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Complex approximations using algebraic integers | IEEE Journals & Magazine | IEEE Xplore

Complex approximations using algebraic integers


Abstract:

The problem of approximating complex numbers by elements ofZ[\omega], the algebraic integers ofQ(\omega), where\omegais a primitiventh root of unity, is considered. The m...Show More

Abstract:

The problem of approximating complex numbers by elements ofZ[\omega], the algebraic integers ofQ(\omega), where\omegais a primitiventh root of unity, is considered. The motivating application is to reduce the dynamic range requirements of residue number system implementations of the discrete Fourier transform. Smallest error tolerances for the case of eighth roots of unity are derived using a geometric argument. Scale factors involved are reduced from\alphato\sqrt{\alpha}for this case with roughly the same percentage errors. The case of sixteenth roots of unity gives even better range reductions and is considered only briefly.
Published in: IEEE Transactions on Information Theory ( Volume: 31, Issue: 5, September 1985)
Page(s): 565 - 579
Date of Publication: 06 January 2003

ISSN Information:


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