Discrete Convolutions via Mersenne Transrorms

@article{Rader1972DiscreteCV,
  title={Discrete Convolutions via Mersenne Transrorms},
  author={Charles M. Rader},
  journal={IEEE Transactions on Computers},
  year={1972},
  volume={C-21},
  pages={1269-1273}
}
A transform analogous to the discrete Fourier transform is defined in the ring of integers with a multiplication and addition modulo a Mersenne number. The arithmetic necessary to perform the transform requires only additions and circular shifts of the bits in a word. The inverse transform is similar. It is shown that the product of the transforms of two sequences is congruent to the transform of their circular convolution. Therefore, a method of computing circular convolutions without… CONTINUE READING
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