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A new efficient algorithm to compute the two-dimensional discrete Fourier transform

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1 Author(s)
Gertner, I. ; Dept. of Electr. Eng., Technion, Israel Inst. of Technol., Haifa, Israel

An algorithm is presented for computation of the two-dimensional discrete Fourier transform (DFT). The algorithm is based on geometric properties of the integers and exhibits symmetry and simplicity of realization. Only one-dimensional transformation of the input data is required. The transformations are independent; hence, parallel processing is feasible. It is shown that the number of distinct N -point DFTs needed to calculate N×N-point two-dimensional DFTs is equal to the number of linear congruences spanning the N×N grid. Examples for N=3, N=4, and N=10 are presented. A short APL code illustrating the algorithm is given

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Acoustics, Speech and Signal Processing, IEEE Transactions on  (Volume:36 ,  Issue: 7 )