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Old 29th July 2008   #62
Dean Roddey
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Joined: May 2008
Location: Mountain View, CA
Posts: 11,329

So, having thought about it a bit while getting some chow, let me sum it up in a way that may help people who were seeing the thing the way I was...

If you take an evenly spaced grid of any number of divisions and lay it across the whole range from 0dB down to the noise floor, then all of the divisions represent an equal change in amplitude (I keep wanting type Amplitube every time I type that.) So, anywhere in that range the quanitization is the same, since all the divisions are equal. And, since you can interpolate the curve between any two points, you effectively have infinite resolution.

Therefore, all that really matters is the ratio between the sample amplitudes, not their absolute values. I.e. if sample A is at 10 and sample B is at 20, that's the same as if sample A was 20 and sample B was 40. Both will reproduce the same curve, one will just be louder than the other. They will both reproduce the same curve, because, in both cases, sample B is twice the magnitude as sample A, and so the same curve shape will be interpolated between them. Only an increase in sample RATE would change that.

So, effectively, all the bits are being used all the time, because the quantization error is the same whether loud or soft, and the ability to interpolate extends the effective resolution such that it's only limited by the sample rate.
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