Orthogonal Transforms for Digital Signal Processing
Orthogonal Transforms for Digital Signal Processing
Discrete Convolutions via Mersenne Transrorms
IEEE Transactions on Computers
Algebraic theory of finite fourier transforms
Journal of Computer and System Sciences
On Fourier Transforms Over Extensions of Finite Rings
IEEE Transactions on Computers
Conditions for the Existence of Fast Number Theoretic Transforms
IEEE Transactions on Computers
IEEE Transactions on Computers
New area-time lower bounds for the multidimensional DFT
CATS 2011 Proceedings of the Seventeenth Computing on The Australasian Theory Symposium - Volume 119
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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.