Comment by sirwitti
14 years ago
i think what jaylevitt is referencing to is that there is interpolation going on in the dac. that could mean (i'm no dac expert, so not sure) that the dac could guess more granular than the sampling rate would allow the start points (of transient e.g.)
but the question for me is how exact that guessing is. correct me if i'm wrong but, that interpolation happens twice: when recording by the adc and on playback by the dac.
so a lot of that whole discussion (yeah, finally something about acousticts :) depends on how accurate interpolation works in adcs and dacs.
This is the core secret of the sampling theorem. It says if you have signals of a particular type (bandlimited) you can do a certain kind of interpolation and recover the original exactly. This is no more surprising than the fact that you can recover the coefficients for an N degree polynomial using any N points on it, though the computation is easier.
It turns out that if you reproduce a digital signal using stair steps you get an infinite number of harmonics— but _all_ of them are above the nyquist frequency. The frequencies below the nyquist are undisturbed. Then you apply a lowpass filter to the signal to remove these harmonics— after all, we said at the start that the signal was bandlimited— you get the original back unmolested.
Because analog filters are kinda sucky (and because converters with high bit depth aren't very linear), modern ADCs and DACs are oversampling— they internally resample the signal to a few MHz and apply those reconstruction filters digitally with stupidly high precision. Then they only need a very simple analog filter to cope with their much higher frequency sampling.