I've been studying digital audio and come across something I can't understand. There appears to be something like a consensus (among those capable of understanding such things) that the impact of aliasing on reconstructed time-domain signals is to ... smear(?) the timing. (Is that the right way to put it?) Here's a quote from a paper by Bob Stuart and Peter Craven, two prominent, respected figures in the audio industry: "Aliasing in the frequency domain is equivalent to the time-domain phenomenon of an impulse response that depends on where, relative to the sampling instants, the original stimulus was presented: see footnote 8." Footnote 8, which refers to a different passage in the article, says, "The complication is that because of the sampling, the total system is not time-translation invariant and so does not have a unique ‘impulse response’ – the response is slightly different according to the position of an original impulse relative to the sampling points."
I did some thinking, and some simple modeling, and came to the conclusion that the effect of aliasing on the reconstructed time-domain signal is to alter the amplitude in a quasi-random way. At the actual sampling instants, the deviation of the reconstructed signal from the original signal resulting from aliasing is zero: At precise sampling instants, aliasing has no effect. But in between those instants there are amplitude errors in the reconstructed signal. This is my conclusion from my own analysis. This is broadly true; I did not do an analysis specifically to determine the effect of aliasing on impulse response.
I cannot see how my conclusion--that of added amplitude noise superimposed on the time-domain signal as a result of aliasing--is equivalent to "the time-domain phenomenon of an impulse response that depends on where, relative to the sampling instants, the original stimulus was presented."