Bits vs. kuttepresisjon

S

Slubbert

Gjest
24-bit precision gives you about 16.77 million values. Assuming a total groove width of 50 x 10^-6m, the maximum movement of the cutter is physically bounded at about half that. Much more and the cutter will be in the space for an adjacent groove. Thus, 50 microns width divided by 16.77 million gives us about 3 x 10^-12m, i.e. ~0.03 angstroms.

The diameter of a hydrogen atom is 1.0 angstroms (1 x 10^-10m). That would make the resolution of a 24-bit digital signal equivalent to an analog cutter whose resolution is just about 1/30 the width of a hydrogen atom. Sadly, this seems to be physically impossible, as none of the particles smaller than atoms are stable enough to be used in records.

Of course, records aren't made of hydrogen, they're made of the polymer pvc. One molecule of pvc is about 100,000 angstroms. This means that, if the cutters were actually removing single pvc molecules the vinyl records would have about 11 bits of resolution. Sadly, they don't get even that precise, though I'm not sure the actual precision. To get down to a record made of hydrogen atoms (possible under very low temp/very high pressure I suppose) one would need 19 bits. Anything beyond that is useless as long as the laws of physics hold.
 

KJ

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Slubbert skrev:
24-bit precision gives you about 16.77 million values. Assuming a total groove width of 50 x 10^-6m, the maximum movement of the cutter is physically bounded at about half that. Much more and the cutter will be in the space for an adjacent groove. Thus, 50 microns width divided by 16.77 million gives us about 3 x 10^-12m, i.e. ~0.03 angstroms.

The diameter of a hydrogen atom is 1.0 angstroms (1 x 10^-10m). That would make the resolution of a 24-bit digital signal equivalent to an analog cutter whose resolution is just about 1/30 the width of a hydrogen atom. Sadly, this seems to be physically impossible, as none of the particles smaller than atoms are stable enough to be used in records.

Of course, records aren't made of hydrogen, they're made of the polymer pvc. One molecule of pvc is about 100,000 angstroms. This means that, if the cutters were actually removing single pvc molecules the vinyl records would have about 11 bits of resolution. Sadly, they don't get even that precise, though I'm not sure the actual precision. To get down to a record made of hydrogen atoms (possible under very low temp/very high pressure I suppose) one would need 19 bits. Anything beyond that is useless as long as the laws of physics hold.
Der vel ikke så mange som hevder at vinyl har en oppløsning tilsvarende 24 bit? Resonementet vedr PVC-molekyler er forøvrig litt sviktende - forst og fems så brukes ikke PVC i kutteprosessen for det andre så kan PVC molyekylene i relativt stor grad «formes» etter svingningene i rillene. Signal støyforholdet/«dynamic range» på gode vinylplater kan ligge omkring 60-70 db i mellomtonen og øker til omkring 70-80dB i diskantområdet dvs ekvivalent med ca. 10-11,7-12,3 bit.

EDIT: modernemusikk produseres jo for tiden med en «effektiv» oppløsning på noen få usle bit så why bother ... ?

mvh
KJ
 
S

Slubbert

Gjest
Vel, poenget var kanskje å punktere litt av det høytsvevende snakket om "analogt" som noe annerledes (og implisitt bedre) enn "digitalt", når alt til syvende og sist er kvantisert. Selv om vinyl kuttes med presisjon på molekylnivå innebærer det spatiell kvantisering med langt mindre enn 24-bits oppløsning. Selv rom og tid er kvantisert (ref. Heisenbergs usikkerhetsrelasjon), så "analogt" i absolutt forstand er egentlig et innholdsløst begrep. Analogt er digitalt.
 
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