Generalized New Mersenne Number Transforms

Author

Boussakta, Said ; Hamood, Monir T. ; Rutter, Nick

Author_Institution

Sch. of Electr., Electron. & Comput. Eng., Newcastle Univ., Newcastle Upon Tyne, UK

Volume

60

Issue

5

fYear

2012

fDate

5/1/2012 12:00:00 AM

Firstpage

2640

Lastpage

2647

Abstract

Two new number theoretic transforms named as odd and odd-squared new Mersenne number transforms are introduced for incorporation into a generalized new Mersenne number transforms (GNMNTs) suite, which are defined in finite fields modulo Mersenne primes where arithmetic operations and residue reductions are simple to implement. This suite is categorized by type, with detailed instructions regarding their derivations. An example is given which shows their suitability for the calculation of different types of convolutions, along with an analysis of their arithmetic complexities for radix-2 and split radix algorithms. This in turn shows that these new transforms are suitable for fast error free calculation of convolutions/correlations for signal processing and other applications.

Keywords

convolution; correlation methods; discrete Fourier transforms; number theory; arithmetic complexities; arithmetic operations; error free calculation; finite fields modulo Mersenne primes; number theoretic transforms; odd-squared new Mersenne number transforms; radix-2 algorithms; residue reductions; signal processing convolutions; signal processing correlations; split radix algorithms; Algorithm design and analysis; Complexity theory; Convolution; Equations; Image processing; Kernel; Transforms; New Mersenne number transform (NMNT); number theoretic transforms (NTTs); odd new Mersenne number transform (ONMNT); odd-squared new Mersenne number transform $({rm O}^{2}{rm NMNT})$;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/TSP.2012.2186131

Filename

6140982