Two-dimensional fast Fourier transform: Batterfly in analog of Cooley-Tukey algorithm

One- and two-dimensional (2D) fast Fourier transform (FFT) algorithms has been widely used in digital processing. 2D discrete Fourier transform is reduced to a combination of one-dimensional FFT for all coordinates due to the increased complexity and the large amount of computation by increasing dimension of the signal. This article provides the butterfly of analog Cooley-Tukey algorithm, which requires less complex operations of additional and multiplication than the standard method, and runs 1.5 times faster than analogue in Matlab.