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New number theoretic transform

New number theoretic transform

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A new number theoretic transform is introduced. This transform is defined modulo the Mersenne primes, has long transform length which is a power of two, a fast algorithm, and the inverse transform has within a factor of (1/N) the same form as the forward transform. Thus, it is well suited for the calculation of error free convolutions and correlations.

References

    1. 1)
      • C.M. Rader . Discrete convolution via Mersenne transforms. IEEE Trans. , 1269 - 1273
    2. 2)
      • I.S. Reed , T.K. Truong . The use of finite fields to compute convolutions. IEEE Trans. , 2
    3. 3)
      • R.C. Agarwal , C.S. Burrus . Fast convolution using Fermat number transforms with applications to digital filtering. IEEE Trans. , 87 - 97
    4. 4)
      • Rader, C.M.: `The number theoretic DFT and exact discrete convolution', IEEE Arden House Workshop on digital signal processing, 11 January 1972, Harriman, .
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