In graphics, it's common to take multiple samples within the bounds of a pixel and combine them together (most commonly just doing an average) for a final sample pixel color. This has the effect of anti aliasing an image.
On one hand this makes sense to me because what you are effectively doing is integrating the color of the pixel over the area that the pixel represents. In this line of thinking, averaging "random" samples seems to be the ideal setup, for doing monte carlo integration. ("random" could be stratified, blue noise based, low discrepency sequences etc)
On the other hand, this feels wrong (or at least not as correct as it could be) from a digital signal processing point of view. From that point of view, it feels like we are taking a lot of samples and then downsampling using a box filter (box blur) to get the final pixel value. In that light, it seems like the ideal thing to do would be to use sinc filtering instead of averaging the samples. I could see that the box filter is a cheaper aproximation to sinc thinking along these lines.
This leaves me a bit confused. Is the core idea that we are integrating the pixel area and averaging is correct? Or is it that we are downsampling and should be using sinc, but are using a box filter because it's fast?
Or is it something else entirely?
A little bit related: Anti-aliasing / Filtering in Ray Tracing