Number theoretic transforms over the golden section quadratic field

Author

Dimitrov, Vassil S. ; Cosklev, T.V. ; Bonevsky, B.

Author_Institution

Center for CAD, Tech. Univ. of Plovdiv, Bulgaria

Volume

43

Issue

8

fYear

1995

fDate

8/1/1995 12:00:00 AM

Firstpage

1790

Lastpage

1797

Abstract

A new number theoretic transform (NTT) over the real quadratic field Q(√5) is suggested and analyzed. Conventional NTTs are used for fast convolution of integer sequences. A new approach for computing number theoretic transforms (NTTs) is proposed, allowing real signals to be processed as well. The method is based on a Diophantine approximation of the input real signal before the NTT. The choice of the three parameters characterizing any NTT-modulus, transform length, and primitive element-is discussed in detail. From a practical point of view, the suggested NTTs offer attractive combinations of these parameters. Much care has been exercised to reduce the computational complexity. The practical usefulness of an irrational number system is demonstrated. Extensions and open problems are discussed

Keywords

approximation theory; computational complexity; convolution; number theory; sequences; Diophantine approximation; computational complexity reduction; fast convolution; golden section quadratic field; input real signal; integer sequences; irrational number system; modulus; number theoretic transforms; open problems; parameters; primitive element; real quadratic field; signal processing; transform length; Arithmetic; Computational complexity; Convolution; Discrete Fourier transforms; Discrete transforms; Galois fields; Gaussian processes; Inductors; Kernel; Student members;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.403338

Filename

403338