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Noise is Noise Or is It?

Posted by Peter Qvortrup (M) on February 23, 2007 at 09:43:25

In Reply to: Re: Noise floor vs. uncorrelated noise posted by theaudiohobby on February 23, 2007 at 06:45:39:

Dear TAH,

OK, so let us look at what these differences are then, since you persist.

Firstly, analogue is quantised, but at a ridiculously low level, Planck time etc, this is true physical quantisation and is quite different to the quantisation we speak of with digital.

Here is why,

The case with digital audio is that there is quantisation in two dimensions, time and amplitude. Dither uses the stochastic resonance effect on the amplitude dimension, but leaves the time dimension rigidly quantised.

Anyway, the digital noise floor is not the same as the analogue floor. If you conceptually look at it, at any moment in time, and considering signal voltage for convenience. The analogue floor, again at any given time, could according exist at any voltage level, there are some levels which are highly improbable, and some which are physically limited however within reason the voltage level could be anything at all.

Adding hither and dither.

By adding dither at the recording end the previously undetectable signal is encoded into the digital data by way of a kind of PWM (pulse width modulation), the higher level the undetectable signal, the more often will it toggle the LSB when ordinarily it wouldn’t do so.

If you apply a low level signal to an ADC, one which never reaches an amplitude which would toggle the LSB (lowest significant bit), you won’t see it. If you add some noise such that there is some proportionality between the signal level and how often the LSB is toggled per unit time, and then you integrate the output, you can detect some kind of representation of it. The smaller the signal is, the longer and longer the time which is required to build up a picture of it.

It isn’t magic though, the dither signal pushing the LSB to toggle means that occasionally the ADC input will clip when it wouldn’t have done with no dither. With CD you have a 16 bit window, but the same applies to any bit window, at one end is no recorded information, at the other end is clip.

By adding dither at the playback end you can lessen the unpleasant effects of noise which is correlated with the signal, and make something which measures like true analogue noise, whether it sounds the same as analogue noise is another matter.

Sample by sample, there can be no information which occupies any level smaller than the LSB of the data, but if the output is integrated, and the “previously undetectable signal” was periodic (or DC), which then had a PWM effect on the ADC data, and you do an FFT of the signal taken over many, many samples you’ll see some kind of representation of it. Once again, by adding dither to the data going into the DAC occasionally it will clip when with no dither it wouldn’t have. So dither increases detectability, but reduces dynamic range, and a compromise is required.

The increase in detectability relies on the signal being periodic or DC, so that you can build up a picture of that signal over more samples than would be required to record a signal which is within the normal 16 bit window.

With music, as far as we are concerned, you need to look at the situation without any kind of averaging or integrating, because it must be assumed there is little or no correspondence between one sample and the next. If this assumption is accepted then dither makes no difference, all that can be recorded must be done so within the 16 bit amplitude window.

Analogue has no such constraints, effectively it has no quantisation in either the frequency or time dimensions and that in our view explains why a good analogue recording will never be bettered by any digital medium regardless of theoretical "resolution", noise or bandwidth.

Sincerely,
Peter Qvortrup
Andy Grove

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