
> > respect to the voltage drive signal for a woofer. The phase shift curve
> > of the current vs freq will have the same shape as the acoustic phase
> > shift (although the degrees are different). If one had a speaker that
> > was flat midband, one could look at the current phase in that range and
> > assume the acoustic phase magnitude was about -90 deg .
> > This acoustic phase IS time, it is essentially ignored in discussions
> > about how speakers sound, yet it accounts for most of what you guys and
> > others are talking about.
> >
> >
> > Tom Danley
the gentlemen (who knows filters very very well imo) talked about that it is difficult to locate an acoustic center , because the acoustic center changes with frequency, whether in a horn or a direct radiator.
And he felt the exchange by Heyser, Lipschitz, and Vanderkooy is purely academic, bearing little relevance to the real world.
My reply to that point-of-view was:
"Yep, my understanding is acoustic phase moves (lags) by 90 degrees, and is frequency dependent, making acoustic center location practically impossible.
I think linear phase can remove that frequency dependent phase lag, and thereby make a stable acoustic center.
The trick i'm finding, is nailing exactly what TOF to phase linearize. TOF found via Hilbert transform, or TOF found more in line with Heyser's paper ?
Which makes it all very real world to me."
I also attached an old Tom Danley forum post, with parts i think that fit that discussion......
Here it is...it's quite a good read on several topics
> > Hi all
> >
> > I am not sure how many Joes are in the "its all magic" camp and how many
> > are interested in how things really work but so far as how a woofer
> > really works, this has been known for some time. Authors like Benson,
> > Heyser have written very good books and papers on the subject.
> > At least from being able to model / predict the performance of a real
> > speaker from its electroacoustic equivalent circuit, there are no
> > missing links or mysteries, just a few things mfr.'s chose not to
> > explain and or things some choose not to look at..
> > Perhaps this explanation will help.
> >
> > The number one misconception about woofers is that moving mass has
> > something to do with "speed" of response or its high frequency limit.
> > It does not, at least directly.
> > What mass effects is efficiency and also the shape of the low frequency
> > roll off.
> >
> > A radiator that is small compared to the wavelength it is producing,
> > experiences an increasing acoustic load with increasing frequency (one
> > of the few places on sees a frequency dependent resistance with out a
> > reactance). That radiator in an infinite baffle, driven at a constant
> > velocity
> > will produce a +6 dB oct rising response because its radiation
> > efficiency increases with frequency.
> > To make a driver like this have "flat response", we must roll off the
> > voltage response 6 dB per octave, one pole.
> > This is done by having a much larger amount of mass or weaker motor such
> > that above some point velocity control is lost and then with increasing
> > frequency, the velocity falls 6 dB oct. It is this range, where the
> > velocity falls 6 dB /oct that one has flat response.
> > Electrically, this speaker looks like and acts like an R/C filter, the R
> > is the coil R+the amplifier source R and the C is the moving mass of the
> > speaker reflected through the motor, which looks /acts like a capacitor.
> >
> > Since the moving part is the C, it is the voltage across it (the voltage
> > /velocity output) which falls 6 dB /oct, which is canceled out by the
> > changing radiation resistance and now gives flat response. The -90
> > degree phase shift of the slope is not canceled out as the radiation
> > resistance is pure resistance. Changing the size of the C (moving mass)
> > has no effect on the slope angle, just its level and starting point.
> >
> > 99% of the people do not realize that when a point source has flat
> > response, its mid band acoustic phase lags behind the input signal by
> > about -90 degrees (once all fixed time delays are accounted for). This
> > broad band lag is equal to a time delay who's amount increases with
> > decreasing frequency. This -90 degree operation is how some of the
> > simpler measuring systems "determine" acoustic phase, it is a Hilbert
> > transform of the amplitude and at low frequencies for a simple piston,
> > this is a safe assumption.
> >
> > Consider how a normal "perfect" speaker spreads out a signal in time.
> > Make an imaginary signal that has equal amplitude content from 100 Hz to
> > 25 Hz, a specific waveshape which has this property.
> > Take an imaginary perfect flat response speaker who's upper and lower
> > cutoffs are way past our needed bandwidth.
> > This mass controlled "flat" response speaker has a -90 degree lag or
> > delay, at 100 Hz the phase shift is equal to a source 2.83 feet behind
> > the speaker cone, at 50 Hz, the delay is equal to 5.66 feet, at 25 Hz is
> > equal to 11.32 feet and so on.
> > This test signal's wave shape defines the input "time" of each frequency
> > component.
> > When reproduced, the highest frequency component at 100 Hz emerges from
> > the radiator 2.5 ms AFTER the signal arrived at the driver terminals.
> > At 50 Hz, this component emerges 5 ms AFTER the signal hit the terminals
> > and at 25 Hz, the signal emerges after 10 ms and so on.
> > With the driver spreading the signals frequency components out in time,
> > it is simply not possible to retain the same waveshape as the input
> > signal, lower frequencies arrive progressively later in time than the
> > original signal.. Any signal reproduced is done so with the spectrum
> > rearranged in time by the drivers acoustic phase response.
> >
> >
> > If one had a driver which had a very strong motor or a normal motor but
> > very low moving mass, one gets an "over damped" response.
> > This term is from filter design meaning that it is not optimally flat,
> > excessively damped, rolling off too soon and gradually
> > Should the slope of the response reach 6 dB per octave, the driver is
> > operating in the Velocity controlled mode, while the response is not
> > flat, the acoustic phase DOES track the input signal (zero degrees) and
> > the different frequency components are not spread out in time.
> > The waveshape of the input signal is more closely replicated as the
> > frequency components are in the original "time" although the amplitudes
> > are off 6 dB/oct. Each 3 dB /oct change in the slope produces a 45
> > degree change in phase.
> >
> > An over damped response more closely retains the time information where
> > a flat amplitude response cannot.
> >
> > A proper LF horn can have flat acoustic response AND roughly zero degree
> > acoustic phase.
> >
> > For a person more sensitive to "time errors", they will likely find an
> > over damped system more realistic.
> > For a person more sensitive to "amplitude errors" the traditional "flat
> > response" system will be more satisfying.
> > For the person lucky enough to have heard a proper lf horn system, you
> > have heard that one can have "lightning fast" sounding bass and still
> > make your pant legs flap.
> >
> > A normal "flat" response point source speaker HAS this kind of delay
> > built right in and it is unavoidable (currently).
> > All conventionally driven point source speakers MUST have the phase
> > shift / delay if they are to have flat frequency response (dictated by
> > the falling velocity, acceleration controlled response needed to offset
> > the changing radiation resistance with frequency).
> >
> > Additional reactance's can alter this phase relationship.
> > For example above midband at the point in the impedance called Rmin, the
> > electrical series "L" is equal but opposite the reflected moving mass
> > (capacitive reactance) of the driver thus canceling each out and being
> > resistive (no phase shift).
> > Above that frequency, the series Inductance dominates and produces a
> > roll off with an inductive reactance.
> > At the bottom end ot the response, for a simple sealed box, there is a
> > point where the parallel spring or "compliance" of the box and driver
> > are equal but opposite the moving mass and this point is also resistive
> > (at box resonance). Below that frequency, the spring constant dominates
> > (an inductive reactance) and the acoustic phase leads
> >
> > More complications from non perfect drivers and alignments..
> >
> > In pro sound it is a common practice to evaluate subwoofers with a kick
> > drum signal.
> > Such a signal has a wide spectrum however it makes a bad test signal for
> > a subwoofer alone.
> > Nearly always, the subwoofer with the best "snap" or attack is the one
> > with the greatest distortion and or the highest low cutoff.
> > Clearly, the ear hears the added hf content and judges it to be more
> > lifelike.
> > In actual operation, the subwoofer is mated with midbass speakers who's
> > job it is to produce the spectrum above the subwoofer.
> > Now, with the actual drum signal being produced in the upper ranges, the
> > subwoofers formerly desirable distortion spectrum interferes with the
> > real drum signal. Now, the subwoofer with the least distortion will
> > often have the best subjective sound.
> >
> > A subwoofer can be made with a under damped low frequency corner, this
> > puts a bump in the response right before roll off.
> > Subjectively, this can make a woofer sound even slower and the "decay"
> > of the too high Q takes more time.
> >
> > Remember that it is acceleration which produces sound, it is the
> > amplifier current which produces the force which produces the
> > acceleration.
> > While few of you may have a TEF machine or are able to measure real
> > acoustic phase, most of you can plot the current phase angle with
> > respect to the voltage drive signal for a woofer. The phase shift curve
> > of the current vs freq will have the same shape as the acoustic phase
> > shift (although the degrees are different). If one had a speaker that
> > was flat midband, one could look at the current phase in that range and
> > assume the acoustic phase magnitude was about -90 deg .
> > This acoustic phase IS time, it is essentially ignored in discussions
> > about how speakers sound, yet it accounts for most of what you guys and
> > others are talking about.
> >
> >
> > Tom Danley
Thank you Mark.
Maybe it's academic. There is a lot of example of fine sounding passive loudspeakers which didn't bother with that specific design area ( or are 'sloppy' about this).
I don't think this should be overlooked though and if we have access to methods and technique we can implement to take care of it then why not?
Of course it point to the direction you mentioned in the exchange you had ( dsp, multiamp and fir).
Very nice post from T.Danley.
Definitely he is very good at popularize not easy to grasp concepts and make interlinks between them simple and obvious.
Maybe it's academic. There is a lot of example of fine sounding passive loudspeakers which didn't bother with that specific design area ( or are 'sloppy' about this).
I don't think this should be overlooked though and if we have access to methods and technique we can implement to take care of it then why not?
Of course it point to the direction you mentioned in the exchange you had ( dsp, multiamp and fir).
Very nice post from T.Danley.
Definitely he is very good at popularize not easy to grasp concepts and make interlinks between them simple and obvious.
Hi,
It should be clear to the reader, that my papers define "acoustic centre" as a point in space, where the acoustic radiator's (the driver) transfer function assumes minimum-phase characteristics. Nothing more and nothing less.
Since the loudspeaker is a minimum-phase device, this definitions seems quite obvious.
It can be determined from measurements, and it fits well into loudspeaker CAD modelling software.
Up until now, the stumbling block was the difficulties with accurate extraction of the minimum-phase phase response. The method I described, removes this problem, so you can accurately extract minimum-phase and then calculate the acoustic centre (as defined above) from there.
Best Regards,
Bohdan
It should be clear to the reader, that my papers define "acoustic centre" as a point in space, where the acoustic radiator's (the driver) transfer function assumes minimum-phase characteristics. Nothing more and nothing less.
Since the loudspeaker is a minimum-phase device, this definitions seems quite obvious.
It can be determined from measurements, and it fits well into loudspeaker CAD modelling software.
Up until now, the stumbling block was the difficulties with accurate extraction of the minimum-phase phase response. The method I described, removes this problem, so you can accurately extract minimum-phase and then calculate the acoustic centre (as defined above) from there.
Best Regards,
Bohdan
I hope to try the software sometime soon.
This thread got me thinking (dangerous i know Lol), and i tried a new raw measurement technique yesterday, with high success so far.
I put a steep linear phase low pass in place for each driver, at a distance above where i intend to low-pass, and far enough up i still get repeatable TOF measurements.
Cleans up all the higher frequency gack, that tries to dominate the impulse response, and force phase rotation down low.
And gives me repeatable smiley-face, flattish phase curves thru the driver's intended passband.
The TOF's to those phase curves seems to more accurately reflect timing to the apparent acoustic center. (Less than usual variation between measurements)
The temporary lin-phase low-pass gets the same size FIR file as the permanent file which has its lower intended lowpass (again lin-phase).
Heck, i don't even have to change delays between raw and processed measurements anymore. Wish i'd thought of this years ago !
Thx again for the papers; and for getting my mellon churning
See any issues with this technique?
This thread got me thinking (dangerous i know Lol), and i tried a new raw measurement technique yesterday, with high success so far.
I put a steep linear phase low pass in place for each driver, at a distance above where i intend to low-pass, and far enough up i still get repeatable TOF measurements.
Cleans up all the higher frequency gack, that tries to dominate the impulse response, and force phase rotation down low.
And gives me repeatable smiley-face, flattish phase curves thru the driver's intended passband.
The TOF's to those phase curves seems to more accurately reflect timing to the apparent acoustic center. (Less than usual variation between measurements)
The temporary lin-phase low-pass gets the same size FIR file as the permanent file which has its lower intended lowpass (again lin-phase).
Heck, i don't even have to change delays between raw and processed measurements anymore. Wish i'd thought of this years ago !
Thx again for the papers; and for getting my mellon churning
See any issues with this technique?
http://www.excelsior-audio.com/Publications/Phase_Response_&_Receive_Delay.pdf
This is a great article by Charlie Hughes and I believe the answer to your question Mark is found in pages four and five.
I guess I have taken having TEF for granted all these years for it’s ease of use in this respect.
Barry.
This is a great article by Charlie Hughes and I believe the answer to your question Mark is found in pages four and five.
I guess I have taken having TEF for granted all these years for it’s ease of use in this respect.
Barry.
Is a loudspeaker driver a minimum phase device, or is it approximately minimum phase?
Meaning; does every driver behave as minimum phase to the extent we can measure? or are most drivers close enough to minimum phase that we can make the convenient assumption that they are minimum phase?
This is not posed as a rhetorical question. I don't know the answer to this, and I have always been curious about the assumption that drivers are minimum phase devices... and how far we can take that assumption.
j.
Meaning; does every driver behave as minimum phase to the extent we can measure? or are most drivers close enough to minimum phase that we can make the convenient assumption that they are minimum phase?
This is not posed as a rhetorical question. I don't know the answer to this, and I have always been curious about the assumption that drivers are minimum phase devices... and how far we can take that assumption.
j.
Bohdan - it is a very cool paper, and a useful tool.. Thanks!
Your paper answered a small mystery I had with some of my measurements:
When I used a 2-channel audio interface + ARTA + Audix TM1 mic, I was able to measure (directly measure) a TOF difference between the mid driver and the tweeter of 84 u-sec, which is 28.8 mm difference in the acoustic centers.
When I used an OmniMic USB mic, I of course do not capture a valid "time of flight" measurement, so I use the Jeff Bagby method: Box
This method uses inference to iteratively march toward the offset values which most closely reproduce the responses of the tweeter and mid driver.
Sometimes these two methods agreed to within 1 mm. But recently the best agreement I could get was 7.5 mm.
Now I know why thanks to the Bohdan paper. The sampling rate is 48k. This means I get a sample every 20.8 usec, which is equivalent to 7.1 mm… this is the resolution limit of my measurement system, both for the OmniMic and the 2-channel audio interface + ARTA + Audix TM1.
Nice to have that mystery cleared up
j.
Your paper answered a small mystery I had with some of my measurements:
When I used a 2-channel audio interface + ARTA + Audix TM1 mic, I was able to measure (directly measure) a TOF difference between the mid driver and the tweeter of 84 u-sec, which is 28.8 mm difference in the acoustic centers.
When I used an OmniMic USB mic, I of course do not capture a valid "time of flight" measurement, so I use the Jeff Bagby method: Box
This method uses inference to iteratively march toward the offset values which most closely reproduce the responses of the tweeter and mid driver.
Sometimes these two methods agreed to within 1 mm. But recently the best agreement I could get was 7.5 mm.
Now I know why thanks to the Bohdan paper. The sampling rate is 48k. This means I get a sample every 20.8 usec, which is equivalent to 7.1 mm… this is the resolution limit of my measurement system, both for the OmniMic and the 2-channel audio interface + ARTA + Audix TM1.
Nice to have that mystery cleared up
j.