The problem of measuring frequency response distortions and group delay in headphones

[yukij]

I want to share an interesting observation. It all started with the fact that I was generally confused by the practice of measuring group delay instead of excess group delay for headphones, and by the observation that closed-back headphones show significantly fewer “time-domain distortions.”

After analyzing measurements of open-back headphone models, I noticed that the more “open” the design is, the more pronounced the comb filtering in the frequency response and the greater the distortions in the group delay. Eventually, after performing measurements with the measurement rig partially surrounded by soft materials, I obtained the results shown here.

Does this mean that what we are seeing in the group delay plots is actually a consequence of room reflections? If so, what is the optimal way to perform such measurements, and does this imply that most existing group delay and frequency response measurements are not truly relevant?

 

[Keith_W]

I'll start with a disclaimer: I have never measured a headphone in my life, so I can not answer headphone specific questions. Maybe @Sean Olive, @amirm or @crinacle would like to chime in.

When you take a loudspeaker measurement, what you will capture is the minimum-phase response of the loudspeaker, any additional phase distortion introduced by the room (the "excess phase" response), and the non-constant group delay of the test signal itself.

If you want to see the minphase response of the loudspeaker, you will need to do everything you can to obtain a minphase response and avoid contamination from reflections. This is commonly done by windowing/gating the measurement, or by suppressing the reflections so much that they do not matter (i.e. anechoic chamber). The problem with gating the measurement is that your are still limited by the wavelength, and by choosing a shorter window you lose resolution.

I would imagine that if you are measuring an open back headphone, and you leave the window open long enough, you will start capturing room reflections. If you don't take care with your measurement setup, e.g. if you are measuring with your headphones on a table with nearby walls and general clutter, you would probably contaminate your measurement. I speculate that the sounds emitted by a headphone should be low enough in amplitude to be easily absorbed so it should be a lot simpler to create an "anechoic" chamber with some acoustic foam. I have no idea if I am right on this one!

What is not commonly known on ASR is that a logarithmically swept sine wave does not have constant group delay. If you listen to such a sweep, you will hear that low frequencies are time stretched and high frequencies are compressed. The test signal itself is time warped. If you want constant group delay, you need a short impulse like a Dirac delta pulse. The problem with these signals is they are very short, so the SNR is extremely poor. You need to take hundreds of these measurements and sum them to get a decent SNR. I don't think REW can take these measurements.

 

[yukij]

I'll start with a disclaimer: I have never measured a headphone in my life, so I can not answer headphone specific questions. Maybe @Sean Olive, @amirm or @crinacle would like to chime in.

When you take a loudspeaker measurement, what you will capture is the minimum-phase response of the loudspeaker, any additional phase distortion introduced by the room (the "excess phase" response), and the non-constant group delay of the test signal itself.

If you want to see the minphase response of the loudspeaker, you will need to do everything you can to obtain a minphase response and avoid contamination from reflections. This is commonly done by windowing/gating the measurement, or by suppressing the reflections so much that they do not matter (i.e. anechoic chamber). The problem with gating the measurement is that your are still limited by the wavelength, and by choosing a shorter window you lose resolution.

I would imagine that if you are measuring an open back headphone, and you leave the window open long enough, you will start capturing room reflections. If you don't take care with your measurement setup, e.g. if you are measuring with your headphones on a table with nearby walls and general clutter, you would probably contaminate your measurement. I speculate that the sounds emitted by a headphone should be low enough in amplitude to be easily absorbed so it should be a lot simpler to create an "anechoic" chamber with some acoustic foam. I have no idea if I am right on this one!

What is not commonly known on ASR is that a logarithmically swept sine wave does not have constant group delay. If you listen to such a sweep, you will hear that low frequencies are time stretched and high frequencies are compressed. The test signal itself is time warped. If you want constant group delay, you need a short impulse like a Dirac delta pulse. The problem with these signals is they are very short, so the SNR is extremely poor. You need to take hundreds of these measurements and sum them to get a decent SNR. I don't think REW can take these measurements.

I understand what you are talking about. The reason I raised this topic is that very few people mention that open-back headphones require the same measurement conditions (quasi-anechoic windowed measurements or fully anechoic environments). From this, I conclude that some people who perform headphone measurements do not take this into account, and as a result their data may be inaccurate.


The main point is that I want to hear other people’s opinions, learn about the measurement conditions they use, and see what results they are getting.

 

[solderdude]

Not room reflections as the distance is too big.
I noticed that the more 'open' the headphone is the worse the effect.

Moondrop Para 2 Planar Headphone Review

I recently picked up the Para II headphones, and—no surprise—they sound amazing after a bit of EQ. After using them for a while, I noticed an interesting phenomenon: when I place the palm of my hand near the outside of the earcup, the sound changes. With my hand positioned roughly 0–15 cm from...

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It appears to have something to do with (membrane) damping which is much higher in closed headphones.
At first I thought it had something to do with sounds from the outside but it always dies out over time so that can't be it.

 

[yukij]

It appears to have something to do with (membrane) damping which is much higher in closed headphones.
At first I thought it had something to do with sounds from the outside but it always dies out over time so that can't be it.

I don’t fully understand how you explains the difference I obtained. In my measurements, nothing about the headphones themselves was changed. Pillows and soft fabric were placed about half a meter away from the headphones. I also included measurements with a time window to demonstrate that these changes appear even with a shortened time window (i.e., with only “early reflections,” for example from the desk).


If we follow your theory, then placing soft surfaces half a meter away affected not the measurement itself, but the acoustic loading of the headphones, which also seems odd.


For example, here are two measurements.
One with a 10 ms window and one with a 500 ms window. If the spike at 10 ms is suppressed, the resulting responses look quite similar. And 10 ms corresponds to roughly 3.4 meters, which fits well within a real room and is quite logically reflected in both the frequency response and the impulse response.

 

[Curvature]

What is not commonly known on ASR is that a logarithmically swept sine wave does not have constant group delay. If you listen to such a sweep, you will hear that low frequencies are time stretched and high frequencies are compressed. The test signal itself is time warped. If you want constant group delay, you need a short impulse like a Dirac delta pulse. The problem with these signals is they are very short, so the SNR is extremely poor. You need to take hundreds of these measurements and sum them to get a decent SNR. I don't think REW can take these measurements.

The group delay in a log-swept sine is frequency-dependent and deterministic. An inverse filter is applied to deconvolve linear and nonlinear components, which will have different group delays. The technique was developed by Farina. I don't believe the measurements presented in REW are artefacts, if that was your meaning. @JohnPM can speak to the implementation in REW.

Jude from Head-Fi uses a custom isolation chamber for measuring headphones. Certainly nice for measurement hygiene.

There is no commonly-accepted interpretive framework for headphone group delay measurements, unfortunately. It is data in which we struggle to find meaning.

 

[amirm]

In my measurements, nothing about the headphones themselves was changed. Pillows and soft fabric were placed about half a meter away from the headphones.

I can't follow all your graphs.

Just like speaker measurements, such effects are strongly impacted by both playback levels, distance from reflective surfaces and sensitivity of the speaker/headphone.

I too tried to lower the impact of room reflections but did not see a noticeable result so don't bother. The microphone is extremely close to the driver and with the right playback level, the reflections which then have to travel through the headphone driver are attenuated a bunch.

 

[yukij]

with the right playback level, the reflections which then have to travel through the headphone driver are attenuated a bunch.

But in that case we would only be changing the absolute signal level. The relative level between the direct sound and the reflections would remain the same, we would merely be burying the reflections below the noise floor.


You’re essentially saying that this is not that important, but what I obtained in my measurements is, in my view, a significant difference. And all I did was use a few pillows. It really does seem like this matters.

 

[solderdude]

If we follow your theory, then placing soft surfaces half a meter away affected not the measurement itself, but the acoustic loading of the headphones

I showed that placing a highly reflective object (I did the same using a hand) even 20cm away did not change anything and this is using an open planar magnetic headphone.
Had a quick look at the GD plots and did not see any differences that stood out (every measurement differed slightly) between 5cm and 'open field' in GD results.

I also showed that if you want to significantly change the sound (or GD or resonances) it takes damping modifications.

Think about the following...
We have a driver at 2cm away from the ear.
We have the rear of the driver that emits the same sound (well, in practice it will be damped a little).
The sound leaves the headphone and makes it to a wall 3.4m away.
Lets make that wall reflect 100% of the sound.
-6dB per doubling of distance compared to the SPL at the driver.
This means any reflected sounds should 'echo' back to the driver at -50dB and has to pass through the driver unattenuated.
This would be 0.3% on your percentage scale for the impulse so would not register.

Now .... have a look after 10ms in my time domain plots.
You will see that the driver (in my measurement) will still ring after 10ms and did so only -20dB attenuated which will drown out a -50dB echo (the same 10ms later).

Removing the grille may have more effect as part of the sound will reflect and part will leave the headphone so the delay will be shorter and the amplitude will be higher.
In a closed headphone all of it will be reflected and some of it might be attenuated at certain frequencies due to damping materials.

GD plots can show resonances (especially pad bounce) a bit clearer than say phase or amplitude measurements and can show certain resonances that also distort timing.
That's what they are useful for (kind-off).

Wall reflections are probably not the reason you see the 'grass' between 1kHz and 3kHz nor are they very audible in music. All instruments also have a decay which usually is much longer than that of a driver.

 

[Keith_W]

The group delay in a log-swept sine is frequency-dependent and deterministic. An inverse filter is applied to deconvolve linear and nonlinear components, which will have different group delays. The technique was developed by Farina. I don't believe the measurements presented in REW are artefacts, if that was your meaning. @JohnPM can speak to the implementation in REW.

Thank you for your comment. Yes I am aware that the deconvolution method corrects the GD introduced by the logarithmic sweep, but I was under the impression that a Dirac delta pulse still gives you a better measurement of group delay.

This is the difference in GD between a logarithmic sine wave sweep of my midrange driver (in red) vs. a Sinc pulse, which approximates a Dirac delta pulse. There is a slight difference at the lower part of the bandpass.

 

[KSTR]

Group delay obtained from unsmoothed data is pretty meaningless. Group delay is the derivative of phase and like with any derivative this makes plots rougher because it is the rate-of-change that is looked at. Noisy data has lots of fast-changing (but meaningless) rate-of-change, polluting/blurring the picture.

In general, proper smoothing not applied to any measurement in attempt to obtain "more detail" is bad practice. HP measurement are very prone to strong changes in the response from minor details of the test setup and have rather poor repeatability. Showing more detail that what the repeatability and general noise base-line allows produces only fake detail.

Headphones, except for a few multi-way-systems, are minimum phase systems, even with internal reflections etc. Thus the group delay (and the phase response it was derived from) doesn't offer any special insights as it is fully determined by the SPL magnitude frequency response, obtained from the root data, the measured impulse response. And the latter needs to have proper smoothing / windowing / gating applied to the raw data.