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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 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.