Why does Upsampling improve sound quality?
From the explanation above, there is apparently no extra information in the upsampled signal that was not present in the initial signal. With a 44.1 kS/s input, both the input data stream and the upsampled data stream will only contain a spectrum that must be between 0 and 22.05 kHz and is probably only between 0 and 20 kHz.
This conventional analysis starts from the viewpoint that the behavior of the ear can be described in mathematical terms using Fourier analysis. This assumption is probably pretty good – it means we are interested in frequency responses, for example, and these do provide good guides to the performance of equipment and to descriptions of what we hear. The analysis was right at the heart of the definition of the audio coding used on CDs.
For those working with audio, it is also apparent that theories based on these descriptions are not completely adequate, and that there can be significant differences in the performances of pieces of equipment with similar "conventional" specifications. It seems that two things are going on here – the ear may have more than one mechanism at work, and sine waves may not be the best function to use as the basis for analysis. On the mechanism front, it seems highly likely that the ear has a sound localization mechanism ("where is it") that is fast, and independent of the mechanism that says "it’s a violin", and that is related to transient response. There may also be a third mechanism at work. On the analysis front, it may be that some form of wavelet is the best basis for mathematical modeling. The problem here is that sine wave theory is relatively simple, and has been fully worked out by generations of mathematicians, following on from Fourier. Wavelet math is just plain hard work, and does not yet have anything like such a solid core of mathematical results to call upon. Our ears, however, are not waiting.
If one gets the frequency response of some equipment right, but the provision of transient information wrong, one or more of the ear’s mechanisms cannot work properly, and so we are unable to separate out echoes and cues about where a sound is coming from the rest of the "what is it anyway" signal. dCS’ upsampling filters are designed to help sort this problem out. They are best analyzed not in sine wave terms, but using wavelets.