DocumentCode
1137906
Title
The Discrete Fourier Transform Over Finite Rings with Application to Fast Convolution
Author
Dubois, Eric ; Venetsanopoulos, Anastasios N.
Author_Institution
INRS Telecommunications
Issue
7
fYear
1978
fDate
7/1/1978 12:00:00 AM
Firstpage
586
Lastpage
593
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;
fLanguage
English
Journal_Title
Computers, IEEE Transactions on
Publisher
ieee
ISSN
0018-9340
Type
jour
DOI
10.1109/TC.1978.1675158
Filename
1675158
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