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Convolution using a conjugate symmetry property for the generalized discrete Fourier transform

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2 Author(s)
E. Dubois ; INRS-Télécommunications, Verdun, P.Q., Canada ; A. Venetsanopoulos

Often, signals which lie in a ring S are convolved using a generalized discrete Fourier transform (DFT) over an extension ring R in order to allow longer sequence lengths. In this paper, a conjugate symmetry property which generalizes the well known property of the complex DFT for real data is presented for this situation. This property is used to obtain a technique for computing the DFT of μ sequences with values in a ring S using a single DFT in an extension ring R of degree μ over S. From this result, a method to compute the convolution of length μn S-sequences using a length n DFT in R is derived. Example of the application to the complex DFT and to a number theoretic transform are presented to illustrate the theory.

Published in:

IEEE Transactions on Acoustics, Speech, and Signal Processing  (Volume:26 ,  Issue: 2 )