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Author Topic: Convolve CSD plots with minimum phase FIR filter?  (Read 9121 times)

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Joe Bloggs

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Re: Convolve CSD plots with minimum phase FIR filter?
« Reply #30 on: October 13, 2012, 03:19:13 AM »

I am with Maverickronin on this one.
The way I see it (and was often told I was wrong) if a driver swings out, this could be compensated by applying the 'opposite signals' (motion feedback/noise cancelling principle but done differently)
This would have to be done at all the specific frequencies or in very narrow bands, when non-active feedback is used and that would amount to a lot of computive power to modify the incoming signal to the 'needed one'.
Also each headphone would have to be compensated individually (look at the DT1350 choclats), not to mention diafragms changing properties over time or temperature change would do to the original compensation.
Another thing..... will the headphone actually sound ideal as well with all these 'modifications' of the original signal ?
Test signals perhaps.. music unsure.

Strange plot it cannot be just FR compensation but time domain must be addressed as well (for the ringing) otherwise a simple EQ would have been enough and it isn't for the 'effen ringin' IMO.

If it were that simple to create the perfect headphone there would have been handy sellers that were already selling headphones with built-in active compensation for large sums of money as they would be very easy to make and sound 'perfect'.
No such thing yet.  :-X

The compensation shown by xnor is in some sense highly idealized but in another sense quite simple.

It is simple in the sense that it is just a minimum phase filter as can commonly be found in EQs.  So the "time domain" was not "addressed"--not beyond the sense that unlike a linear phase EQ, a minimum phase EQ will alter phase response in a fixed relationship with the magnitude response alteration.

It is highly idealized in the sense that... I'll just quote xnor's message to me:
Quote (selected)
3. What did "It's not perfect but that's not surprising considering I used the raw data" mean?

3) It means that I didn't do any averages over positional changes. I didn't re-measure the headphones with the inverse filter applied (you could do this multiple times trying to improve the filter each time). Also there was no smoothing, so narrow 20 dB dips would be narrow 20 dB peaks in the inverse filter which could cause problems if you used that filter for listening.

Still, overall you can generate filters to flatten the FR which will also improve the impulse response, provided they're mostly min phase (so no crazy multi-way crossover stuff) . You can also do it by hand, but it's a lot more work if you have to do it for multiple headphones over and over again.

AFAIK it means that you can obtain the pictured corrected response if
1. You never take off or move your headphones on your head again after the measurement and correction (impossible)
2. You have enough amp power to compensate for the 10+dB loss of efficiency that results from the EQ (possible)
3. The drivers' non-linear distortion does not get worse because of your systemetically boosting its weak frequencies (impossible)
and finally
4. You measure the impulse response with the phones on your own ears.  Then you have to supply your own HRTF to compensate for the fact that flat response sounds close to perfect comi ng from speakers but perfectly awful coming from headphones because of HRTF effects. (not commercially possible)

AFAICT The first 3 points are technical difficulties that would make the compensation less perfect than it appears on xnor's graph whereas [4] is the real reason no digitally compensated headphones have come out: individual differences (plus individual preferences!) make a one-size-fits-all headphone FR such a crapshoot that you can basically throw out anything and (with the help of some marketing) *someone* out there is guaranteed to like what he hears from it.

[4] is commercially impossible but possible on an individual basis... in fact I have been doing this for all my headphones without even using any measurement equipment.  I tried to detail my method here but TBH it's not very well organized (understatement)
http://www.head-fi.org/t/615417/how-to-equalize-your-headphones-advanced-tutorial-in-progress

If anyone's interested but can't understand what I wrote do please leave a message here or in my pm (here or on head-fi) and I'll answer all your questions :D
« Last Edit: October 13, 2012, 03:26:18 AM by Joe Bloggs »
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rhythmdevils

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Re: Convolve CSD plots with minimum phase FIR filter?
« Reply #31 on: October 13, 2012, 03:41:47 AM »

I think xnor's plot is a bit idealized as there would be positional variations and distortion that would not result in such an ideal response. The purpose was to show that equalization can indeed make corrections to the CSD response.

Acoustic equalization through damping offers similar benefits (or if wrongly applied... issues):

TR50P

Paradox:
http://www.changstar.com/index.php/topic,41.0.html
http://www.changstar.com/index.php/topic,17.0.html

Koda:
http://www.changstar.com/index.php/topic,208.msg2304/topicseen.html#new

I couldn't find measurements of the stock YH-3s here at effin' ringin', but here are the results after some well thought modifications:
http://www.changstar.com/index.php/topic,388.msg6294.html#msg6294
This is an old post but I just saw it...


Damping doesn't just change the FR though.  It changes how the driver operates because of putting different "pressures" on the movement of the diaphragm.  At least IMO/E.  And it definitely also actually eliminates resonance separate from FR.  You could have a lot of different sounding T50rp mods with wildly different FR but all very clean.  With the riht mods that is. 
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ultrabike

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Re: Convolve CSD plots with minimum phase FIR filter?
« Reply #32 on: October 13, 2012, 06:49:44 AM »

I think xnor's plot is a bit idealized as there would be positional variations and distortion that would not result in such an ideal response. The purpose was to show that equalization can indeed make corrections to the CSD response.

Acoustic equalization through damping offers similar benefits (or if wrongly applied... issues):

TR50P

Paradox:
http://www.changstar.com/index.php/topic,41.0.html
http://www.changstar.com/index.php/topic,17.0.html

Koda:
http://www.changstar.com/index.php/topic,208.msg2304/topicseen.html#new

I couldn't find measurements of the stock YH-3s here at effin' ringin', but here are the results after some well thought modifications:
http://www.changstar.com/index.php/topic,388.msg6294.html#msg6294
This is an old post but I just saw it...


Damping doesn't just change the FR though.  It changes how the driver operates because of putting different "pressures" on the movement of the diaphragm.  At least IMO/E.  And it definitely also actually eliminates resonance separate from FR.  You could have a lot of different sounding T50rp mods with wildly different FR but all very clean.  With the riht mods that is. 

Yes. FR amplitude is not everything. There is non-linear distortion (THD, IMD and all that deal) and FR phase. However, FR phase is IMO hard to read. See the attached plots of the AKG K701 FR amplitude and phase. I can sort of make sense of the FR amplitude, but I have a hard time with the phase.

The plots of the FR phase were derived from Innerfidelity's IR (which impose a limitation of 200Hz given the excessive resolution and lack of samples to cover the lower frequencies)

I feel CSD convey FR phase issues (some related to resonance) in a much more readable way.

On cup damping, removal or addition of cup reflections is equivalent to modifying digital filter taps. Consider a tone. Adding the same tone with a different amplitude and phase corresponds to a two tap FIR filter...

This is my understanding which may be flawed. I have been proven wrong many times :)p5
« Last Edit: October 13, 2012, 06:55:23 AM by ultrabike »
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Solderdude

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Re: Convolve CSD plots with minimum phase FIR filter?
« Reply #33 on: October 13, 2012, 07:27:41 AM »

Well it is interesting subject, correction that is.
I have passively corrected quite a few headphones (with all the 'side effects' that come with it) and IF the headphone responds well you can get an overall improvement of SQ where the cure outways the sideeffects with a wide margin.
Too much EQ (compensating severy rolled off hedaphones) never gives the desired effect even when done with digital minimal phase filtering.
Even if you have very narrow band linear phase filters and get it 'flat' it will still 'ring' and distort.
Certainly when you need to compensate 20 dB or more non linearities will give audible distortion.
Ortho's (with magnets on both sides) may be excellent candidates though.

There are many headphones around that do not show very obvious FR problems (just a few dB) yet are ringing at that frequency.
So if you address that minimal amount of amplitude correction the ringing will not be affected much I reckon but could be mistaken of course, never having actually tried that.

This is what 'puzzles' me in the discussed plot.
The ringing appears to have been gone and the membrane seems to 'stop' instantly dead in the water.
It's not entirely impossible but when break-up is in play I cannot see how 'simple' FR compensation can prevent those artifacts.

You would have to have a good measurement with a 'flat' microphone to create the correction IMO.
You cannot use plots out there on the web (DT1350 choclats effect) so only a manufacturer or well equiped DIY'er can get the correct 'correction' which will also be hard to implement in portable gear (I mainly use HP's portable)

Did he mention (and what's your opinion) the headphone sounded a lot better also ?
I didn't read his original thread which I suppose should and will.  ::)

...Nice to see screenshots of Ubuntu window frames.  :)


« Last Edit: October 13, 2012, 07:37:18 AM by Solderdude »
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ultrabike

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Re: Convolve CSD plots with minimum phase FIR filter?
« Reply #34 on: October 13, 2012, 08:49:35 AM »

My understanding is that CSD ringing is not necessarily the exact same thing as IR (time domain) ringing. Also, AFAIK all bandlimited systems will have memory in the time domain, i.e. they will never "'stop' instantly dead in the water."

Something that will start and stop instantaneously would have a Dirac delta function for an impulse response (and infinite bandwidth.) Such systems are really mathematical constructs (they don't exist in real life.) 

But who cares, most of us can't hear past 20kHz (I can't past 15kHz I think.) All we need to do is remove issues in the audible range, and that does not require an infinitely fast membrane.

Also, I'm almost certain the AKG K701 is not minimum phase (did a zero plot of the IR and there seem to be quite a few zeros outside the unit circle - see figures.) That said, the rceps approximated minimum phase IR is very close to the measured one, and it may be possible to do a decent job at equalizing (also see figures.)

Regarding equalizers, I'm more familiar with convolution. A few thousand taps could possibly bring the IR back in line, but that may be difficult to do manually and by ear. Furthermore, it will not be a perfect solution given nulls, distortion, positional variations, etc... Just a potential improvement.

As far as Ubuntu... Got this Windoze 7 HP laptop with craptastic beatsaudio tatooed somewhere in the OS. So double booting to Ubuntu which has it's pluses (and minuses) :) Should have gotten a MAC :'(
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Solderdude

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Re: Convolve CSD plots with minimum phase FIR filter?
« Reply #35 on: October 13, 2012, 09:13:20 AM »

Since I have never tinkered with headphones in this particular way I wonder how they sound after the 'near ideal'  response is created ?

I mean polishing a  poo will still be a polished  poo
Can you get a HD201 to sound like the SR009 or will it still sound like a HD201 but 'imporoved' ?

I have tried to 'speed up' severely rolled off HP's by EQ but do not get the desired results as the membrane simply cannot create the needed movement.
Similar to turning up the bottom end on a bass-shy HP, this too will never give a good bass reproduction.

Starting base would have to be a very good headphone that only needs a few nudges.
my personal FR is limited to about 16kHz, though the 16.265kHz I can still detect (but not as loud as when I was young)
Although some claim related harmonics above the audible range contribute to the overall SQ I feel that 20kHz (-0.1dB) is sufficient.

As long as I can get risetimes of the membrane fast enough to follow those that exist in music signals I can't complain.
Usually the fast moving amplitudes are very low in amplitude so very fast risetimes are not mandatory (for me)
« Last Edit: October 14, 2012, 07:15:38 AM by Solderdude »
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ultrabike

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Re: Convolve CSD plots with minimum phase FIR filter?
« Reply #36 on: October 13, 2012, 07:45:53 PM »

Since I have never tinkered with headphones in this particular way I wonder how they sound after the 'near ideal'  response is created ?

I mean polishing a  poo will still be a polished  poo
Can you get a HD201 to sound like the SR009 or will it still sound like a HD201 but 'imporoved' ?

I have tried to 'speed up' severely rolled off HP's by EQ but do not get the desired results as the membrane simply cannot create the needed movement.
Similar to turning up the bottom end on a bass-shy HP, this too will never give a good bass reproduction.

Starting base would have to be a very good headphone that only needs a few nudges.
my personal FR is limited to about 16kHz, though the 16.265kHz I can still detect (but not as loud as when I was young)
Although some claim related harmonics above the audible range contribute to the overall SQ I feel that 20kHz (-0.1dB) is sufficient.

As long as I can get risetimes of the membrane fast enough to follow those that exist in music signals I can't complain.
Usually the fast moving amplitudes are very low in amplitude so no full range squarewave response is needed (for me)

I agree. The first headphone I bought after much research (performance/price) was a pair of HD202s. I could have done better with a set of KSC-75s but I did the best I could at the time. I had time limitations to make my purchase: my son was born and I wanted to watch movies at night with my wife without waking him up.

The difference in sound quality between an HD202 and an HD558 is considerable. And the difference in sound quality between properly driven HD558 and SR009 is quite considerable too, specially when the SR009 is driven by a Cavalli LL.

I do not believe one can make an HD201/202 sound exactly like an SR009. What you can do is approximate the sound to within the physical limitations of the headphone. You will definitively make an improvement, but that's about it.

Also, a properly implemented and setup equalizer can potentially improve the sound quality of any can.
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arnaud

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Re: Convolve CSD plots with minimum phase FIR filter?
« Reply #37 on: October 14, 2012, 12:01:02 AM »

I have to get back to this and complete what I started with CSD post-processing...

One comment on the IR ringing being different of the CSD ringing: they're actually the same thing except that the IR is dominated by the largest amplitude resonance and / or longest decay resonance. Since for the same damping (or Q if you will), the higher the frequency, the shorter the decay (so called T60), you are likely to see only the "low" frequency ringing by looking at the IR. Or if you look at the SW response, the resonances most excited by the signal (e.g. SW fundamental and possibly some of the first order harmonics).

The thing is, nobody looks at CSD in engineering except speaker designers. For room acoustics and general vibro-acoustic in the mid-high frequency range, we looks at time decay (T60), which is nothing more than the envelope of the IR after it's been filtered in 1/3 Octave Bands. It is a "coarser" look at the damping of the system, with the T60 (or damping loss factor) of a given band corresponding to the average damping of all the resonant modes in that band. Basically, when you get to room acoustics for example, there are so many zillion modes it makes no sense to look for / attempt to extract the ringing of one more but rather look at 1/3OB decay of a group of modes.

In regards to the interpretation of the phase response, I have actually also looked into this as part of my previous investigation but decided not to post the results because it wasn't too clear. You have to "unwrap" the phase response of the headphone to check if it has minimum phase characteristics. You also obviously need to remove the "propagation delay" of the original headphone IR (e.g. shift the IR so the peak pulse occurs at the beginning of the time window) as this adds up to the unwrapped phase response. For instance, a pure dirac has no phase change while the unwrapped phase of a time delayed (t_0) pure dirac unwraps at the rate of exp(-i 2*pi*f*t_0) or some like that. Once you've removed the propagative phase component of the headphone response, you may be able to see how much the headphone deviates from minimum phase characteristics (the minimum phase version naturally has no "propagation phase" component, e.g. the peak occurs at t=0). I haven't bothered going there yet and probable the bode plot approach is much more convenient...

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Joe Bloggs

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Re: Convolve CSD plots with minimum phase FIR filter?
« Reply #38 on: October 14, 2012, 03:38:30 AM »

In regards to the interpretation of the phase response, I have actually also looked into this as part of my previous investigation but decided not to post the results because it wasn't too clear. You have to "unwrap" the phase response of the headphone to check if it has minimum phase characteristics. You also obviously need to remove the "propagation delay" of the original headphone IR (e.g. shift the IR so the peak pulse occurs at the beginning of the time window) as this adds up to the unwrapped phase response. For instance, a pure dirac has no phase change while the unwrapped phase of a time delayed (t_0) pure dirac unwraps at the rate of exp(-i 2*pi*f*t_0) or some like that. Once you've removed the propagative phase component of the headphone response, you may be able to see how much the headphone deviates from minimum phase characteristics (the minimum phase version naturally has no "propagation phase" component, e.g. the peak occurs at t=0). I haven't bothered going there yet and probable the bode plot approach is much more convenient...

I googled "minimum phase room acoustics" and came across this
http://www.gearslutz.com/board/studio-building-acoustics/504980-minimum-phase-room-response.html

This article by JohnPM seems helpful
www.hometheatershack.com/roomeq/wizardhelpv5/help_en-GB/html/minimumphase.html

In particular, there are analysis plots called "excess phase" and "excess group delay" which appear to much more clearly demonstrate how a system deviates from minimum phase.  I still don't know exactly how to read this though and I'd take JohnPM's assertions with a grain of salt because he makes some outrageous sounding claims in the subsequent argument with SAC and appears to mix up "minimum phase" and "stable" criteria.  But then SAC doesn't seem to be the paragon of knowledge either as he seems to think not minimum phase = not invertible.  I guess he hasn't heard of DRC?

I still hope that an impulse response convolved with its minimum phase "inverse" would provide a meaningful visualization in CSD.  If you're afraid it'd show as a flat wall like xnor's plot you could try measuring phones with no cup damping (like the infamous Beyer T1?) or even multi-driver IEMs, which would introduce crossover phase distortions that should be easily visualized.
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arnaud

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Re: Convolve CSD plots with minimum phase FIR filter?
« Reply #39 on: October 14, 2012, 04:06:02 AM »

Joe, I haven't checked your links but there is some info in the litterature as a result of research work. For instance, there has been quite a bit of interest in the field of room acoustics to create artificial room response based on geometric characteristic and source/receiver distance. It goes beyond just room acoustics, I worked on virtualization of high frequency simulations (where phase/individual resonances cannot be tracked individually) and it isn't an easy thing to come with representative phase.

Anyhow, for the reference, please have a look to the intro here, in particular the mention of Lyon's work in 3rd paragraph: http://www.acoust.rise.waseda.ac.jp/~takahashi/AES28-000046.pdf . Lyon compared typical room response unwrapped phase minus the propagation phase (estimated from source / receiver distance) vs. minimum phase response. Result is that anechoic room has minimum phase characteristics while reverberant room has non-minimum random phase. Actual listening hall falls somewhere in between depending on how close you are to the source (and thus how much predominant the direct field is...)
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