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In Reply to: Re: A lot of people don't understand dither posted by Werner on March 4, 2007 at 23:59:30:
*** How about the thermal noise generated in all (equivalent) circuit resistances ***I've already covered this in my other post.
"A good mic, mic pre amp and analog console have dynamic range of around 130dB. A good ADC will have dynamic range slightly exceeding 20 bits.
So, the noise floor of electronics alone are too low to produce self dithering when truncating from 24 to 20."*** Have a look at the self-noise of your own minimalist recording setup. ***
Yes I have. I have two mixers, 4 sets of 24-bit ADCs, a few amps, mics, lots of keyboards (I did my thesis in computer music) so it's hardly "minimalist". I have also used a few studios.
*** Your analogy is wrong because in the case of truncating an image from 8/8/8 to 5/6/5 the target quantisation noise floor is so high that there is no dither-able noise present in the image at that level. ***
The analogy is apt because I am asserting (based on my experience) that there is usually no "dither-able noise" present above 20 bits in audio, therefore there is a benefit to dithering if truncating to 20 bits.
*** Most of the noise visibly present in the source image is correlated and/or of insufficient bandwidth (shot-noise, algorithm quantisation and errors, dark current, and the shot-noise of the dark current ... none of them remotely gaussian). That's why you need to add external dither. ***
Your argument applies equally to audio. That's why it's a good analogy. As I've mentioned in my other post, you can do the measurements and check it out yourself. The "thermal noise" that you speak of is typically not at -120dB, it's much lower than that (at least on my equipment anyway). What's at -120dB are harmonic spikes which is insufficient to cause dithering, and will *benefit* from being smoothed out through dithering. :-)
Put it this way, if the statement was whether there is any benefit in dithering when truncating to 22 bits (instead of 20) - I would say "probably not". But those 2 bits make a big difference, because that's where the "wideband" noise you speak of resides.
Follow Ups:
"A good mic, mic pre amp and analog console have dynamic range of around 130dB. A good ADC will have dynamic range slightly exceeding 20 bits.
So, the noise floor of electronics alone are too low to produce self dithering when truncating from 24 to 20."Please read back and consider the case that I outlined, where 24 or more tracks have to be mixed to a final stereo master. Or do you deem this not representative for the present state in the music industry? Even when all individual tracks are at around 20b dynamic range, their sum will have a higher noise floor unless massive-scale noise gating is used during mixdown (as in the old days).
There are a handful of ADC chips that resolve near to 120dB of dynamic range (a toddler's hand at that). Far from all convertors in present-day studio gear use these chips. Many use ADCs limited at 17-18b performance.
You seem to be focusing on the best case scenario. It may exist (would you care telling me which ADC you use, or provide me with a spectrum plot of you system's noise floor with shorted input?), but it is not quite typical for the general state of affairs, unless I'm grossly mistaken.
I'm sorry, but you are trying to change the subject.To quote the original statement made by Todd:
"This is also why applying dither noise isn't necessary when truncating data of 24 bits or more down to 20 bits or more. The ambient noise alone would be adequate for such application."
As I've shown, this statement is NOT true (at least not generally). Ambient noise alone is not adequate (and I think we both agree on this).
You seem to be arbitrarily trying to limit the scope of the discussion to specific situations such as poor quality DACs or noisy preamps or mixing a LOT of tracks. Whilst we can argue on and on about specific cases (and whether they represent a "norm" or not), the original statement without qualifications is not factual. Remember, it only takes one counter example to disprove a generalisation.
Even if we wanted to discuss your specific cases, your examples are not valid.
Let's consider your example of mixing 24 or more tracks. You said:
*** Even when all individual tracks are at around 20b dynamic range, their sum will have a higher noise floor unless massive-scale noise gating is used during mixdown (as in the old days). ***
I suspect you don't have a lot of experience mixing. If you mix a lot of tracks, the final mix will exceed 0dBFS unless you attenuate the levels of individual tracks. Therefore the noise floor does not necessarily increase. For example, let's say I have 2 tracks (both with peaks just under 0dBFS). The overall mix will have peaks potentially at +3dBFS unless I attenuate each track by -3dB. Doing so reduces the noise floor of each by -3dB, so the noise floor of the mix is actually at the same level as for the individual tracks.
In fact what typically happens in a mixer is by the time you attenuate the levels of individual tracks, noise levels below 20 bit of the individual tracks are in danger of being "truncated" out of the mix. For example, if we assume noise is at the 20 bit level, attenuating the track level by say -20dB (not atypical for a multi-track mix) causes the noise level to be now at 24 bit level where it is in danger of being truncated out of the final mix altogether (assuming that the mixer operates at internal resolution of 32-bit floating point).
Dithering is advisable to reduce the quantisation noise generated by this truncation, even if the final mix is at 24-bit depth. So mixing actually makes it even more neccesary to apply dithering.
*** Many use ADCs limited at 17-18b performance. ***
No. You are confusing between the measured dynamic range of an ADC and the actual level at which the noise is sufficiently "dense" or "wideband" (your terminology) to act as an effective ditherer. The laws of physics does not change depending on the quality of the ADC. An ADC with a dynamic range of say 102dB (corresponding to your "17 bit" of performance) will have a "thermal noise" envelope far lower than -102dB. Measure it yourself. What you see around -102dB are harmonic spikes that are not sufficient to cause dithering.
"Measure it yourself"I did. Do you think I'm stupid? Do you think I don't know the nature of noise?
Best I ever got was a PCM1804, which after having discarded
any structural noise left me at -108dB rms. Going to evaluate
the new PCM4202 in the coming weeks, I hope.
It was fun for a while, but now I'm signing off, ma'am-your-honour.
*** Best I ever got was a PCM1804, which after having discarded
any structural noise left me at -108dB rms. ***Care to show us a graph of your results?
I checked the data sheet for the PCM1804, and the noise curves on page 11 and 12 (Figures 8-15) clearly show that in PCM mode for single rate and dual rate, the noise levels are close to -140dB apart from a few spikes (which are not ditherable, but these spikes lower the dynamic range to 112dB). In DSD mode, the noise levels are just under -120dB. Even in quad rate mode, the noise levels are around -140dB below 48kHz.
For the PCM4202, the corresponding figures are on page 9-10 of it's data sheet, and show underlying noise to be very similar, just under -140dB. The main difference between the two chips are the lack of harmonic spikes on the PCM4202 (as it's a higher quality ADC), which results in better SNR and THD measurements.
This is consistent with my own measurements of similar ADCs. The laws of physics don't change for different ADCs.
If your results are wildly different, it either means what you are measuring is broken, or there's something screwy with your measurement method.
"I checked the data sheet for the PCM1804, and the noise curves ... clearly show that ... the noise levels are close to -140dB apart from a few spikes (which ... lower the dynamic range to 112dB)"No. The curves show the noise DENSITY, which is, by definition, the specific noise power measured over a unit bandwidth of 1 Hz.
In order to obtain the noise LEVEL (which is what you need for SNR and dynamic range calculations, and which is also what figures in the infamous SNR = 6 x NumberOfBits shortcut), you have to integrate the DENSITY over BANDWIDTH.
For a white noise spectrum with given noise density of Vn (dB) the resulting (RMS) noise level is then Vrms = Vn + 10*log(bandwidth), all in dB.
An ideal 16 bit system with 96 dB SNR over a bandwidth of 22kHz (CD) then has its density at -96-10*log(22000) = -139dBFS.
My PCM1804 with measured 108dB SNR over a bandwidth of 48kHz (running the recorder at 96kHz), has its density at -108-10*log(48000) = -155dBFS.
So if you measure -130dBFS for your system, then the equivalent RMS level (assuming 22kHz BW) is -87dBFS and that's 14.5 bits ;-)
But don't worry, chances are that if you were only looking at FFT-generated plots of the noise density floor your 'measurement' was wrong anyhow, as the plotted level depends on the size of the FFT itself. Try it. Take a white noise signal into Audition and take its spectrum with 1024, 4048, 32000 point FFT ...
The plots in the PCM1804 datasheet are made with 8192 point FFTs. The resulting levels don't show the true per-1-Hz noise density, but rather the density per frequency-bucket of Fsample/8192 Hz. So the floors in the plots are artificially high. That is OK, because to a skilled engineer the 'N=8192' tag in the plot says all.
Included link may help.
- http://lad.linuxaudio.org/events/2004_zkm/slides/saturday/fons_adriaensen-jaaa.pdf (Open in New Window)
... sit down and think about what you've said.What does this say about "noise levels" required for "self-dithering"?
Think about it *really* hard.
PS - I never did say my *system* measured -130dBFS. I said analog circuits can exceed 130dB dynamic range. Not quite the same thing. As for my "measurements" being "wrong", I don't recall giving you any noise level measurements at all. But I'm glad you got really excited.
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