Title :
The Discrete Fourier Transform Over Finite Rings with Application to Fast Convolution
Author :
Dubois, Eric ; Venetsanopoulos, Anastasios N.
Author_Institution :
INRS Telecommunications
fDate :
7/1/1978 12:00:00 AM
Abstract :
Necessary and sufficient conditions for a direct sum of local rings to support a generalized discrete Fourier transform are derived. In particular, these conditions can be applied to any finite ring. The function O(N) defined by Agarwal and Burrus for transforms over ZN is extended to any finite ring R as O(R) and it is shown that R supports a length m discrete Fourier transform if and only if m is a divisor of O(R) This result is applied to the homomorphic images of rings-of algebraic integers.
Keywords :
Digital filtering; FFT; fast convolution; finite computation structures; generalized discrete Fourier transform; modular arithmetic; number theoretic transforms; Algebra; Convolution; Discrete Fourier transforms; Fast Fourier transforms; Filtering; Fourier transforms; Hardware; Modules (abstract algebra); Sufficient conditions; Zinc; Digital filtering; FFT; fast convolution; finite computation structures; generalized discrete Fourier transform; modular arithmetic; number theoretic transforms;
Journal_Title :
Computers, IEEE Transactions on
DOI :
10.1109/TC.1978.1675158
