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.



Reading for finite Fourier analysis
There's Audrey Terras' "[Fourier Analysis on Finite Groups and Applications](http://rads.stackoverflow.com/amzn/click/0521457181)", which covers both the commutative and non-commutative settings (about half the book focuses on finite abelian groups). It's a fairly good introductory text, although it doesn't run very deep. 


