This diagram might help to understand sinc interpolation.

Figure 1 shows what a sinc function looks like. It can be calculated from the formula shown.

Note that the peak value equals 1 and it continues to plus and minus infinity time and never completely decays to zero.

It is scaled so that the nulls of the sinc (where it equals zero) line up with the sample period and it is multiplied by the value of the sample.

This is done for every sample so you get the overlapping sinc functions shown in Figure 2.

Notice that at each sample, only the one sinc function contributes to its value and all the remaining sincs sum to zero at that point (see blue arrow).

This is the same for every other sample point too. To reconstruct between the sample points, say where the red arrow is,

you add up the value of all those overlapping sinc functions at that point and that will give the reconstructed value at that point.

That is the basic concept. Do this 16 times between each sample period and you have 16x upsampling.

With a 44.1kHz song that is 4 minutes long, it would have 10,584,000 samples and we would need that many overlapping sinc functions.

They would need to be long enough to cover the entire song and we would need to wait for all the samples before we reconstructed.

This isn't practical, so we have to truncate the sinc function and do the reconstruction over smaller time periods with a smaller amount of samples.

How you do this and the precision of the calculations affects the reconstruction and the sound quality (this is where WTA plays a part).

In a computer algorithm it is done more efficiently than this but this helps to visualize how it works.

blob:

https://www.head-fi.org/5303cc79-2d16-4fac-8410-5e975fd5f1bbClick to expand...