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| 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, September, 1977. | |||
| BibTex | x | ||
| @article{ 10.1109/TC.1977.1674935, author = {I.S. Reed and T.K. Truong and Y.S. Kwoh and E.L. Hall}, title = {Image Processing by Transforms Over a Finite Field}, journal ={IEEE Transactions on Computers}, volume = {26}, number = {9}, issn = {0018-9340}, year = {1977}, pages = {874-881}, doi = {http://doi.ieeecomputersociety.org/10.1109/TC.1977.1674935}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, } | |||
| RefWorks Procite/RefMan/Endnote | x | ||
| TY - JOUR JO - IEEE Transactions on Computers TI - Image Processing by Transforms Over a Finite Field IS - 9 SN - 0018-9340 SP874 EP881 EPD - 874-881 A1 - I.S. Reed, A1 - T.K. Truong, A1 - Y.S. Kwoh, A1 - E.L. Hall, PY - 1977 KW - Convolution KW - cyclic groups KW - dynamic range KW - FFT KW - Fermat prime KW - Fourier transform KW - Galois field KW - Mersenne prime. VL - 26 JA - IEEE Transactions on Computers ER - | |||
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.
Citation:
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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