What do you mean, not much intuition for Fourier transforms? Sure, sometimes you get weird results and need to work with fairly generalized versions of function

What do you mean, not much intuition for Fourier transforms? Sure, sometimes you get weird results and need to work with fairly generalized versions of functions, and a bit of background in functional analysis is helpful, but a strong intuition about the Fourier transform is both extremely useful, and not that hard to develop. For starters, I'd recommend the course notes to Stanford's EE261 (https://see.stanford.edu/materials/lsoftaee261/book-fall-07.pdf https://see.stanford.edu/materials/lsoftaee261/book-fall-07....) - well written, very funny, a nice level of rigour, etc...