DocumentCode :
941862
Title :
An algorithm for complex approximations in ![Z[e^{2{\\pi}i/8}]](/images/tex/126.gif)
(Corresp.)
(Corresp.)Author :
Games, Richard A.
Volume :
32
Issue :
4
fYear :
1986
fDate :
7/1/1986 12:00:00 AM
Firstpage :
603
Lastpage :
607
Abstract :
An algorithm is described that approximates complex numbers by elements of the algebraic integers of ![Z[e^{2 \\pi i / 8}]](/images/tex/6024.gif)
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}](/images/tex/6025.gif)
gor any integer 
are determined. A particular sequence of such points forms the basis of the algorithm. An example of 
-bit ![Z[\\omega ]_{M}](/images/tex/6026.gif)
- approximations of the 128th roots of unity is considered. The algorithm yields 
with scaling is reduced to 
.
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 gor any integer are determined. A particular sequence of such points forms the basis of the algorithm. An example of -bit - approximations of the 128th roots of unity is considered. The algorithm yields with scaling is reduced to .Keywords :
Approximation methods; Approximation algorithms; Convergence; Region 2; Research and development;
fLanguage :
English
Journal_Title :
Information Theory, IEEE Transactions on
Publisher :
ieee
ISSN :
0018-9448
Type :
jour
DOI :
10.1109/TIT.1986.1057203
Filename :
1057203
Link To Document :
