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In Reply to: Linearly quantized posted by WinthorpeIII on March 2, 2007 at 20:11:26:
HowdyNope, no correlation.
I'm not even sure where you might get that idea. Here's a guess: Since 20 log base 10 of 2 is 6.02059991328 we often use the rule of thumb that it's exactly 6. Hence it takes more than 24 bits before it's wrong rounded off (24 * 6 is 144 and 20 log (2^24) is approx 144.494397919 which is still 144 when rounded. However none of this has any bearing on "minimum quantization".
Follow Ups:
What I was doing was taking a dynamic range and dividing it up linearly by the number of bits. What am I missing? What would be the differential of amplitude in dB at the lowest levels of signal using 16, 20 or 24 bits?Is this not the reason for the limited low level resolution of the 16 bit format?
The idea that 20 bits would be more than adequate because of the noise of the electronics does not hold water.
HowdyYou said "The idea that 20 bits would be more than adequate because of the noise of the electronics does not hold water." Well, 20 bits is just about as good as can be done right now in hardware. That's a fact. Over time we'll slowly be adding bits but we'll never need more than 24 bits for a ADC or DAC (tho more for processing is a necessity.)
(Ignoring dithered signals) the maximum dynamic range of PCM is the ratio of the loudest representable signal to the smallest, roughly 6dB per bit. I don't know what you mean when you say you were dividing that by bits :)
I'm sorry that I'm not understanding your point.
Thanks for the responses Ted.What I was trying to describe was simply the action of taking the signal and then quantizing it with a grid -- F(s) and the number of amplitude quanitizations possible given the number of bits. With linear quantitization for amplitude there are more gradations for a louder signal. When I was refering to "dividing by the number of bits" I was talking about dividing the signal up by 65,536, not 16.
My apologies for not making my point more clearly and for using confusing language.
Looking at the first few quantizations, I see the second quantization is 2x the voltage of the first, or 6dB, the 3rd is 1.5x the voltage level of the second or 3.5dB higher, the 4th point is 4/3x the voltage of the 3rd or 2.78 dB and so on. The very lowest level signals are crudely recorded in terms of dB differences. The 64,001 gradation is just .0001 dB louder than the 64,000th.
It's surprising what we can hear -- differences in line level amplifiers and cables, even when much grosser distortions exist elsewhere. The low level signal performance of the CD has often been described as inadequate or lacking in comparison to the LP, even when much higher noise levels are present in the LP and LP playback system.
HowdyOne of the differences is that the signal to noise ratio for PCM depends on the current level of the material, on analog media the signal to noise ratio is more or less constant. So as far as signal to noise ratio on quiet material analog wins and on loud material CD wins. Perhaps this is what you were getting to.
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