I just learned about the Modified Discrete Cosine Transform (MDCT) and I see that it's not only used in mp3 compression, but is also often applied on overlapped power-of-two windows like an FFT. When I say "learned about" I don't mean I understand it, I just mean "became aware of".
I've always wondered why some of my FFT resynthesis patches, when run under smaller block sizes, have that low bitrate mp3 sound. I would describe it as squeggy bubbling. Are the two transforms related? Is that crappy sound due to something they both share, or is it just coincidence?