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September 1977 (vol. 26 no. 9)
pp. 874-881
I.S. Reed, Department of Electrical Engineering, University of Southern California
A transform analogous to the discrete Fourier transform is defined on the Galois field GF(p), where p is a prime of the form k X 2n + 1, where k and n are integers. Such transforms offer a substantial variety of possible transform lengths and dynamic ranges. The fast Fourier transform (FFT) algorithm of this transform is faster than the conventional radix-2 FFT. A transform of this type is used to filter a two-dimensional picture (e.g., 256 X 256 samples), and the results are presented with a comparison to the standard FFT. An absence of roundoff errors is an important feature of this technique.
Index Terms:
Convolution, cyclic groups, dynamic range, FFT, Fermat prime, Fourier transform, Galois field, Mersenne prime.
I.S. Reed, T.K. Truong, Y.S. Kwoh, E.L. Hall, "Image Processing by Transforms Over a Finite Field," IEEE Transactions on Computers, vol. 26, no. 9, pp. 874-881, Sept. 1977, doi:10.1109/TC.1977.1674935
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