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

Author

Games, Richard A.

Volume

Issue

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 $Z[e^{2 \\pi i / 8}]$ 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 $18$ .

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

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=941862

An algorithm for complex approximations in (Corresp.)

Games, Richard A.

jour

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