[bobbooo]

Quote:

  There is absolutely no audible difference in crosstalk at 49dB vs 75dB. In both cases there will be no discernable crosstalk at all. It's just a numbers game.

 
Right, I see no reason to 'upgrade' from my S7 then.
 

  Well, I cheated and put the whole formula into a spreadsheet about 30 years ago (in the original issue of Excel, on a Mac Plus!), but it's all shown here.
 
Using Voltage Divider 1, what you have can be simplified to a voltage divider with the source Z entered as Z1 and the load Z (headphones Z at a particular frequency) as Z2.  Using an arbitrary 1V as the applied voltage, you calculate the voltage drop across the load at 0.823V.  Then, using the next calculator block, enter Vin as 1, Vout as .823, you get 1.69dB.  Next run the same calculations, this time using the average headphone Z of 27, which comes out to a drop of .9V, 0.91dB.  Subtract that from the maximum change at the minimum impedance dip, you get .78dB. dip vs average.  If you run the entire calculations again, this time using the maximum Z of the phones, you'll get the maximum response variation.  
 
Edit: The calculations are approximate because we don't really know enough about the amplifier output impedance, so in the calculations it is considered to be purely resistive, with no reactive components, which is probably not precisely true.  
 
The numbers don't reflect audibility, but they are quite small already.  The audibility characteristic of a narrow band frequency change is a matter of psychoacoustics, related to a combination of the area of the response dip/peak, and the strong or dominant presence of audio in that band as balanced against the rest of the total spectrum.  The area affected the most by the impedance change is around 10kHz and less than an octave wide.

 
Thanks for the explanation, much appreciated.
 

The point is, if earphones have a cliff-face CSD plot if you EQ them to flat, (and I have reason to believe this is the case for IEMs even more so than headphones) then whatever decay you see in a CSD plot of the earphones with their default frequency response, are entirely the result of the earphones having that frequency response. In mathematical terms, we say that the earphones are already "minimum phase" and it is technically impossible to improve on the earphones' impulse response performance (another way of saying reducing CSD decay) without improving the earphones' frequency response, e.g. via minimum phase EQ.

The reason why this is so is, soundwaves can be decomposed into individual frequency sine waves, which each have infinite decay times. An ideal impulse response is composed of a superposition of all frequencies, all in phase and *in equal proportion*. They all cancel out each other, except at the point of the impulse, where they all reinforce each other. Anytime the proportionality of the frequencies is not perfectly even, the cancellation of individual frequencies becomes imperfect and so the impulse cannot possibly start and stop on a dime as desired.

 
I'm aware that the impulse and frequency response are each individually sufficient to characterize headphones' sonic behaviour, as the latter is just the Fourier transform of the former. This is why I concluded the impulse response of my headphones would change with changing output impedance if the frequency response does. My original question was whether these changes would be audible, and it seems they wouldn't be in my case. I still don't think presenting the CSD with the headphones EQed to flat is useful though, as this is never practically done when listening to music, and due to the exact mathematical relationship between the impulse and frequency responses, if all measured headphones are perfectly EQed to be exactly flat, they will necessarily all have the same, perfect CSD plot, and if not, this will only tell you that either the EQing was not perfectly identical between headphones, or there's some discrepancies in the measuring processes. Of course, as the frequency and impulse responses are so intimately related, in real-world listening there's a trade-off between achieving accurate frequency reproduction and fast impulse response.

 

[Joe Bloggs]

I'm aware that the impulse and frequency response are each individually sufficient to characterize headphones' sonic behaviour, as the latter is just the Fourier transform of the former. This is why I concluded the impulse response of my headphones would change with changing output impedance if the frequency response does. My original question was whether these changes would be audible, and it seems they wouldn't be in my case. I still don't think presenting the CSD with the headphones EQed to flat is useful though, as this is never practically done when listening to music, and due to the exact mathematical relationship between the impulse and frequency responses, if all measured headphones are perfectly EQed to be exactly flat, they will necessarily all have the same, perfect CSD plot, and if not, this will only tell you that either the EQing was not perfectly identical between headphones, or there's some discrepancies in the measuring processes. Of course, as the frequency and impulse responses are so intimately related, in real-world listening there's a trade-off between achieving accurate frequency reproduction and fast impulse response.

Well not exactly, for example loudspeakers in a room wouldn't have such a simple relationship between its frequency response and impulse response, because they would have crossovers and room echoes, neither of which are minimum phase phenomena. Neither would any multi-driver earphones. The housing of closed earphones should also deviate from minimum phase a bit. An FR-corrected CSD plot would reveal such actual deviations from minimum phase much more clearly.

 

[bobbooo]

Well not exactly, for example loudspeakers in a room wouldn't have such a simple relationship between its frequency response and impulse response, because they would have crossovers and room echoes, neither of which are minimum phase phenomena. Neither would any multi-driver earphones. The housing of closed earphones should also deviate from minimum phase a bit. An FR-corrected CSD plot would reveal such actual deviations from minimum phase much more clearly.

 

True, but we’re talking about headphones. I’d be interested to hear more about the relationship between frequency and impulse response for multi-driver earphones, as the measurements I’ve posted in this thread are for such earphones. The problem with trying to reveal deviations from minimum phase by using flat-EQed CSD plots is it’s impossible to EQ any headphones to have a perfectly flat frequency response, so you wouldn’t be able to tell if the deviations in the plot are due to this imperfect EQing, or minimum phase deviations. I still think the standard CSD plots are useful for visualising impulse response, as long as care is taken to look at the steepness of the curve, and not the absolute decay time, to judge real-world decay rate.

 

[Joe Bloggs]

The problem with trying to reveal deviations from minimum phase by using flat-EQed CSD plots is it’s impossible to EQ any headphones to have a perfectly flat frequency response, so you wouldn’t be able to tell if the deviations in the plot are due to this imperfect EQing, or minimum phase deviations. I still think the standard CSD plots are useful for visualising impulse response, as long as care is taken to look at the steepness of the curve, and not the absolute decay time, to judge real-world decay rate.

xnor's plot was performed using a mathematical process, which does yield a perfectly flat frequency response (not possible or desirable to replicate in real world of course, but would have been useful for the cases I mentioned in the previous post). Basically he took the measured impulse response, convolved it with its minimum phase inverse before making the CSD plot.

 

[bobbooo]

xnor's plot was performed using a mathematical process, which does yield a perfectly flat frequency response (not possible or desirable to replicate in real world of course, but would have been useful for the cases I mentioned in the previous post). Basically he took the measured impulse response, convolved it with its minimum phase inverse before making the CSD plot.

 
Interesting. I suppose the best way to present headphones' sonic behaviour then would be to have one CSD plot like that to show minimum phase deviations, and one unaltered plot to show decay rate.