Headphone Measurements Explained - Square Wave Response Page 2

Interpreting Headphone Square Wave Response
The reason why I test square wave response at 300Hz and 30Hz is because the high frequency components of the wave form are tightly squished into the early part of the square wave. So to interpret the treble to mid range we have to "zoom into" the first few moments of the wave form using the 300Hz square wave. When inspecting the mid to bass transition, we have to pull back and look at a longer period of time with the 30Hz square wave. The information from the 300Hz square wave is in the first 10% of the 30Hz wave form, but it's difficult to inspect because it's so compressed.

In the illustration above, you'll find most of the basic information about how to interpret square waves, but I think it's a good idea to look at some actual waveforms and tell you what I see. Generally speaking, I'll be moving from overly bright cans to overly warm ones. Graphs to the left have the 30Hz square wave at the top and the 300Hz square wave below.

Pioneer SE-A1000
Science_InterpretingSquareWaves_Graph_Pioneer SEA1000This is a very poorly measuring headphone. From the steeply descending 30Hz square wave we can expect a very bass shy headphone; the significant undershoot below the zero line indicates a sloppy, non-tight bass. The general downward tilt of the 300Hz waveform indicates a thin sound with a stronger treble than mid-range, and very strong first overshoot and strong subsequent ringing make me think these will be very piercing in sound quality. I don't remember listening to these cans...I've probably suppressed the memory of a bad experience.
Grado PS1000
Science_InterpretingSquareWaves_Graph_GradoPS1000From the 30Hz square wave we can see that the low frequency response doesn't extend well into the bass notes, and in going below the zero line indicates some low frequency phase shift that may result in a lack of punch and tightness in the lows. In the 300Hz response we can see an excessive first overshoot and a significant amount of subsequent noise, possibly due to resonances behind the driver in the tubular shaped capsule housing. In listening, I find these headphones bass shy, and very piercing.
AKG K701
Science_InterpretingSquareWaves_Graph_AKGK701The 30Hz square wave of the K701 presents a fairly strongly descending and bowed waveform, which indicates a fairly strong roll-off in the bass, but it doesn't go below zero, which indicates its bass is tighter than the two headphones above. 300Hz wave shape shows a significantly smaller first overshoot, but one that is still a bit too high for me, likely resulting in the slightly piercing sound of these cans. The remainder of the 300Hz waveform top has little noise showing these cans are nicely damped and will deliver a clear, grain-free sound.
Sennheiser HD 800
Science_InterpretingSquareWaves_Graph_SennheiserHD800Surprisingly similar to the AKG K701 above, but with somewhat better performance. 30Hz square wave is slightly less bowed downward indicating better bass response. 300Hz plot shows slightly quicker rise time, and slightly less noisy waveform indicating an even more articulate and clean headphone than the K701 above. Waveform is less tilted than the K701 indicating these cans will have a slightly better treble to mid proportion. First overshoot is still too high, however, so the slightly piercing character remains.
Beyerdynamic T70
Science_InterpretingSquareWaves_Graph_Grado PS1000Here we see in the 30Hz response a headphone with better extended and tighter bass than those so far shown. Waveform top is quite a bit more linear, but small kinks indicate a slightly uneven low to mid response. 300Hz waveform has an overall better shape than the previous two, leading me to believe I'd hear better proportion between treble and mids, and the first overshoot is about the right level. But significant noise and double peak on the leading edge indicate significant resonance, which may make for poorer imaging and a grainy sound.
Audeze LCD2
Science_InterpretingSquareWaves_Graph_Grado PS1000Here we see an essentially perfect 30Hz square wave response with a nearly horizontal and ruler flat waveform top. These cans do indeed have stunning bass response, extremely well extended and tight. The 300Hz wave form has about the right amount of, or maybe slightly low, first overshoot, but it is followed up by a nearly equal in height second spike. I've begun to believe that this second blip is interfering with the ear's ability to discriminate leading edge transients in the audio, which may reduce one's ability to acquire the timing information needed to properly create an audio image. The idea here is that when we see headphones with hash on the front end of the 300Hz square wave, we might be able to predict poor imaging. The remainder of the 300Hz waveform is somewhat non-linear, which may lead to some unevenness in the mid to treble transition, but I've not heard that in particular with these cans.
Shure SE535
Science_InterpretingSquareWaves_ShureSE535This is one of my favorite in-ear headphones. The 30Hz square wave clearly shows a powerful and linear bass response. The 300Hz square wave shows excellent shape but for one unusual feature: a brief movement in the negative direction prior to moving upward. This is a 3-driver balanced armature headphone with a cross-over circuit. I think what we're seeing here is that the tweeter is out of phase with the other two drivers due to high order filters. Having a driver out of phase relative to other drivers in a multi-way speaker is not uncommon, but I haven't seen it elsewhere with headphones. The rise time of the front of the square wave doesn't look very fast, but you must remember that it's the tweeter going in the negative direction at first that's providing the speed. This is one of those cases where we're not seeing all of the information needed as some phase information is hidden from view.
Fostex TH900
Science_InterpretingSquareWaves_Graph_FostexTH900Here, we see in the 30Hz square wave a hump early in the wave shape followed by a nice linear trailing down slope. The trailing down slope indicates a tight, well extended bass. The beginning of the hump at the start is magnified in the 300Hz square wave, and indicates stronger mids relative to the highs, and generally leads to a punchy, snappy sound. The first overshoot, however, will deliver a little extra crispness to its reproduction, and the subsequent noise will bring some graininess.
Philips L1
Science_InterpretingSquareWaves_Graph_PhilipsL1Similar to the Fostex above, the L1's 30Hz square wave indicates a punchy sound and taut, nicely extended bass. This time, however, the leading edge doesn't overshoot, but rather undershoots on the second swing before returning to the waveform top. My experience with this type of headphone is that it has an artificial sounding treble. The only way I can describe it is that it sounds sort of like crinkling the transparent colored cellophane wrapping of fruit baskets. I suspect it will also disturb imaging.
Koss PortaPro
Science_InterpretingSquareWaves_Graph_KossPortaProThis is an inexpensive and small on-ear headphone that sounds great for what it is. You can see in its 30Hz square wave the bass response is limited, but it doesn't go very far out of phase, so it's tight. The 300Hz square wave doesn't overshoot quite enough, which means its treble transient response is a bit poor, but it doesn't do very much wrong either. Really a stunning result for a compact $40 headphone.
Sony MDR-V600
Science_InterpretingSquareWaves_Graph_SonyMDRV600Here's a headphone designed back in the day when mid-heavy headphones that lacked bass and treble responsiveness were pretty much the norm. In fact, I think the V600 is one of the better Sony cans of this type. Here you can see the strongly bowed 30Hz response going somewhat under zero indicating lack of both extension and tightness. And in the 300Hz response a driver struggling to snap up to level. This is a pretty boring headphone.
Sony XB500
Science_InterpretingSquareWaves_Graph_SonyXB500My favorite of the Sony Extra Bass line of headphones, here you can see a headphone that draws a pretty good 30Hz plot with a fairly linear wave top indicating both good extension and bass punch. But the 300Hz leading edge appears to...wait, what leading edge? Yes, treble speed is virtually non-existent with these cans, and the tortuous wriggling the signal does before it finally makes its way to the top about half way through the cycle clearly indicates a great deal of unevenness in the treble to mid transition. In some ways this is not so much a bass-emphasis headphone as a treble/upper-mid reduced one.
Monster Beats Solo HD
Science_InterpretingSquareWaves_Graph_BeatsSoloHDLast, and without doubt among the least, is the Beats by Dre Solo HD. The rounded, broke-back look of its 30Hz square wave is a clear indication of phase problems and indicate a loose, boomy bass. The fact that it remains high in level throughout means you'll have poor quality bass all the way down to 30Hz pummeling your ears. The quick features of the 300Hz leading edge, unlike the XB500 above, means that you'll get a little bit of articulated treble, but the rapidly rising remainder of the waveform indicates it will be overwhelmed by the mids and bass.

Well, there you go, a pretty full run-down on square waves. If you've got any questions, feel free to post them in the comments and I'll try to help you out. To look at all the headphone measurement data sheets go here. You can view the individual sheets or download a .pdf of all graphs in the link near the top of the page.

I found few pieces of information on interpreting square waves for frequency response but there's a little here and here.
Here's a cool applet with which you can generate square waves from odd harmonics.
Information on testing of amplifiers with square waves here and here.


dalethorn's picture

Reading page 2 here brought tears to my eyes in a couple places, but when I got to the PS-1000 - yikes! Glad I didn't buy that one.

Jazz Casual's picture

So the PS1000's square wave response isn't up to snuff. And it has an abundance of treble, a slightly recessed midrange compared to the Prestige and Reference series Grados and a mid-bass hump. But the PS1000's treble is not at all sharp and nor is it bass lite to my ears. I've read criticisms of this phone for having too much bass. Having heard the Fostex TH900, which has a measurably better square wave response, I found it suffered from a noticeably recessed midrange and overpowering bass. So let's not make the mistake of judging a headphone on how well it measures alone. Imagine if you had judged your Grado PS500 on that basis. You would have denied yourself the opportunity of hearing a headphone, that compelled you to share your positive experience in a forum thread at this very site.  

Alondite's picture

The problem with your ears is that perception differs from person to person, and even within one person's perception as they "adapt" to a particular signature. I occasionally have to check to make sure I don't have the bass boost turned on on my amp with my AD900s, but they certainly have light bass. My GR07s are much closer to neutral in terms of quantity, but when I go to them from my AD900s they sound like nothing but bass. The opposite is true when I do it in reverse. 

These graphs show the objective qualities of the cans. That is, they show how they actually sound regardless of perception. Now even Tyll has said that they don't tell the whole story, but they can give you an idea of the sound characterisitcs of any given headphone. Unless your ears and personal preferences are identical to mine, we are likely going to percieve headphones differently. Such is the problem with subjective experience: it is only valuable to you as an individual. The same is true for any subjective experience. 

However, perceived relativism can still be valuable. You may not find the PS1000 treble to be piercing, but I'm sure you will still find cans that measure as having less treble presence than the PS1000 to, in fact, have less treble. For example, you experience with the TH900 as being recessed in the midrange is likely relative to your own experience rather than to neutral (though there is a bit of a notch in the midrange). 

dalethorn's picture

Now here's a thought Sir Jazz - I just picked up a Sennheiser Amperior at the Apple store in Akron Ohio, where the manager and asst. manager were curious about the headphone business. I pointed them here. But back to the Amperior - very rich sound - the sort of sound I would expect of a Grado PS1000. My wife tried them and remarked "Wow - the bass is great, the highs are rich, and you can hear every detail in the mids. So I was thinking, if you could borrow these for 2 or 3 days and give them a thorough shakedown, how the PS1000 might sound after that.

At $350 USD you wouldn't expect a lot of refinement, but there's still a lot to like...

Jazz Casual's picture

I'd be happy to audition it Mr Thorn. I'll see what I can do. However, being a closed design I wouldn't expect it to have the clarity, airiness and grand soundstage of the PS1000.  

dalethorn's picture

Definitely not the soundstage. No comparison there. But since these properties are interrelated (soundstage does affect perception of clarity and airiness too), that might make the suggestion moot.

Jazz Casual's picture

I've found that closed-back headphones lack the openness and clarity of open-backed models, which I suppose isn't all that surprising. Grados excel at conveying this and the PS1000 even more so.  

frenchbat's picture

Great piece Tyll. Is it your "As I see it" piece ?

Anyway I surely do understand your methodology much better now. Thanks a lot.

Phos's picture

I half suspect if you were to fully dissasemble the XB500 you'd find an inductor in the signal path somewhere.  


Take apart the solo HD and you'd probably find a talking action figure in each cup.  

Tyll Hertsens's picture

"Take apart the solo HD and you'd probably find a gold tooth and a 40 of Old English 800 in each cup."

yuriv's picture

Sounds pretty good too. Better than the UE700 IMO. Time for a proper review?

Also, almost all cheapo IEMs have that extreme elevated bass response with the peaky treble, like you have in the last graph for the Turbines and Beats. For example, JVC, Panasonic, and Philips IEMs. A notable exception is the Monoprice MEP-933.

In some cases, there's an easy mod that fixes the response: Make the vent hole bigger until you get the bass response you want. But if you do only that, you get more noticeable treble peaks, which sound harsh. For that, place a tiny amount of acoustic dampener material in front of the nozzle opening. Tips like Comply TX400 have a wax guard that can hold the absorber in place. (Actually the TX400 by itself helps a lot.)

The result is a much, much better sounding cheap IEM. It works for the Panasonic HJE120 and the Philips 3580. I wonder what the square waves will look like? Maybe we can send you some modded ones for measurements?


Tyll Hertsens's picture

I've measured some of the UEs and heard more at RMAF last year.  I thought they were remarkable good.

Sure, If you want me to send some modded cans, I'm always ready to run them through. Contact me at tyll(at)tyllhertsens.com.

donunus's picture

very cool article, among the best and most informative I've seen!

dalethorn's picture

Yes, this is the best presentation I've seen so far for interpreting square waves etc.

ClieOS's picture

Fully agree. Another excellent writeup, Tyll!

Willakan's picture

Wonderful article! I would be very interested to hear more about your rationale behind links between blips on the edges of the waveform and imaging ability.

Tyll Hertsens's picture

The primary mechanism that contributes to our ability to create and aural image is interaural time difference (ITD). The ITD is the arrival time difference between ears for an off-axis signal. For a 30 degree off-axis speaker to the right, the left ear hears the audio 400 micro seconds after the right. You brain listens for arrival ITDs by listening to the "edges" in the sound, typically in the upper midrange and low treble.  But if your headphone is adding a second edge to each feature at about the normal ITD, it's likely going to confuse your brain as it searches for exactly where the delay is.  The second blip in the LCD-2 is about 300 micro seconds after the initial edge, so it's right in the region of ITDs needed to build an audio image between two speakers.

I'll that if you look at all the 300Hz square waves measured so far, the great majority do have significant features after the leading edge, and generally headphone imaging is fairly poor.  I'll also mention that the HD800, a headphone that has an extraordinarily clean leading edge with little secondary features, is well know to image very well.

Hope that helps.

Willakan's picture

It did indeed. I hope that the forthcoming "Headphone Measurements Explained" maintains this level of detail throughout, because this is great.

Tyll Hertsens's picture

Wouldn't have it any other way.

I took me a week to research and write though ... I learned a hell of a lot in the process too.  Unfortunately it won't do a lot for long term page views, but I think it's terribly important to improve the level of understanding among the headphone faithful. My hope with this stuff is the raise the collective wisdom of headphone enthusiast dialog, so sometime I feel like I have to do things that don't directly increase pageviews.

You'll understand though, I hope, if these types of posts aren't quite as frequent as we all might like. 

ultrabike's picture

I see visually significant differences in the 30Hz and 300Hz SW responses between the Grados and a DT770. Same could be said about the PortaPros and the Philips L1's. More importantly, the explanations and discussion in the article regarding the audio qualities assigned to each of the characterization plots are invaluable, as they seem well correlated to the real world audio experince.

That said, some SW curves are a little more difficult for me to differenciate. I was comparing the SW responses between the HD650 and the DT880-600ohm and they seem more similar than different. They sort of seem to fall between the HD800 and the DT770. Yet, the HD650 has been described as sort of dark compared to the DT880-600 and the FR seems to back this up. Same could be said when comparing the SkullcandyHesh2 and the Noontech Zoro. Similar SW responses in my opinion, yet very different distortion and FR curves.

My comments here are not geared towards nit picking. In fact, because I'm more familiar with other characterization measurements, I have learned quite a bit from this and many other articles here at IF. I'm an avid reader of them smiley. My point is that, as with any characterization tool, it is important to understand it's limitations, so as to not go out with a feeling that these and other measurements tell the whole story. Different set of measurements provide us with different views, and understanding, of a system's behaviour.

I also would like to add that I very much apreaciate your discussion regarding headphone FR phase impact.

Tyll Hertsens's picture

"My point is that, as with any characterization tool, it is important to understand it's limitations, so as to not go out with a feeling that these and other measurements tell the whole story. "

Absolutely. One really has to scan the whole page of graphs to get a reasonable picture. Even then it's missing things like CSD plots that are extremely valuable. 

I think one of the most valuable things measurements provide is something to have in mind when you do listening test. You can make observations from the data and then see if you can hear what the measurements indicate. Most times you can but sometimes you can't. Listening is such a different thing than measuring, and it can be quite disorienting to try to objectively parse a subjective experience. The measurements provide a little road map for headphone evaluation, but it's in the listening we actually travel the territory.

HammerSandwich's picture

Fantastic article, Tyll.

Think I found a typo in the LCD2 section.  When you mention "the 30Hz wave form" & it's 2nd spike, aren't you talking about the 300Hz?

Also, do you believe that imaging is more dependent on clean transients or channel matching?  And how the hell could we test that without a zillion samples?




Tyll Hertsens's picture

Man, that little zero messes me up ... a lot. 

"Also, do you believe that imaging is more dependent on clean transients or channel matching?"

I've read studies where researchers would make a left speaker a little louder but advance the right signal in time so it's signal arrived first at the ears. What they found was the interaural time difference was something like ten times more powerful than level differences in developing localization experience. So I believe clean transients are significantly more important than level matching. 

AstralStorm's picture

Not to mention that while linear effects like frequency response are easy to correct, nonlinear ones like phase issues or ringing (visible on CSD) are really hard to fix, if not impossible altogether.

ultrabike's picture

FR phase and CSD issues are linear since they are derived from the impulse response though linear operators.

However, the fact that these issues are linear, does not mean they are fixable. In the digital domain, impulse response issues due to zeros outside the unit circle cannot be corrected (requires an unstable filter) Severe notches may not be corrigible either as signal may be attenuated bellow the noise floor if not completely absent... Furthermore, the fact that headphone impulse response is a bit positional variant complicates things.

That said, a good equalizer can go a long way in fixing some FR magnitude/phase and CSD issues.

dalethorn's picture

EQ'ing small frequency response deviations may be easy when they're small and the fix is simple, but when a bigger fix is needed the simpler fixes tend to create large narrow peaks and dips between the sliders' center frequencies. So then you get to 30 or more band equalizers and a lot of tedium. I think these big equalizers were made for loudspeakers and people with sound meters where most of the process can be automated. With headphones I don't think the fixes are easy because you really have to go by your hearing and not a meter, and you're equalizing the device and your ears at the same time.

Tyll Hertsens's picture

Much better, IMHO.

HammerSandwich's picture

Meant to ask another question: why do you consider an initial overshoot to be ideal?  Is this because the electronics send that signal, so measuring it implies an accurate headphone?  Or do you believe that characteristic indicates that the whole system is more accurate overall?

Tyll Hertsens's picture

Remember that while I have HRTF curves to compensate the frequency response, I don't have compensation information to correct the time based signals. I'm thinking that the small overshoot feature is a result of sound being modified by the pinnae. But the main reason for the observation is that when I do see a headphone that has a 300Hz square wave with a nice square leading edge without overshoot, it tends not to sound fast enough to me. So it's purely an imperical thought at the moment and I have no technical justification.

HammerSandwich's picture