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Efficient algorithms for computing the new Mersenne number transform

Lookup NU author(s): Monir Hamood, Professor Said Boussakta



This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License (CC BY-NC 4.0).


The new Mersenne number transform (NMNT) has proved to be an important number theoretic transform (NTT) used for error-free calculation of convolutions and correlations. Its main feature is that for a suitable Mersenne prime number (p), the allowed power-of-two transform lengths can be very large. In this paper, efficient radix-2(2) decimation-in-time and in-frequency algorithms for fast calculation of the NMNT are developed by deriving the appropriate mathematical relations in finite field and applying principles of the twiddle factor unscrambling technique. The proposed algorithms achieve both the regularity of radix-2 algorithm and the efficiency of radix-4 algorithm and can be applied to any powers of two transform lengths with simple bit reversing for ordering the output sequence. Consequently, the proposed algorithms possess the desirable properties such as simplicity and in-place computation. The validity of the proposed algorithms has been verified through examples involving large integer multiplication and digital filtering applications, using both the NMNT and the developed algorithms. (C) 2013 Elsevier Inc. All rights reserved.

Publication metadata

Author(s): Hamood MT, Boussakta S

Publication type: Article

Publication status: Published

Journal: Digital Signal Processing

Year: 2014

Volume: 25

Pages: 280-288

Print publication date: 01/02/2014

Online publication date: 05/11/2013

Date deposited: 27/06/2014

ISSN (print): 1051-2004

ISSN (electronic): 1095-4333

Publisher: Academic Press


DOI: 10.1016/j.dsp.2013.10.018


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