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Discrete Convolutions via Mersenne Transrorms

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1 Author(s)
Rader, C.M. ; Lincoln Laboratory, Massachusetts Institute of Technology

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 quantization error and with only very few multiplications is revealed.

Published in:

Computers, IEEE Transactions on  (Volume:C-21 ,  Issue: 12 )