Family of fast linearly independent ternary arithmetic transforms

Author

Falkowski, Bogdan J. ; Fu, Cheng

Author_Institution

Sch. of Electr. & Electron. Eng., Nanyang Technol. Univ., Singapore

Volume

51

Issue

6

fYear

2004

fDate

6/1/2004 12:00:00 AM

Firstpage

1132

Lastpage

1147

Abstract

In this paper, the family of fast linearly independent ternary arithmetic (LITA) transforms, which possesses fast forward and inverse butterfly diagrams, has been identified. This family is recursively defined and has consistent formulas relating forward and inverse transform matrices. The LITA transforms, which require horizontal or vertical permutations to have fast transforms are also discussed. Computational costs of the calculation for presented transforms are also discussed and compared with multipolarity ternary arithmetic transform for ternary benchmark functions.

Keywords

matrix algebra; transforms; LITA transforms; arithmetic transforms; fast forward diagram; forward transform matrix; inverse butterfly diagram; inverse transform matrix; linearly independent transforms; multipolarity ternary arithmetic transform; ternary benchmark functions; ternary logic transforms; Arithmetic; Boolean functions; Circuit analysis; Circuit testing; Computational efficiency; Data structures; Logic circuits; Logic design; Logic functions; Multivalued logic; Arithmetic transforms; fast transforms; linearly independent transforms; ternary logic transforms; ternary transforms;

fLanguage

English

Journal_Title

Circuits and Systems I: Regular Papers, IEEE Transactions on

Publisher

ieee

ISSN

1549-8328

Type

jour

DOI

10.1109/TCSI.2004.829238

Filename

1304970