I’m thankful for Andy posting that clear explanation too. Sometimes I understate things—when I said that it would be “pretty hard to avoid” having ample gaussian noise to self-dither in the A/D process, I was thinking cryogenics (LOL).
> On Feb 9, 2015, at 7:54 AM, Vicki Melchior <vmelch...@earthlink.net> wrote: > > 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 -- 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
