Файл: Ersoy O.K. Diffraction, Fourier optics, and imaging (Wiley, 2006)(ISBN 0471238163)(427s) PEo .pdf

where N2 equals N/2. It is observed that U1½k& and U2½k& are computed by DFTs of size N/2 with the even and odd-numbered points of the original signal.

The procedure described above is continued iteratively until reaching size 2 DFT, which consists of adding and subtracting two points.

The radix-2 decimation-in-frequency algorithm can be similarly developed. However, its implementation turns out to me more complex.

The 2-D FFT is obtained from the 1-D FFT by applying the 1-D FFT first to the rows of a signal matrix, and then to its columns or vice versa.

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