| > 16-bit which is already at the limit of human perception Nitpick: 16-bit fixed point is not at the limit of human perception. It's close, but I think 18-bit is required for fixed point. Floating point is a different issue. > If you have 32 steps in your signal path and each is +/- 0.5 then the total is +/- 16. Uncorrelated error doesn't accumulate like that. It accumulates as RSS (root of sum of squares). So, sqrt(32 * (.5 * .5)) which is about 2.82 (about 1-2 bits). > You can have a suuuuuuuper long signal path that accumulates 16 or 32 or 48 bits of error and nobody notices because you still have 16 good bits. Generally the thing which causes audible errors are effects like reverb, delay, phasors, compressors, etc. These are non-linear effects and consequently error can multiply and wind up in the audible range. Because error accumulates as RSS, it's really hard to get error to additively appear in the audible range. tl;dr recording engineers like to play with non-linear effects which can eat up all your bits |
Uncorrelated average error, yes. Uncorrelated maximum error accumulates as a linear sum, as he calculated.
But yes, you're absolutely correct in that it tends to be nonlinear effects that cause issues.