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  • 2Bdecided
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People showing how great their turntables sound
Reply #100
TPDF dither when applied with sufficient ampltude is supposted to decorrelate the second moment.
Speaking from ignorance and still without the paper in front of me, I would venture to guess that in this case it's the third and higher moments which are not decorrelated by correct TPDF dither.

Ah, this probably helps if you have a spare month to follow it all...
http://audiolab.uwaterloo.ca/~rob/abstracts/ieee.pdf
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It is shown that by the use of dither having a suitably-chosen probability density function, moments of the total error can be made independent of the system input signal, but that statistical independence of the error and the input signals is not achievable.

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For many applications, controlling relevant error moments is just as good as having full statistical independence of the input and error processes.


I've never seen any evidence that this is audible. It just means that dither makes things audibly fine, but not statistically perfect.

Of course there's plenty of evidence that the noise/distortion/error of various analogue sources is highly dependent on the input signal - often in an audible way.

Cheers,
David.

People showing how great their turntables sound
Reply #101
Of course there's plenty of evidence that the noise/distortion/error of various analogue sources is highly dependent on the input signal - often in an audible way.


Relevant example: modulation noise in magnetic tape.  BTW, one can use a very high frequency tone as if it was dither to vastly reduce the audibility of quantizaiton distortion.  Magnetic tape was arguably the first use of quantization as part of audio recording...

  • Woodinville
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People showing how great their turntables sound
Reply #102
TPDF dither when applied with sufficient ampltude is supposted to decorrelate the second moment.
Speaking from ignorance and still without the paper in front of me, I would venture to guess that in this case it's the third and higher moments which are not decorrelated by correct TPDF dither.

Ah, this probably helps if you have a spare month to follow it all...
http://audiolab.uwaterloo.ca/~rob/abstracts/ieee.pdf
Quote
It is shown that by the use of dither having a suitably-chosen probability density function, moments of the total error can be made independent of the system input signal, but that statistical independence of the error and the input signals is not achievable.

Quote
For many applications, controlling relevant error moments is just as good as having full statistical independence of the input and error processes.


I've never seen any evidence that this is audible. It just means that dither makes things audibly fine, but not statistically perfect.

Of course there's plenty of evidence that the noise/distortion/error of various analogue sources is highly dependent on the input signal - often in an audible way.

Cheers,
David.


To this point, consider what the ear can detect, which is a frequency analysis of sorts of the noise (and signal, of course).

When you have a white spectrum for the noise, you've accomplished what you needed to do. It is, of course, possible to use a gaussian dither, as well. But how far down the central limit theorem do we need to travel?
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J. D. (jj) Johnston

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People showing how great their turntables sound
Reply #103
To this point, consider what the ear can detect, which is a frequency analysis of sorts of the noise (and signal, of course).

When you have a white spectrum for the noise, you've accomplished what you needed to do. It is, of course, possible to use a gaussian dither, as well. But how far down the central limit theorem do we need to travel?

That's not a rhetorical question, right?

I mean... the ear is at a very fundamental level sensitive to signal energy, which is intrinsically linked to the second moment. If any higher moments were to be audibly significant in and of themselves, that would suggest to me that phase distortion would be orders of magnitude more audible than it is observed to be.

QED?

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People showing how great their turntables sound
Reply #104
That's not a rhetorical question, right?
I was hoping it was!

What we're talking about is subjective - we know there's a difference, the question is whether humans can hear it.

Imagine trying to design a test to see if there is an audible difference between having a correlated vs decorrelated third moment of the error. It's "easy" because you can use 8-bits, and simply add yet another RECT PDF noise source to the dither. Problem is, you know people can hear that - it's more noisy - so ABX will be positive, but prove nothing about what you want to know!

You could flip to and from a higher bitdepth and do some gain twiddling there to match dither noise power between the two cases. That way, I think it would be possible to make a "fair" experiment, but people might argue that whatever method you used to match dither noise power (e.g. RMS level) wasn't quite justified, or may be problematic enough to give a false positive. If you're trying to ABX something which is generally believed to be inaudible, you'd better make damn sure the levels are matched - and in this case, it could be hard to say (hand on heart) that they were. Different PDFs. What is a "match". etc.

Even if the level matching seems justified, and there was a weak preference for adding 3 RECT PDF noise sources rather than 2, in the real world you don't get the luxury of level matching and the 3 noise source dither is louder, which is objectionable in itself. So overall it might be a bit pointless.

I know we could use Gaussian, but when people say that, they usually mean using it at a level far lower than I think is "correct" - i.e. a level at which it seems to work OK most of the time, but without the mathematical guarantee that it's even decorrelating the first and second moments of the error properly. If we move from RECT to TRI (2 * RECT) etc etc and keep adding RECT noise sources, we get a lot more noise by the time it's something like Gaussian.

(I'm not trying to speak with a position of authority here - I'm hoping other people here can help think this through and point out any misconceptions I might have)

Cheers,
David.

  • Paulhoff
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People showing how great their turntables sound
Reply #105
It is funny how a friend of mine recorded a Vinyl record and made a CD of it. He could not get over how is sounded like the Vinyl he loved, with all its added distortion and noise. 

Paul

     
"Reality is merely an illusion, albeit a very persistent one." Albert Einstein

  • Woodinville
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People showing how great their turntables sound
Reply #106
It is funny how a friend of mine recorded a Vinyl record and made a CD of it. He could not get over how is sounded like the Vinyl he loved, with all its added distortion and noise. 

Paul

     


Almost like you can capture all that analog distortion on CD. Imagine.
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J. D. (jj) Johnston