Fourier analysis notes

There are six or eight ways to define a Fourier transform. The differences in the various conventions are minor, but they lead to differences in the basic results. So whenever you look up a result, you have to make sure the reference's definition matches the one you're expecting. Or maybe you re-derive the result. This is good exercise, but it's a distraction when you're in the middle of working on something else.

This has annoyed me periodically since shortly after I learned what a Fourier transform was. I've thought about making a Rosetta stone of sorts for Fourier transforms, listing the basic formulas using each of the various conventions, and now I finally did it. See these notes:

Fourier transform results under various conventions