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.

Resources
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.

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