Abstract:
An algorithm is described that approximates complex numbers by elements of the algebraic integers ofZ[e^{2 \pi i / 8}]with integer coordinates of at most a prescribed siz...Show MoreMetadata
Abstract:
An algorithm is described that approximates complex numbers by elements of the algebraic integers ofZ[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 ofZ[e^{2 \pi i / 8}]_{M}gor any integerMare determined. A particular sequence of such points forms the basis of the algorithm. An example of8-bitZ[\omega]_{M}- approximations of the 128th roots of unity is considered. The algorithm yieldsM = 186;with scalingMis reduced to18.
Published in: IEEE Transactions on Information Theory ( Volume: 32, Issue: 4, July 1986)