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

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
.