gregorio
Headphoneus Supremus
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[1] I don't believe I wrote anything that was incorrect if dither were not in use.
[2] Also despite you acting as if no dither isn't an option, plenty of software will allow you to do things without dithering. It isn't a wise choice to make, but it happens.
1. It's maybe just a misunderstanding, due to the fact that I didn't find it clear that your example and statements excluded dither and a few statements appeared not quite right, for example:
"If you wish to discuss accuracy of the frequency then 44/16 can do so down to 55 picoseconds which is in a around about way the accuracy limits of depicting frequency. However, dither will decrease that number further. 24 bit could depict frequency to a finer level of accuracy." -
Dither will indeed increase that number further, to infinity. Undithered 24bit will give greater accuracy/resolution than undithered 16bit but dithered 16bit has more resolution than undithered 24bit. Dithered 16bit and dithered 24bit have exactly the same (infinite) resolution! lol ... And:
"With enough bit depth you can describe to any level of accuracy desired." - In an undithered system infinite resolution would require infinite bit depth, which is why it's always applied in the quantisation process.
2. It's not an option in the quantisation process. Any recorded/acquired signal will be dithered as all ADCs automatically dither and signals generated in the computer will either not incur quantisation or the processor generating the signal would be expected to internally dither if it does. It's only in the mixing/summing of those dithered signals where a "re-quantisation" process is likely to occur and where dithering that/those re-quantisations is optional. Therefore, I can't think of any commercial digital audio recording scenario in which dither is completely absent, although this doesn't exclude the possibility that at some points in the chain dither hasn't been applied to re-quantisation processes (typically because it's irrelevant) or hasn't been applied correctly.
Even If you have complete perfection for a very short band limited area, you will still need infinite amount of data thus storage. There is no other way.
This is another way, it's called dither!!! That's why dither is a fundamental requirement of digital audio, because without it digital audio is not linear and to make it linear you would need infinite bit depth. That's what the original post explains and why the whole post is effectively based on dither. So, saying that if you eliminate dither the original post is incorrect is completely nuts! Of course it would be incorrect if you exclude dither, which is precisely why the OP does NOT exclude dither!!! Is it just me or are we well past the point of surreal?
G
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