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Computing the discrete Fourier transform using residue number systems in a ring of algebraic integers

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2 Author(s)

A new method is described for computing an N = R^{m} = 2^{\upsilon m} -point complex discrete Fourier transform that uses quantization within a dense ring of algebraic integers in conjunction with a residue number system over this ring. The algebraic and analytic foundations for the technique are derived and discussed. The architecture for a radix- R fast Fourier transform algorithm using a residue number system over Z[\omega ] , where \omega is a primitive R th root of unity, is developed; and range and error estimates for this algorithm are derived.

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Information Theory, IEEE Transactions on  (Volume:31 ,  Issue: 5 )