Abstract
One-dimensional fast Fourier transform (FFT) is the most popular tool for computing the two-dimensional Fourier transform. As a rule, a standard method of combination of one-dimensional FFTs—the so-called algorithm “by rows and columns” [1]—is used in the literature. In [2, 3], the authors showed how to compute the FFT for a signal with the number of samples 2s × 2s with the use of an analog of the Cooley-Tukey algorithm. In the present paper, a two-dimensional analog of the Cooley-Tukey algorithm is constructed for a rectangular signal with the number of samples 2s × 2s + ℓ. The number of operations in this algorithm is much less than that in the successive application of a one dimensional FFT by rows and columns. The testing of the algorithm on image-type signals shows that the speed of computation of the FFT by the algorithm proposed is about 1.7 times higher than that of the algorithm by rows and columns.
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This paper uses the materials of a report that was submitted at the 11th International Conference Pattern Recognition and Image Analysis: New Information Technologies that was held in Samara, Russia on September 23–28, 2013.
Valeriy Sergeevich Tutatchikov. Born 1988. Graduated from the Institute of Space and Information Technology, Siberian Federal University, in 2011. Currently a postgraduate at the same university. Scientific interests: fast Fourier transform and parallel algorithms. Author of 12 publications.
Mikhail Valerianovich Noskov. Born 1947. Graduated from the Krasnoyarsk State Pedagogical Institute in 1969. Received candidates degree in 1987 and doctoral degree in 1992. Currently a professor at the Siberian Federal University. Scientific interests: cubature formulas, methods for training mathematics. Author of 58 publications.
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Noskov, M.V., Tutatchikov, V.S. Modification of a two-dimensional fast Fourier transform algorithm by the analog of the Cooley-Tukey algorithm for a rectangular signal. Pattern Recognit. Image Anal. 25, 81–83 (2015). https://doi.org/10.1134/S1054661815010137
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DOI: https://doi.org/10.1134/S1054661815010137