On 2012-08-01, robert bristow-johnson wrote:
well, it works pretty fine. theoretically, of course, DC is constant. but really we think of DC (or the coefficient applied to any other frequency component) to be slowly-varying.
Or in other words, something like the stuff that happens below 1Hz. Nobody hears that, so that it can be safely filtered away, using even the kinds of nasty first order IIR filters which would wreak havoc if used higher up the band. In DC removal we can just say that "it removed DC", and sleep well at night.
if DC is slowly varying, small displacements of a windowed section of DC (which is what comes out of any weighted moving-average filter) does not change it much.
More precisely, quite a number of waveforms like these can be put into closed form, or if not that, at least into the form of a combination of piecewise linear functions, impulses, certain second degree polynomials, gaussians, plus sparse convolutions between them. In the end that kind of an analysis will yield a second degree error term in the error term, which will be negligible in usual audio practice. At the same time it will yield an in-band frequency modulation signal, which will also be negligible, also by empirical A/B/X measurement from something like the 60es.
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