# Phase measurement of a speaker system



## AraiYuichi (Dec 8, 2014)

My Basic question is how to measure the correct [phase property] of a speaker system.

I obtained TSP signal thru the DUT speaker and the mic. Then, t=o set at IR peak. This means that the sound fly time is removed. So, The Phase must be displayed correctly, I think. It looks working well.
My question is that [this phase curve] and the [Minimum phase curve] which is generated by [Generate minimum phase button] does not match. Not a small difference in some cases.
I have adjusted IR window setup with several ways. 
So, which is correct? or what is cause of the differences is my question.

Yuichi Arai


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## jtalden (Mar 12, 2009)

Measured at the LP room modes, reflections, and diffraction cause the phase to be chaotic at some frequencies. We often are interested in the direct sound phase response and thus measure and analyze in a way to minimize the room impact. To do this we can place the speaker away from close boundaries, place the mic 1m from the baffle and, if needed, use a frequency dependent window on the resulting measurement. It all really depends on our purpose and thus what info we are looking to obtain. 

Typical common multi-way loudspeakers have crossovers that add significant excess phase to the speaker. The measuring system; mic, soundcard, AVR, etc., can also add a little bit of excess phase if it is not well calibrated. The phase response = minimum phase + excess phase.


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## AraiYuichi (Dec 8, 2014)

Thank you jtalden!

Thanks for your explanation. The best way is to see the same data for better understanding each other. I attached a REW data, for your ref.

This is 4way speaker system and corrected thru PEQ and FIR filters. So, all the phase and time alignment should be done.
Therefore, you can see the flat SPL and very sharp IR, which look ideal.
But, phase is not on the SPL/Phase screen. 
Using the same data, I see almost flat minimum phase curve by using the [Generate minimum phase] on the SPL/Phase screen. 

Why?

Yuichi


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## jtalden (Mar 12, 2009)

The SPL looks great as you noted.
The IR looks great also, but the appearance an IR only gives a hint to us as what is going on at the HF end of the measurement. It is not a good indicator of all the details. That is purpose of all the other charts.
The Phase is as you no doubt saw, linear from 800-22k Hz, but <800Hz the phase delay is rapidly increasing. This is clearly reflected in the step response as well.

























I don't know the equipment and process used. Assuming this setup was done using phase aligned IIR XOs and then applying an FIR phase correction filter to make the phase linear, the error is in the design of the FIR filter. Possibly the XOs were not properly phase aligned to start with. If needed, and you provide some more info on the equipment and process used, I may be able to suggest a method to isolate the problems.


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## AraiYuichi (Dec 8, 2014)

Hi Mr. Jtalden

Thank you for your answer.
1) About the system, this is actually a 4 channel system. The system configuration is as fig.1
Crossovers are 200Hz, 600Hz and 4000Hz. 
2) The process I took is the numbering order on fig.2. This is miniDSP 2x4 HD block diagram.
3) After the signal passed thru the FIR filter, all the phase and the time alignment are adjusted to IR peak which is the center of FIR delay., I think.
4) However, there was one exception. Which is shown on the Fig 3 chart. One of the speaker(B) is not aligned. May be because of larger physical distance from other speakers. 
5) I adjusted this by using Delay function (step 6 on fig.2).
6) This generated the final result as I sent you in the previous mail.

As a bottom line, the IR looks nice, This means that all the phase and time alignment process is mode, I thought.
For your ref. I use REW for PEQ generation and rePhase for FIR.

Then, I got ideal SPL and IR, but not Phase. Why??
One more why is that the [minimum phase] display is fine. So, what is the difference?

I hope can have your comments on this.
Thank you for your advice in advance.

Yuichi


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## jtalden (Mar 12, 2009)

Your basic equipment setup has some similarity to mine. From your process description and the posted mdat, the first concern with the accuracy of the driver delays. The excessive phase rotation measured is unlikely to be completely due to the FIR filter. 

The delays need to be adjusted properly before the FIR filter is designed. It is not correct to set delays only by aligning the 2 impulse peaks. We should instead target close phase tracking through as much of the XO range as possible. This is done before the FIR phase correction filter is designed.

Below are some charts and the mdat of the MR and TW of my right channel as an example. It is the result setting the XO and delay properly. This is an idealized example to demonstrate the target. It took careful adjustment of the XO filters and EQ settings as well as the delay to achieve tracking this close. We only need achieve the best alignment possible for each XO given the XO settings you have chosen. There will likely be crossing of the Phase traces at the XO frequency with some divergences of the traces away from that point. We just want to chose the delay that provides the closest phase tracking possible. Note that, in my chart below, the IR peak of the MR driver lags the TW driver. This is typical of the proper IIR XO setup.

I can help with more detail on the process if needed. Once all the XO delays are confirmed then we can review the rePhase FIR filter design.

























View attachment FR Phase.mdat


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## AraiYuichi (Dec 8, 2014)

I will take a look, and try. Thanks anyway. Yuichi


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## jtalden (Mar 12, 2009)

Yuichi,
FYI - I found reference indicating that there is a 7.5 ms delay capability in the MiniDSP 2x4. That will provide capability for roughly 2.5m of acoustic offsets between the drivers. This should be more than enough to provide proper delays for all 4 drivers. The Woofer is normally the most delayed and would thus be given a delay of 0ms. In your staggered offset configuration possibly it is another driver that is the most delayed. In any case, the most acoustically delayed driver can be set at 0 ms delay. That leaves the entire 7.5 ms delay range to adjust the other drivers appropriately.

John


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## AraiYuichi (Dec 8, 2014)

Hi John

Thank you your suggestion. I understood the delay settings on miniDSP2x4HD.
My approach is to adjust [phase] and [time alignment] by FIR filter with one time. 

One question about the Phase measurement on REW.
What is the difference between [Phase] and [Minimum phase] on the [SPL/Phase screen]. The [Phase] with t=0 at IR peak situation and [Minimum phase] the same? Those look to me different.
[Minimum phase] curve is created based upon SPL property, you said a year ago as far as I remember?? 

Yuichi


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## jtalden (Mar 12, 2009)

AraiYuichi said:


> My approach is to adjust [phase] and [time alignment] by FIR filter with one time.


It seems I misunderstood your design approach. You are designing 8 FIR filters for the drivers. Each filter to correct time delay between drivers and phase rotation within the driver? My understanding of this approach is limited as I have never used it. It is a very popular approach. I would have tried it, but just don't own the needed equipment. Please take the following thoughts accordingly.

I now see the 2x4 can accommodate a 6144 tap size per output channel. This is very limiting particularly in regard to dealing with delays. Considering that you have set delays in the 2x4 to removed most of the timing offset by aligning the IR peaks. That would greatly reduce the tap size wasted on timing delay. You did indicate though that the midrange driver was not time aligned properly. That would suggest that some additional 2x4 delay adjustment on that driver would resolve that problem. The closer the delay timing is to ideal using the 2x4 delay feature, the smaller FIR filter needs to be. 

With only 6144 taps the low frequency phase rotation cannot be fully removed so we need to expect that the phase rotation can only be corrected to be flat for the higher frequencies and not for the bass range. That would explain some of the low frequency phase rotation present in your measurement. 

So my suggestion would be that due to very limited tap size, readjust the delay of at least the midrange horn and recreate that FIR filter. That may improve the overall phase rotation greatly. We should still expect some of that low frequency phase rotation to exist due to the limited tap size. 

More experienced users of this method and this equipment may have a better input for you.



> [Minimum phase] curve is created based upon SPL property, you said a year ago as far as I remember??


Yes, the minimum phase is calculated on the SPL measurement without regard to the measured phase. It reflects the causal phase variation that correlates with the SPL response. The difference between the actual phase response and the calculated minimum phase response is the excess phase response. See Wiki or other more technical references as my understanding doesn't extend very deeply. 



> What is the difference between [Phase] and [Minimum phase] on the [SPL/Phase screen]. The [Phase] with t=0 at IR peak situation and [Minimum phase] the same? Those look to me different.


They are different; different by the impact of the excess phase in the system. In your measurements you have successfully eliminated most all the excess phase in the higher frequencies. There remains only a minuscule amount there. 

Is it the minor 70° spread in the response at 20k that is concerning you? That is practically nothing in group delay due the small wavelength. It is no practical concern. I suspect it may be due to the measurement extending to 22kHz where the SPL is falling off rapidly. I am unsure as to the exact cause, but one source could be that the inductance of the TW voice coil is adding excess phase at those frequencies. It could also be related to the impact of other aspects of the driver design or even the horn design. Drivers are basically minimum phase devices, but not entirely. They are likely to show excess phase particularly as they are pushed out of their bandpass range. 

I designed my FIR filter to correct the actual phase response without regard for the minimum phase. It just makes sense to me that we want the sound to arrive at LP in its proper timing regardless if the SPL falls off due to the house curve or system bandpass limits. This is different from the generally offered advice to target minimum phase. I have not seen others suggesting this though. I just have not yet understood why minimum phase is preferable from a theoretical perspective. In practice, either approach should be perfectly fine. We should all agree that it is indistinguishable at the high frequencies. There may be an arguable difference in the bass range where some report hearing differences.


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## AraiYuichi (Dec 8, 2014)

Hellow

I understood what you said. Those are very informative to me. Thank you.

Here, I am not questioning you, but try to explain what I did.

Yes, I feel that the number of taps is smaller to my application. I use miniDSP 2x4 HD. Number of taps per channel which is allocated is max 1024. This number is a little bit short to correct SPL in lower frequency zone.
Considering the 2x4 HD's sampling frequency [96KHz] and max. taps [1024] give s us FIR delay is approx. 10msec. Which means a FIR can adjust timing 5msec assuming IR peak is set at the center of the filter delay. This is a reason why I assumed all 
four speakers time-alignment those are located within 170 cm can be done.
But actually only the Mid Horn was not time aligned. Others were well matched.
Then, I forced to align arrival timing of the Mid Horn by using Delay function of 2x4 HD. Actually, the delay was added to the lest of speakers. The result was fine as I sent. The IR looks perfect, SPL, too.
I assumed phase must be perfect because IR is good. But not. What is the situation? 
when all the frequency components get the IR center without phase mismatch condition.

Thank you anyway. You gave me a lots of idea to try. I appreciate very much.

Yuichi


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## jtalden (Mar 12, 2009)

Yuichi,
Very good.
Yes, the very small number of taps significantly limits the ability for SPL and phase correction of the lower frequencies. Hopefully, since you corrected the delay on the midrange horn timing, the phase rotation was improved at least a little bit. The step response should look much better. Remember that the appearance of the IR doesn't mean to much. The SPL, phase and step charts are much more informative. Get those right and enjoy the music! 

I'm glad I could at least provide some helpful comments. Good luck.

John


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## AraiYuichi (Dec 8, 2014)

Hi,

One additional question.

In case of 2 way system, we can align [Phase] and [Time alignment] by using FIR filter at the same time.

In case of 2 channel system, we design FIR filter for each channel separately to correct the phase.
In this case, the [Time alignment] also automatically made?
My experiment shows that both [Phase] and [Time alignment] are made. 

Yuichi


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## jtalden (Mar 12, 2009)

I am a little unclear of the situation so I hope my comments address your question.



AraiYuichi said:


> In case of 2 channel system, we design FIR filter for each channel separately to correct the phase.


If the objective is only to remove the excess phase or total phase rotation of L, R channels in a stereo situation then only one filter is needed. With identical multiway speakers on each channel the direct sound phase rotation will be identical. The filter can be designed on either channel and applied to both of them.



> In this case, the [Time alignment] also automatically made?


A phase correction filter has no net effect on timing. That is, it adds a fixed delay corresponding to the sample rate and the number of taps in the filter. So long as the filters on both channels are identical in this regard the delay is identical on both channels.



> My experiment shows that both [Phase] and [Time alignment] are made.


?? Maybe you are also including EQ filters that are different for each channel in the FIR filters. In that case it is necessary to assure the location of the filter impulse peak is at the same tap location for both FIR filters. The channel delay timing would otherwise be different depending on the tap location of the IR peak and the sample rate. rePhase allows the IR peak location to be locked to the center of the filter or to another location with various setting options. See the 'Centering' Section on the rePhase main screen. If the 'energy' setting is selected then there is no assurance that the peak locations of the 2 filters will be similar. Your can look at the 2 filters in Audacity or similar to confirm the IR peak locations and also help to choose where the IR peaks should best be located to optimize the utilization of the available tap size.


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## AraiYuichi (Dec 8, 2014)

Your explanation clears my question. Thanks a lot,

Yuichi


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