How far can EQ really go towards truly equalizing headphones?

I tend to agree with what LFF said, and with udauda's references (btw thanks): Weird phase would likely mess with how everything sounds (sound quality) in mono or stereo... and in particular with stereo, probably will mess directional cues in some weird ways to. How much... I don't know.
 
For mono in particular, and in headphones, since left and right play the same thing, the result would be the absence of directional cues ... and "plant mono firmly in the middle of" our noggin 

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lff said:

Not so....
 
Phase does play a big importance in headphones. One of the problems Sony solved with the R10 was how to eliminate these problems in a novel way. Based on many headphones I have heard...phase issues are still there. A slight difference can lead to a massive loss in quality.

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I don't think those were phase issues, but FR (more correctly magnitude response) issues, since phase is "determined" by it.
 
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udauda said:

Audioholics talked about the audibility of phase distortion on headphones before: http://www.audioholics.com/education/acoustics-principles/human-hearing-phase-distortion-audibility-part-2
 
So it is audible, yet we must not forget; In headphone acoustics, a minimum amount of phase delay can be good for satisfactory bass reproduction: http://www.aes.org/e-lib/browse.cfm?elib=16014
 
According to this https://secure.aes.org/forum/pubs/conventions/?elib=14449, the phase issue is simply negligible above ~1kHz with headphones.

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From that audioholics page:
 
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• Phase distortion is audible, but only under very specific circumstances, using very specific, types of test signals.
• There exists in this study no statistically significant evidence supporting the audibility of phase distortion in the musical samples provided, using the all-pass filter implementations chosen by the researchers.
• Introducing the room acoustic variable in to the equation further lowers the already poor scores phase distortion audibility scores.

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(Emphasis by me.)
 
Additionally, they used all-pass filters that cause huge phase shifts. Not something that would happen in a single driver headphone.

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xnor said:

I don't think those were phase issues, but FR (more correctly magnitude response) issues, since phase is "determined" by it.

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If the system (headphone) is minimum phase then there is a unique relationship between the FR magnitude and it's FR phase!
 
Thanks xnor!
 
If headphones are indeed minimum phase in real life, I can see why that's a good thing (in so many ways: reversible, unique FR phase and mag relationship, transient time duration...)
 
As far as phase or magnitude issues affecting the sound quality... well I sort of see a chicken and egg dilemma there given their unique relationship ... You can't really affect the phase without affecting the magnitude and keep the system minimum phase... unless in those studies somehow they set the overall system to non-minimum phase? Anyway, I'm very happy with what I got from this: I can get phase out of the magnitude FR.

Note that while there is a very close relationship between frequency response magnitude and phase, if you go back a few posts(http://www.head-fi.org/t/612665/how-far-can-eq-really-go-towards-truly-equalizing-headphones/75#post_8455577), it is evident that looking at the whole picture (phase and magnitude as opposed to just magnitude) is important to determine how the output signal is going to behave!
 
Now: How far can eq really go toward truly equalizing headphones?
If the headphone is well behaved: relatively time invariant (positional invariant here might be a challenge though), very linear, and minimum phase... Well pretty darn far. Make a filter with poles and zeros where the headphone's transfer function (z-transform) has zeros and poles respectively and you might get a flat line (where the headphone can reproduce signal of course - best not to equalize close to perfect notches there for SNR considerations). Furthermore, cascade a second filter to tailor things to your liking... Not saying all this is super easy though. Note there are positional variations in response, THD, SNR issues... Just, I can see EQ can help to a good degree to the best of my knowledge.

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xnor said:

From that audioholics page:
 
(Emphasis by me.)
 
Additionally, they used all-pass filters that cause huge phase shifts. Not something that would happen in a single driver headphone.

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According to Lip****z & Cabot, it is evident the phase issue is more distinguishable with headphones for sure. And take a good look at the other two articles too.

Are there any headphones that actually have a serious problem with phase, or are we talking purely in theory?

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bigshot said:

Are there any headphones that actually have a serious problem with phase, or are we talking purely in theory?

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We are talking about equalizing headphones, and the phase issue that may be associated with it. 

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ultrabike said:

Note that while there is a very close relationship between frequency response magnitude and phase, if you go back a few posts(http://www.head-fi.org/t/612665/how-far-can-eq-really-go-towards-truly-equalizing-headphones/75#post_8455577), it is evident that looking at the whole picture (phase and magnitude as opposed to just magnitude) is important to determine how the output signal is going to behave!

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No it's just the nature of the butterworth filter that tries to "stay" as flat as possible in the passband, i.e. trades flattness in the magnitude response for a greater phase delay. Take a look at the gain and group delay plots on wikipedia and compare butterworth with bessel.
It's that sudden and steep change in the magnitude response that causes a peak in the phase delay. Like both of us have said before, the phase response can be reconstructed from the magnitude response alone.
 
 
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Now: How far can eq really go toward truly equalizing headphones?
If the headphone is well behaved: relatively time invariant (positional invariant here might be a challenge though), very linear, and minimum phase... Well pretty darn far. Make a filter with poles and zeros where the headphone's transfer function (z-transform) has zeros and poles respectively and you might get a flat line (where the headphone can reproduce signal of course - best not to equalize close to perfect notches there for SNR considerations). Furthermore, cascade a second filter to tailor things to your liking... Not saying all this is super easy though. Note there are positional variations in response, THD, SNR issues... Just, I can see EQ can help to a good degree to the best of my knowledge.

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I agree.

udauda said:

We are talking about equalizing headphones, and the phase issue that may be associated with it. 

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Headphones aren't that far apart in response. It wouldn't take a lot to EQ any headphone into sounding like any other. I can't imagine that causing phase problems.

The only headphone (with measurements available) that I think could have problems with phase is the DT 48 E, but the magnitude response is a much, much greater problem and there's no question about the audibility.

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bigshot said:

Headphones aren't that far apart in response. It wouldn't take a lot to EQ any headphone into sounding like any other. I can't imagine that causing phase problems.

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There are some limitations though. One can not expect to fully EQ apple ear buds into LCD-2s or HE-400s with their deep and relatively clean lows. Some of the biggest offenders are deep notches and early roll off at ether side of the spectrum which can be challenging to fix.

Well, you certainly can't make a silk purse from a sow's ear, but I bet you can make a pretty fine apple out of an orange.

LOL
 

Take a look at these papers:

http://www.cpt.univ-mrs.fr/~briolle/11thAESpart1.pdf

http://www.cpt.univ-mrs.fr/~briolle/11thAESpart2.pdf



Even with a 200-tap FIR filter @ 44.1 kHz, which is of a rather poor quality, the author was able to match the sound quality of a poor quality headphone to that of a high quality headphone subjectively. Thus, in conclusion, as long as the filter is not a linear phase(pre-ringing) & there's no excursion issue, you can freely equalize headphones however you see them fit.

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I think you are not interpreting these papers correctly. First of all, the author does not say what headphones were used. This makes it very difficult to draw accurate conclusions. For all we know, he was simulating one $20 headphone with another $20 headphone. Somehow, I doubt they were transmuting iBuds into Stax 009s Second of all, if you look at figure 6 on p. 258 of the second article, you will see that the match was far from perfect. The best headphone sounded better when representing itself than when being simulated by another headphone.

I am curious enough to write the author and ask him which headphones were used, but not right now, maybe later today or tomorrow.

Another point to keep in mind is that the authors only used one minute of jazz as a test track; this would not be enough variety of music to fully test the headphones. Indeed, the piece used (Glenn Miller, "In The Mood") does not have much deep bass, which might be one of the most difficult parts of the frequency range to equalize -- it would be more subject to distortion.