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An algorithm for complex approximations in Z[e^{2{\pi}i/8}] (Corresp.)

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1 Author(s)

An algorithm is described that approximates complex numbers by elements of the algebraic integers of Z[e^{2 \pi i / 8}] with integer coordinates of at most a prescribed size. The motivating application is to reduce the dynamic range requirements of residue number system implementations of the discrete Fourier transform. The closest points to zero of Z[e^{2 \pi i / 8}]_{M} gor any integer M are determined. A particular sequence of such points forms the basis of the algorithm. An example of 8 -bit Z[\omega ]_{M} - approximations of the 128th roots of unity is considered. The algorithm yields M = 186; with scaling M is reduced to 18 .

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Information Theory, IEEE Transactions on  (Volume:32 ,  Issue: 4 )