Linear phase discussion

Discussion in 'Speakers' started by Serious, Jun 21, 2017.

  1. Serious

    Serious Inquisitive Frequency Response Plot

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    This doesn't really belong here, but I still want to reply to UB. This should probably be moved somewhere else.

    I think we are talking about different things here. It's not about picking one thing. Obviously a perfectly flat FR, perfectly linear phase would be best in terms of measurements.
    Yes, this is what I was talking about. I think I got confused a bit here. All I really wanted to say is this:
    HD800 free air.jpg
    Here you can see the phase response and the minimum phase response. I used an old HD800 free air measurement I had for this example, but it really doesn't matter which headphone, which coupler, etc. This is just an example and the measurement as such isn't the most accurate.*
    As you can see the phase response tracks the minimum phase response (calculated from the FR) perfectly - the excess phase is 0. The slight deviation is probably from stuff such as ADC, DAC and other general measurement setup issues. The time-delay might also not be set 100% perfectly as there's a tiny bit of HF droop at >30kHz, but you get what I mean.
    You will get the same result with a single-driver, single diaphragm speaker in a sealed box, infinite baffle, OB, etc. But you will not get the same result with most speakers and their crossovers and drivers that aren't time aligned. How much this matters is a different issue.

    Here's a measurement of an old two way speaker I have. I think the crossover is around 1.3kHz and both drivers are connected in the same polarity. I think this one might actually be a 3rd order design, though. The step response looks similar in shape to the one @Marvey showed us. Again, this isn't really about the specific measurements, it's about the overall picture. I had to quite aggressively window the measurements because when I measured these I didn't make any attempts to get close to anechoic conditions, despite measuring them outdoors. This is why the FR starts to drop off below 400Hz.
    Two way speaker.jpg
    The range below the crossover frequency is delayed by multiple tenths of a ms.

    *Hahaha, I bet some of you will also notice something weird about the measurement. But this doesn't really matter here. It was just a random measurement I picked.
     
    Last edited: Jun 21, 2017
  2. ultrabike

    ultrabike Measurbator - Admin

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    So creating a new thread for this.

    The deviations between the minimum phase equivalent and the actual phase response are more than likely due to the driver (and maybe the driven volume or room or whatever), not necessarily the DAC or ADC.

    You will not get a continuous phase with many closed full size headphones and some over the ear ones. Some full size open headphones are also not continuous in the phase. I will look at some of my measurements, but for example, I don't think most Grados are continuous in the phase.

    As far as results with multi-driver speakers and their crossovers, I though the JBL LSR plots by @Marvey showed no discontinuities. At least not obvious ones. I can later go dig my MR measurements.

    Bare in mind that due to room interactions, one might have to kiss smooth phase goodbye, whatever random driver one chooses, OB, full range pureness, horny stuff and so on.
     
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  3. Serious

    Serious Inquisitive Frequency Response Plot

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    Might be, but I think even when there are resonances with ringing in the CSDs there is still almost no difference. Even with crappy 20$ Superlux headphones that have nasty ringing the excess phase response that I measured is virtually 0 across the whole range. I wouldn't worry about small 5° phase shifts here or there. The phase response does look wild, but so does the minimum phase response.

    As I said, I'm pretty sure that wasn't the actual phase response of the speakers, but the minimum phase response created from the FR. The step response looks like there's a lot of phase shift around the crossover frequency.

    For example here are a few measurements for 2nd and 4th order crossovers:
    http://www.troelsgravesen.dk/DiscoveryW18_crossovers.htm
    Note how the LR4 crossover has a step response that looks very similar to the JBL LSR305
    Troels sometimes likes to show the minimum phase response for some of his speaker projects, something that I think is of no use when the actual phase response will look very different. In this case you can see the phase response of the individual drivers.

    I prefer to think of them as two different issues. First you have the FR and phase response of the speaker and then you have whatever the room adds to it. Two different issues, but both get mixed together when you take measurements in-room. One has to take into account the room for voicing the speaker, but the speaker measurements should still be done in anechoic conditions. You will still get your original response as the direct sound in-room, but you also have the reflections.
     
  4. ultrabike

    ultrabike Measurbator - Admin

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    I'll see what I can dig from my measurements later tonite.

    Cross-over should matter, and it's obvious that if the individual impulse responses of the drivers don't align one will have a discontinuity. The alignment might be pick up position dependent. It's something to look at.

    Again, don't assume just because you have a single driver that things are minimum phase, continuous and all around awesome-sauce. On first pass it seems that could be the case. But one has to see that it does, and indeed not all things out there behave the same way. Most headphones are single driver animals. And some suck ballz in the phase response (no room interaction to blame, the assembly is part of the headphone).
     
    Last edited: Jun 21, 2017
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  5. ultrabike

    ultrabike Measurbator - Admin

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    Alright, here is the phase response of the MR5 MK3 (semi-anechoic i.e. park measurements).Based on the phase plot, what's the cross-over frequency?

    Phase.png

    The green are both frequency response magnitude and phase. The white plot is the excess phase and the gray is the minimum phase.

    These were taken about 1 meter away from the tweeter, 0 degrees azimuth.
     
    Last edited: Jun 22, 2017
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  6. ultrabike

    ultrabike Measurbator - Admin

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    Headphones. Single driver. KSC75. Does this look minimum phase?

    Phase.png

    Same as before. Green are frequency response, and the phase response. Gray is minimum phase and white is excess phase.
     
    Last edited: Jun 22, 2017
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  7. ultrabike

    ultrabike Measurbator - Admin

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    Your second plot about the old two-way speaker. It is continuous. The phase is just wrap-ing around 180 degrees. 180 degrees and -180 degrees are one and the same. You need to un-wrap the phase. I cannot tell the crossover is at 1.3 kHz just by looking at the plot. Much less what order the filter is.
     
    Last edited: Jun 21, 2017
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  8. The Alchemist

    The Alchemist MOT: Schiit - Here to help!

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    thank you for the phase measurements @ultrabike
     
  9. ultrabike

    ultrabike Measurbator - Admin

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    AKG812:

    Phase.png

    Looks like this single driver, full size, open back headphone has a cross-over between 4 kHz and 5 kHz, if we were to go by discontinuities and excess phase. Except it doesn't.
     
    Last edited: Jun 21, 2017
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  10. ultrabike

    ultrabike Measurbator - Admin

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    HD600:

    Phase.png

    Now we are talking.

    Even so. If the equivalent minimum phase response does not completely and perfectly align with the phase response, the system is not minimum phase. In the HD600 and in other headphones, it's close, but it's not.

    Based on the above, I don't think it's easy to tell cross over frequencies by just looking at the composite phase response. Or even tell if the system only has one driver, or two. At least I can't tell right now. Look at the KSC75 and AKG812. If I was to guess I would say two drivers. It's only one.

    Anyhow, that's where I'm coming from.
     
    Last edited: Jun 21, 2017
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  11. Serious

    Serious Inquisitive Frequency Response Plot

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    Isn't that what it's supposed to be? The excess phase wraps at the crossover frequency? If it's unwrapped or not doesn't really change the picture. Your Mackie plot also does that.

    Those two other headphones ... interesting. Minimum phase up to the nasty break-up and then it shifts, after which it's close to flat again. I had the same thing with my in-ear measurement method, but not on my couper or my free-air measurements. My Superlux HD681 measurements (modded) look like this:
    HD681B L.jpg
    Even with the nasty dip+peak at 4 and 5kHz the phase is still mostly minimum. There seems to be about 7° of excess phase around 5kHz.

    I guess I was talking more about in the context of good headphones that don't have such nasty breakup like the HD600 or HD800, but I guess it doesn't work that way for every headphone. So what does this phase shift mean? What does the IR look like? Where does it come from? Why does ringing sometimes have it and it sometimes doesn't?

    Could the slight phase shifts with the HD600 be from driver modes that essentially slightly change the position where sounds are coming from? Looks like when there's driver ringing (at 5k and at 12kHz) there's also some excess phase)
     
    Last edited: Jun 22, 2017
  12. frenchbat

    frenchbat BritishBat's arch enemy - Friend

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    Any of you guys have the same type of measurements for different tech headphones (i.e. planar and e-stat) ?
     
  13. Serious

    Serious Inquisitive Frequency Response Plot

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    Actually, now that I think about it this might explain some stuff.

    Here's my SR202 plot. This one bugged me at the time, because essentially every sound >38kHz seems to be 0.9ms early. The IR looks funny with a peak that settles and then the regular IR peak. Could just be that the measurements are shit above 40kHz.
    SR202.jpg

    There seem to be these bumps in the excess phase. Could this be from modes in the diaphragm, some of which effectively move the acoustic center away from the microphone, compared to where it is for other frequencies?
    14.3kHz seems to be 0.01ms "late".

    EDIT: Looking through my other SR202 measurements it might just be the coupler or something. Some of my other measurements don't seem to have the tiny bumps in the excess phase. The ultrasonic stuff still seems to be too early, though.
    Other measurements have the bumps at different frequencies. Modes on the diaphragm actually seem likely to me now, with a slightly different microphone position causing a different pattern in the excess phase.
     
    Last edited: Jun 22, 2017
  14. frenchbat

    frenchbat BritishBat's arch enemy - Friend

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    40khz is very high indeed. Especially since it's commonly admitted that anything past 6khz is uncertain at best.

    Anyway, maybe dynamics vs planar vs e-stat would give us some more food for thought. I was thinking driver flexing or something like that.
     
  15. Serious

    Serious Inquisitive Frequency Response Plot

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    The SR202 left driver seemed to have its peak at a slightly lower frequency and the bumps were also lower, so could be that it has something to do with tension.
    With the HD800 there seemed to be 180° of phase shift at its breakup frequency of 38.2kHz. After that, nothing.

    On my head some headphones seem to have such a sudden phase shift at 8kHz and some others don't.
    On my coupler the excess phase seems to be linear with the Code-X and HE1000, even at the 5kHz peak. The ortho wall doesn't seem to cause any weirdness in the excess phase. But those plots, which were taken with my laptop ADC, have some phase shift at the very top end.
     
    Last edited: Jun 22, 2017
  16. briskly

    briskly Friend

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    When looking for resonances, it would be better to look at the change of the phase shift rather than the total excess phase. Perhaps look at this from its frequency derivative, the group delay.

    I'm not too comfortable with REW, but these are from a series of botched measurements.

    Phase
    Phase.png

    Group delay
    group delay.png

    CSD after EQ
    CSD.png
     
    Last edited: Jun 22, 2017
  17. Serious

    Serious Inquisitive Frequency Response Plot

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    In this case yes, the lower frequencies are delayed a bit. Actually I think I thought of a 4th order filter in terms of the phase, but the actual crossover point should be close. Crossover point also moves depending on the angle.

    In headphones I don't think this should be the case. With the phase unwrapped it essentially says that the frequencies below the resonance are delayed by some time. But the IR usually still looks pretty normal. I think I'm missing something here; why do your phase response plots look like that? And why then does my Superlux not look like that? I know that when I use my in-ear method the resonances caused by the ear (so not caused by the driver) make the excess phase look like that. So could it be that with those two phones it's not the driver that causes it? That doesn't seem to make sense to me. The KSC-75 is pretty much only the driver.

    Also with speakers and their crossover I'm pretty sure that you can calculate the order of the crossover based on how much phase shift there is, what the Q is, etc. Doesn't every crossover order add 90° phase shift (between the drivers) at the crossover frequency? So 180° for 2nd order and 360° for 4th order, etc.

    When I unwrap the phase measurements that I take with my speakers in-room the phase response varies a lot, but in anechoic conditions it's close to flat. I think it's much better to just ignore the room effects and look at the shape of the overall phase response, so no unwrapping. Excess group delay is the same story. Close to 0 overall, but with peaks at room mode frequencies. That is what I thought your headphone measurements would look like, but they probably do with the phase wrapped.

    Yes, true. But what are those measurements? In-ear measurements? In-ears?
     
    Last edited: Jun 22, 2017
  18. briskly

    briskly Friend

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    Model pinnae with mic terminated at the end, circumaural headphones.
     
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  19. ultrabike

    ultrabike Measurbator - Admin

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    So first things first @Serious. What is the crossover frequency and the order of the crossover filter on my Mackie MR5MK3 based on these plots?

    http://www.superbestaudiofriends.org/index.php?threads/linear-phase-discussion.4594/#post-145324

    Excess phase does not wrap around the crossover frequency.

    Good or bad or whatever headphones. The point is that single driver headphones are not necessarily minimum phase.What does the phase shift and break-up mean? I believe the driver vibrates differently as a function of frequency. One would likely have to take some sort of video of the driver as it vibrates as a function of frequency. It will likely exhibit a bit of delay as a function of frequency. Or more like you said, the vibrations will come from different spots on the driver, causing different delays since the waves travel different paths. Or a combination of things depending on the driver.

    The headphone almost always exhibits ringing at the break-up frequency.

    Yes. I think planar and e-stat are not minimum phase either. And frequencies will not be aligned in time, since the phase is not exactly linear.

    I believe the issues we are seeing with these single driver systems has to do with the modes in the diaphragm indeed.

    The coupler might have a hand on it. But I believe those modes on the driver causing things to not line up and in some cases breakups are very real.

    I don't think you can tell the cross-over and the order of the filter by just looking at the phase response of the full system. Again. What is the cross-over and the order of the filter in my Mackies?

    Phase wrapped or un wrapped, phase is time. Any deviation from zero is a delay in time. Wrapped or not.

    When you un-wrap the phase all you are doing is visualizing delay over multiple cycles and removing ambiguities.

    My phase responses look like that because frequencies are not being delayed by the same amount. Some cases the delay is over multiple cycles, i.e. definitively not minimum phase. And I feel it is the driver that causes it.

    As far as filter order, how do you discriminate between the filter and the driver response? How do you separate between the tweeter and the woofer once everything is mixed together? Where is the cross-over of my Mackies? What's the order of the filter? It has nothing to do with using an an-echoic chamber or not.
     
    Last edited: Jun 22, 2017
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  20. Serious

    Serious Inquisitive Frequency Response Plot

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    Lol, based on the graph I'd guess somewhere around 2.5-3kHz, 2nd order? Can't really say exactly. Would probably be easier with the step response. It will also depend on if the drivers are aligned. Most likely the tweeter is a bit in front of the woofer or something, but this also depends on the angle.
    What I'm saying is the crossover and time-alignement will make itself known in the phase response and you could probably simulate the crossover based on the phase response. But I can't do it off the top of my head.

    Yes, but in the case of the KSC 75 it's not like all of the frequencies below 4kHz are suddenly delayed by one full cycle. How could the driver do that? Maybe I'm just not getting something about the phase unwrapping.

    Let's look at my speakers for example:
    Note that I have some issues with my setup causing phase shift that can't be fixed with time-alignement. This seems to get worse the longer the sweep I use in REW. Without the extension cord I use for my USB microphone this goes away. This is causes the treble to be inverted in the impulse response and this is what it looks like in the phase. Normally >5kHz should be in line with the phase in the lower midrange and there should be a 45° phase shift around 3kHz from the crossover from big cone to whizzer cone.
    Speakers unsmoothed.jpg
    If I were to unwrap the phase it would be all over the place, but that's not actually meaningul. The overall shape of the phase is what's important, disregarding the steps caused by room modes and other sorts of reflections. The same thing goes for my in-ear measurements. It's not like there's a delay to frequencies on the left side of these sudden phase shifts.

    I'm just wondering why you get these results from the KSC 75 and the K812, but I'm not getting similar stuff from my Superlux, even if the FR has a similarly bad peak. I guess the only way to be sure is for me to measure a KSC 75.

    Dynamic drivers should be minimum-phase in their pistonic region, right? Planars and stats maybe less so, because they're not pistonic. But TBH I still don't get where all that excess phase is coming from.
     

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