Generalized New Mersenne Number Transforms

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 reducti...

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Bibliographic Details
Published in:IEEE transactions on signal processing 2012-05, Vol.60 (5), p.2640-2647
Main Authors: Boussakta, S., Hamood, M. T., Rutter, N.
Format: Article
Language:English
Subjects:
Algorithm design and analysis
Algorithms
Applied sciences
Arithmetic
Complexity theory
Convolution
Derivation
Detection, estimation, filtering, equalization, prediction
Equations
Exact sciences and technology
Image processing
Information, signal and communications theory
Kernel
Mathematical analysis
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})
Residues
Signal and communications theory
Signal processing
Signal, noise
Telecommunications and information theory
Transforms
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Summary: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.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2012.2186131