I'll try to explain my curiosity as best I can; currently working on no sleep because of university.
Assumption 1: Ideal for speakers is to reproduce real life
Assumption 2: The ideal square wave, in real life, though impossible is a perfect square wave
Conclusion 1: Therefore the ideal speaker should produce as close to a perfect square wave (and therefore impulse response??)
Assumption 3: The goal of headphones is to sound like real life, and therefore to produce the same square wave as a speaker AT the ear.
I would say this conclusion is correct, and it shows in our speaker and headphone measurement standards: speakers are measured with a flat microphone (or as close to flat as possible), and plotted more or less as-is. Headphones are designed in a manner that tries to reproduce the same sound at the ear as a flat speaker.
The problem is that this makes headphones a non-flat speaker in practise. Therefore, you will have distortions to the square wave and impulse response, no matter how perfect other aspects of the design are. Of the top of my head the problems are as follows;
1. Treble deficiency causes square waves to become rounded (more sinusoidal).
-> The reason for this is that a perfect square wave is a stack of an infinite number of odd harmonic sine waves.
2. Treble excess causes a "downwards slope" and ringing in the square wave
3. Treble excess causes ringing (and overshoot?) in the impulse response.
Now, as is my understanding; you can create the squarewave response and the frequency response from the impulse response. Meaning that, with the fourier transforms, they have a strong correlation.
I noticed, in my many hours of analysing headphone graphs a trend in headphones; they all slope downwards, something you'd expect for excess treble.
Now, someone might pipe up and say that it's because headphones are typically bad at producing bass, because of their small surface area. And that's fine. Allow me to post some headroom graphs (Feel free to remove them if you don't want them posted here). Please feel free to paruse them.
Now, based on these graphs: it is my contention that this method headphone analysis is
FUNDAMENTALLY WRONG. A bassy speaker should produce a rounded square wave, and a trebly speaker shoudl produce a "sloped" (and ringy) square wave. I feel I've demonstrated the strong correlation between the two.
So, why then, do bassier headphones produce nicer looking square waves than ones that look flat? The answer I have come up with is Equalisation. I'll repost that moller graph from another thread.
Look at the curves (specifically the diffuse field for headphones, because Tyll uses a ID equalisation for his HRTF). Unless I am blind, the difference between the treble spike, and the bass is 105-96=~ About 9dB.
Now, if you'd kindly look at the graph with the LCD-2 (headphonemeasurements3.png). The square waves look pretty good, don't they? I'd like you to work out the difference between the bass and the treble. To my eyes, it looks like the LCD-2's bass curve is centred around about +4 dB, while the higher treble (2.5khz) is what,about -3dB. A 7dB difference, close to the moller curve. There is still a little more treble than the moller curve, which is why the square wave still has some ringing and downward slope.
Notice that every headphone in that graph has a similar square wave. It's not a unique property of amazing LCD-2 technology In fact, it looks like the LCD-2 doesn't qutie have the best square wave response there. Why? Because it has the least bass, and therefore, it is further away from the Moller graphs than one of the others. Note that some go over 9dB difference, and there is some rounding in those, instead of the slope.
I hope you can see my reasoning, and a
re interested in this too.
Let me be perfectly clear:
It is my contention that people have been mislead by dodgy measurement practise that the LCD-2 and other headphones produce "good bass" based on the square wave, when what it actually produces, at the ear is a slightly rounded square wave compared to a square wave produced by a flat speaker.That is not to say that the square wave responses we receive are wrong. I think they're pretty close to correct, given the consistency. What I do believe is that Tyll, and others are mixing methods; for frequency response they present headphones as "how they sound compared to a speaker in the field we recorded in", for square wave, I believe they're presenting "This is just what it puts out". If theyre going to do one or the either, they should do it for ALL measurements, and not one. I'd personally prefer RAW responses for all of them because it just makes more sense to me, as I can identify which headphone is designed to which method/standard/field more easily.
I'd really love someone to try and publish the square waves produced by headphones, with their frequency response compensated (via EQ, to save changing the methods of measure).
But to be honest, I haven't really though seriously about this in a long time, so feel free to chime in with corrections/thoughts. I could be completely wrong, and would like to be proven so (to avoid the upset of others). But honestly, I expect that, correctly compensated, we will see that Neutral (i.e. diffuse field, free field etc) headphones produce exactly the same square wave pattern as a speaker that is flat in the same listening conditions (diffuse field, free field). I hope someone does try it, the vindication of being correct, or the humilation of being wrong. I'd still like to see it. Of course true vindication won't be possible unless someone with a flat speaker set (I believe you have nearfield monitors, they're close enough) can demonstrate that they can reproduce, say the square/impulse response (or close enough to it), on their speaker by modifying the frequency balance to be equal to the raw response of a particular headphone.
If you ask me, we are on the cusp of a revolution. Maybe not of the entire measurement practice, but of people at least thinking before they trust anyones graph.
