TITLE: Reading for finite Fourier analysis
QUESTION [9 upvotes]: Can anyone recommend some good reading for Fourier analysis (and the Fourier transform) over finite abelian groups? I've found it given brief descriptions in both books on representation theory and on regular Fourier analysis (the best so far in the chapter in Tao and Vu's Additive combinatorics), but can't find a dedicated, detailed exposition of this area proper.

REPLY [3 votes]: Belatedly, considering that the question was asked 13 years ago: I have some notes on Fourier analysis on finite abelian groups, as an early part of a repn theory course. Just a few pages, but trying to be forward-looking.
https://www-users.cse.umn.edu/~garrett/m/repns/notes_2014-15/01_finite_abelian.pdf