Fast n-D fourier-heisenberg transforms1

We develop fast Fourier-Heisenberg number theoretical transforms on discrete 1-D and n-D Heisenberg groups (H[3, GF(p), GF(p)] and H[n + 2, GF
ⁿ
(p), GF
ⁿ
(p)]) and over an arbitrary commutative ring K, where GF(p) is the Galois field, p = q
^m
and g is a prime.