I'm not even sure if Nyquist applies here since the GIF is already a non-continuous function and therefore has potentially infinite frequency components. The in

I'm not even sure if Nyquist applies here since the GIF is already a non-continuous function and therefore has potentially infinite frequency components. The input itself is not band-limited. Another way to put this is that a GIF is already a sampled function. For example imagine intensity of each pixel in a particular GIF is a function sin(x * t). Nyquist just says you can only accurately reconstruct this for 25px wide GIFs at 50FPS without aliasing. And as you pointed, you'd still have to bandlimit the output.