That's a clear explanation of the self-dither assumed in A/D conversion, thanks for posting it.
Vicki On Feb 8, 2015, at 9:11 PM, Andrew Simper wrote: > Vicki, > > If you look at the limits of what is possible in a real world ADC > there is a certain amount of noise in any electrical system due to > gaussian thermal noise: > http://en.wikipedia.org/wiki/Johnson%E2%80%93Nyquist_noise > > For example if you look at an instrument / measurement grade ADC like > this: > http://www.prismsound.com/test_measure/products_subs/dscope/dscope_spec.php > They publish figures of a residual noise floor of 1.4 uV, which they > say is -115 dBu. So if you digitise a 1 V peak (2 V peak to peak) sine > wave with a 24-bit ADC then you will have hiss (which includes a large > portion of gaussian noise) at around the 20 bit mark, so you will have > 4-bits of hiss to self dither. This has nothing to do with microphones > or noise in air, this is in the near perfect case of transmission via > a well shielded differential cable transferring the voltage directly > to the ADC. > > All the best, > > Andy > -- cytomic -- sound music software -- > > > On 9 February 2015 at 00:09, Vicki Melchior <vmelch...@earthlink.net> wrote: >> I have no argument at all with the cheap high-pass TPDF dither; whenever it >> was published the original authors undoubtedly verified that the moment >> decoupling occurred, as you say. And that's what is needed for dither >> effectiveness. If you're creating noise for dither, you have the option to >> verify its properties. But in the situation of an analog signal with added, >> independent instrument noise, you do need to verify that the composite noise >> source actually satisfies the criteria for dither. 1/f noise in particular >> has been questioned, which is why I raised the spectrum issue. >> >> Beyond that, Nigel raises this issue in the context of "self-dither". In >> situations where there is a clear external noise source present, whether the >> situation is analog to digital conversion or digital to digital bit depth >> change, the external noise may, or may not, be satisfactory as dither but at >> least it's properties can be measured. If the 'self-dithering' instead >> refers to analog noise captured into the digitized signal with the idea that >> this noise is going to be preserved and available at later truncation steps >> to 'self dither' it is a very very hazy argument. I'm aware of the various >> caveats that are often postulated, i.e. signal is captured at double >> precision, no truncation, very selected processing. But even in minimalist >> recording such as live to two track, it's not clear to me that the signal >> can get through the digital stages of the A/D and still retain an unaltered >> noise distribution. It certainly won't do so after considerable processing. >> So the sho r > t >> answer is, dither! At the 24th bit or at the 16th bit, whatever your output >> is. If you (Nigel or RBJ) have references to the contrary, please say so. >> >> Vicki >> >> On Feb 8, 2015, at 10:11 AM, robert bristow-johnson wrote: >> >>> On 2/7/15 8:54 AM, Vicki Melchior wrote: >>>> Well, the point of dither is to reduce correlation between the signal and >>>> quantization noise. Its effectiveness requires that the error signal has >>>> given properties; the mean error should be zero and the RMS error should >>>> be independent of the signal. The best known examples satisfying those >>>> conditions are white Gaussian noise at ~ 6dB above the RMS quantization >>>> level and white TPDF noise at ~3dB above the same, with Gaussian noise >>>> eliminating correlation entirely and TPDF dither eliminating correlation >>>> with the first two moments of the error distribution. That's all >>>> textbook stuff. There are certainly noise shaping algorithms that shape >>>> either the sum of white dither and quantization noise or the white dither >>>> and quantization noise independently, and even (to my knowledge) a few >>>> completely non-white dithers that are known to work, but determining the >>>> effectiveness of noise at dithering still requires examining the >>>> statistical properties of the error signal and showi n > g >> >>> th >>>> at the mean is 0 and the second moment is signal independent. (I think >>>> Stanley Lipschitz showed that the higher moments don't matter to >>>> audibility.) >>> >>> but my question was not about the p.d.f. of the dither (to decouple both >>> the mean and the variance of the quantization error, you need triangular >>> p.d.f. dither of 2 LSBs width that is independent of the *signal*) but >>> about the spectrum of the dither. and Nigel mentioned this already, but >>> you can cheaply make high-pass TPDF dither with a single (decent) uniform >>> p.d.f. random number per sample and running that through a simple 1st-order >>> FIR which has +1 an -1 coefficients (i.e. subtract the previous UPDF from >>> the current UPDF to get the high-pass TPDF). also, i think Bart Locanthi >>> (is he still on this planet?) and someone else did a simple paper back in >>> the 90s about the possible benefits of high-pass dither. wasn't a great >>> paper or anything, but it was about the same point. >>> >>> i remember mentioning this at an AES in the 90's, and Stanley *did* address >>> it. for straight dither it works okay, but for noise-shaping with >>> feedback, to be perfectly legitimate, you want white TPDF dither (which >>> requires adding or subtracting two independent UPDF random numbers). and i >>> agree with that. it's just that if someone wanted to make a >>> quick-and-clean high-pass dither with the necessary p.d.f., you can do that >>> with the simple subtraction trick. and the dither is not white but >>> perfectly decouples the first two moments of the total quantization error. >>> it's just a simple trick that not good for too much. >>> >>> -- >>> >>> r b-j r...@audioimagination.com >>> >>> "Imagination is more important than knowledge." >>> >>> >>> >>> >>> -- >>> dupswapdrop -- the music-dsp mailing list and website: >>> subscription info, FAQ, source code archive, list archive, book reviews, >>> dsp links >>> http://music.columbia.edu/cmc/music-dsp >>> http://music.columbia.edu/mailman/listinfo/music-dsp >> >> -- >> dupswapdrop -- the music-dsp mailing list and website: >> subscription info, FAQ, source code archive, list archive, book reviews, dsp >> links >> http://music.columbia.edu/cmc/music-dsp >> http://music.columbia.edu/mailman/listinfo/music-dsp > -- > dupswapdrop -- the music-dsp mailing list and website: > subscription info, FAQ, source code archive, list archive, book reviews, dsp > links > http://music.columbia.edu/cmc/music-dsp > http://music.columbia.edu/mailman/listinfo/music-dsp -- dupswapdrop -- the music-dsp mailing list and website: subscription info, FAQ, source code archive, list archive, book reviews, dsp links http://music.columbia.edu/cmc/music-dsp http://music.columbia.edu/mailman/listinfo/music-dsp
