I see. The nice thing about nonsubtractive dither theory is that it gives you a straight answer to what the probability distribution of the dither has to be to make the first n statistical moments of the dithered quantization error independent of the signal. It has to be equivalent to the sum of n independent uniformly distributed random signals of 1 LSB peak-peak each. The only vague part is picking the correct n.
A value n = 1 is sufficient to make the expected value independent of the signal, which eliminates distortion in the sense of spectral lines that shouldn't be there. n = 2 also eliminates noise modulation. It is often claimed that higher values of n produce no audible effect anymore (when the RMS noise is kept equal, that is), but I doubt that after an experiment on this forum with Mooly and PMA as test persons. Still, they did not have a preference for n > 2, so in that sense n = 2 is a good choice.
When you don't have enough quantization levels to dither according to theory, like in a straight single-bit sigma-delta modulator, there is not much you can do other than experimenting with the dither.
A multibit modulator brings back the matching issues that single-bit modulators eliminated, so you have to find a way around that again. One approach is using unit DACs and a mismatch-shaping DEM algorithm (which should also not create any tones, this method is very common on DAC chips), another is the trick with an embedded pulse width modulator.
A value n = 1 is sufficient to make the expected value independent of the signal, which eliminates distortion in the sense of spectral lines that shouldn't be there. n = 2 also eliminates noise modulation. It is often claimed that higher values of n produce no audible effect anymore (when the RMS noise is kept equal, that is), but I doubt that after an experiment on this forum with Mooly and PMA as test persons. Still, they did not have a preference for n > 2, so in that sense n = 2 is a good choice.
When you don't have enough quantization levels to dither according to theory, like in a straight single-bit sigma-delta modulator, there is not much you can do other than experimenting with the dither.
A multibit modulator brings back the matching issues that single-bit modulators eliminated, so you have to find a way around that again. One approach is using unit DACs and a mismatch-shaping DEM algorithm (which should also not create any tones, this method is very common on DAC chips), another is the trick with an embedded pulse width modulator.
Indeed, because the embedded pulse width modulator converts it to a single-bit format again. You just need a higher oversampling ratio than with a plain single-bit modulator.
By the way, when you use normal PWM rather than PWM with randomly rotated patterns, you get a tone at the quantizer sample rate again, because for every quantizer sample, you get a pulse-width-modulated pulse. One way to get rid of it is putting a notch of a FIRDAC on top of it.
By the way, when you use normal PWM rather than PWM with randomly rotated patterns, you get a tone at the quantizer sample rate again, because for every quantizer sample, you get a pulse-width-modulated pulse. One way to get rid of it is putting a notch of a FIRDAC on top of it.
But then the penalty with a higher oversampling ratio may be increased close-in phase noise (which IME is most likely going to prove audible to at least a few people in this thread), unless maybe we can do some of the oversampled multibit processing without too much regard to close in phase noise, then maybe reclock the data just before conversion back to analog without using excessively high clock frequencies? Otherwise we may be stuck with a practical RTZ DSD sample rate of DSD256 (22/24MHz MCLK), with whatever that implies for the practicality of sigma delta PWM.
Anyway, the problem may turn out to be to find an optimum, a sweet spot as it were, where the various complicating issues (including close-in phase noise) are more or less traded off equally from a perceptual standpoint.
Anyway, the problem may turn out to be to find an optimum, a sweet spot as it were, where the various complicating issues (including close-in phase noise) are more or less traded off equally from a perceptual standpoint.
It depends. When you have a many-bit ADC and more than 0.5 LSB of Gaussian noise with a flat spectrum from 0 to half the sample rate, it's an imperfect but fairly good dither. In the case of a sigma-delta modulator with its very coarse quantizer running at a much higher rate than the signal bandwidth, the effect is much less, although it still smears out the idle tones near fs/2 to some extent.
Agreed, it depends. The usual answer is that for a 24-bit ADC there is enough natural random noise to make additional dither unnecessary. For a high quality 16-bit ADC the answer might not be so simple.
Regarding noise sources, for things like helicopters, heart beats, cars, etc., most of them do not produce noise that is sufficiently random.
Regarding noise sources, for things like helicopters, heart beats, cars, etc., most of them do not produce noise that is sufficiently random.
In general: yes.
What I wrote about sigma-delta converters applies equally to those used in DACs. They also have an oversampled coarse quantizer that doesn't get dithered all that well by noise in the input signal.
When you use a non-oversampled many-bit DAC with a smaller wordlength than the recording, you have pretty much the same situation as in a non-oversampled many-bit ADC. If the noise is more than about 0.5 LSB of the DAC and has a white spectrum, it works reasonably well without extra dither.
What I wrote about sigma-delta converters applies equally to those used in DACs. They also have an oversampled coarse quantizer that doesn't get dithered all that well by noise in the input signal.
When you use a non-oversampled many-bit DAC with a smaller wordlength than the recording, you have pretty much the same situation as in a non-oversampled many-bit ADC. If the noise is more than about 0.5 LSB of the DAC and has a white spectrum, it works reasonably well without extra dither.
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Doesn't a random phase distribution of the white frequency spectrum also have something to do with it? 
EDIT: Actually, the subject of dither can get somewhat complicated. Modern dither algorithms used in mastering of music these days often involve complex adaptive-noise-shaped dithering. Different algorithms are used for different types of music. Some of the algorithms are proprietary secrets.
EDIT: Actually, the subject of dither can get somewhat complicated. Modern dither algorithms used in mastering of music these days often involve complex adaptive-noise-shaped dithering. Different algorithms are used for different types of music. Some of the algorithms are proprietary secrets.
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That's what I meant. A Dirac impulse wouldn't be suitable as dither despite its flat spectral magnitude, but I wouldn't refer to that as noise. By the way, coloured (random) noise should also work when you can regard it as the sum of at least 0.5 LSB of white Gaussian noise and some independent extra noise.
Yes, but its not that simple either. Please consider the old UV-22 "dither" from Apogee. Its a deterministic signal close to fs/2.
UV-22 does not constitute a “new flavor” of dither noise. Instead, UV22 essentially modulates the data from the least significant bits of a signal on to the 16-bit signal according to a special algorithm, which adds an inaudible high-frequency “bias” to the digital bit stream, placing a “clump” of energy at around 22 kHz. This results in an essentially flat noise floor, at the theoretical 16-bit level – 4 to 5 dB below that of conventional “flat dither. In addition, the noise floor does not have the distinctive and annoying “hissiness” of conventional dither. Thus the UV22 noise floor sounds audibly quieter and less objectionable than other techniques. In addition, you cannot hear any audible artifacts. Yet, as with analog, you can hear coherent audio signals several dB below the noise “floor” – thus retaining much of the detail and audio quality inherent in the original signal.
https://knowledge.apogeedigital.com...does-dither-do-why-do-digital-systems-need-it
UV-22 does not constitute a “new flavor” of dither noise. Instead, UV22 essentially modulates the data from the least significant bits of a signal on to the 16-bit signal according to a special algorithm, which adds an inaudible high-frequency “bias” to the digital bit stream, placing a “clump” of energy at around 22 kHz. This results in an essentially flat noise floor, at the theoretical 16-bit level – 4 to 5 dB below that of conventional “flat dither. In addition, the noise floor does not have the distinctive and annoying “hissiness” of conventional dither. Thus the UV22 noise floor sounds audibly quieter and less objectionable than other techniques. In addition, you cannot hear any audible artifacts. Yet, as with analog, you can hear coherent audio signals several dB below the noise “floor” – thus retaining much of the detail and audio quality inherent in the original signal.
https://knowledge.apogeedigital.com...does-dither-do-why-do-digital-systems-need-it
You are right, it doesn't need to be white.
If it's a tone, it doesn't meet the criterion from nonsubtractive dither theory that there should be no spectral lines, but if I remember correctly, you can according to nonsubtractive dither theory use coloured dither as long as the probability distribution is correct. There are a couple of limitations, though.
First, the dither has to be statistically independent of the signal and that criterion is usually not met when you use coloured dither in a system with feedback around the dithered quantizer, such as a noise shaping loop/sigma-delta modulator. There is at least one exception: when the loop coefficients are chosen such that previous decisions of the quantizer only affect the integer part of the quantizer input signal, there is no problem.
Second, there must be some practical limitation to the autocorrelation, as dither noise that has so much autocorrelation that it on average only changes once per hour cannot be very suitable for audio. I don't remember what the theory says about that.
Besides, as always, the question is how bad it is when you don't follow the theory. Dithering with Gaussian noise is in theory only correct when it has an infinite RMS value, but practically, anything above half an LSB works fairly well. The dither schemes used for single-bit sigma-delta modulators cannot follow theory, but are often quite effective.
If it's a tone, it doesn't meet the criterion from nonsubtractive dither theory that there should be no spectral lines, but if I remember correctly, you can according to nonsubtractive dither theory use coloured dither as long as the probability distribution is correct. There are a couple of limitations, though.
First, the dither has to be statistically independent of the signal and that criterion is usually not met when you use coloured dither in a system with feedback around the dithered quantizer, such as a noise shaping loop/sigma-delta modulator. There is at least one exception: when the loop coefficients are chosen such that previous decisions of the quantizer only affect the integer part of the quantizer input signal, there is no problem.
Second, there must be some practical limitation to the autocorrelation, as dither noise that has so much autocorrelation that it on average only changes once per hour cannot be very suitable for audio. I don't remember what the theory says about that.
Besides, as always, the question is how bad it is when you don't follow the theory. Dithering with Gaussian noise is in theory only correct when it has an infinite RMS value, but practically, anything above half an LSB works fairly well. The dither schemes used for single-bit sigma-delta modulators cannot follow theory, but are often quite effective.
So the background noise in every acoustical recording don't serve as dither when playing it back by a DAC. Why not?
It's random /non-correlated and there should be things going on flipping the least bit.... Isn't dither after all a laboratory / clinical measurement "tool" that has no relevance for real music recorded in a real environment... You may say.. but I can hear it when added... well perhaps, but isn't it better without it?
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It's random /non-correlated and there should be things going on flipping the least bit.... Isn't dither after all a laboratory / clinical measurement "tool" that has no relevance for real music recorded in a real environment... You may say.. but I can hear it when added... well perhaps, but isn't it better without it?
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I didn't write anything that black and white, and neither did Mark. There are cases where the background noise works fairly well as dither and there are cases where it doesn't.
Frankly, I don't understand why anyone would want to avoid it. In cases where there is already plenty background noise acting as dither, adding 2 LSB peak-peak triangularly distributed white noise is not going to increase the noise floor much and in cases where there isn't, it is necessary to avoid gross distortion on low-level signals.
Frankly, I don't understand why anyone would want to avoid it. In cases where there is already plenty background noise acting as dither, adding 2 LSB peak-peak triangularly distributed white noise is not going to increase the noise floor much and in cases where there isn't, it is necessary to avoid gross distortion on low-level signals.
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Practically, in the case of sigma-delta modulators, either the ones used in ADCs or those in DACs, a wideband noise signal injected at the quantizer input tends to work better than audio noise, because audio noise is simply too narrowband compared to the sample rate of the quantizer (typically well in the megahertz range).
Today I tested Marcel's LC+MFB filter from post #3028 with OPA1632 as opamp. To my surprise "harmonics" at -60dBFS did not improve at all. Different versions of PCM2DSD work exactly the same as before (v03 having splitted peaks and v04 without).
I also tested the difference of PCM2DSD v03 and v04 with DeltaWave audio null comparator. The difference was very small and by all accounts below audibility. Actually the difference between v03 & v04 was much smaller than e.g. between ESS/AKM dac vs. RTZ dac.
I also tested the difference of PCM2DSD v03 and v04 with DeltaWave audio null comparator. The difference was very small and by all accounts below audibility. Actually the difference between v03 & v04 was much smaller than e.g. between ESS/AKM dac vs. RTZ dac.