Acid—I'm sorry, I'm at a total loss of what it is you're disagreeing with me about. I didn't know which point of my long post (or if it was me you were addressing) when you posted only "actually, that is true." Now you've posted a bunch of other comments that don't seem to disagree with me (or do they?) about any point in particular, though it's clear you're addressing me this time.aciddose wrote:because of noise, you get dither. when you average dither the number of bits increases by one every time you filter away 6db of noise.codehead wrote:Hard to know what you're referring to without a quote. I hope you're not referring to my last sentence (if so, you didn't get my point; if thermal noise is a problem—and it already dominates waaaayyy before you get out to 64 bits—adding addition bits does nothing to help in that regard, so saying it might not be enough makes no sense).aciddose wrote:actually, that is true.
that means we can for example input a signal to a 1-bit ADC (a compare > 0) and mix it with high-frequency noise.
by filtering away this noise with a low-pass filter, every time we decrease the noise level by half we gain one bit.
let's say we use 40khz sample rate. we want at least 1khz frequency for our input.
to get 25-bits, we need a filter with a cutoff of 1khz we need a filter with at least 30db/o slope. easy to achieve.
also, yes float does have "virtually" 25 bits, but it isn't because of any phantom bit. it's because we take away half the range of precision from the exponent and apply that to the mantissa by normalizing the mantissa to a half range. (0.5 - 1.0, not 0.0 to 1.0.)
so yes it's true to say that float has at least 25 bits accuracy in a normalized range like 0.0 - 1.0, but it isn't smart to say this accuracy comes from magic; which is what "normalization and implied bit" tends to sound like. easier to just describe it as having 23 bits that apply to half as much range.
Sorry for being dense, but is there a point that you think I've said something wrong? Could you quote the part of my post that applies? I didn't say anything about a "phantom bit", for instance—I said a bit was gained from normalization, same as you said (though it's not 0.5-1.0, as you said—it's 1.0—1.99999..., but that's a trivial detail, since you could redefine the exponent offset and say it's 0.5-0.99999...—though not 1.0).