The new algorithms for 2-dimensional FFT with prime size

Two algorithms for the 2D fast Fourier transform (FFT) are developed, where the prime size p≡3 mod 4 and p≡2 mod 3. The indexing set in each case forms a field, and the computation of the 2D FFT can be completely transferred into one dimension which is identical to the computational structure of the 1D FFT with prime size. Instead of the row-column algorithm which was designed based on the 1D FFT, an algorithm based on 1D cyclic convolution is designed. It is shown that this algorithm is efficient for some sample points and flexible for parallel or vector processing