Among the butterflies in the structure of the VR-2 x 2 FFT, the 2 x 2 butterflies related to only the newly imported input data must be calculated in the VR-2 x 2 SFFT. For the N x N input data, the number of 2 x 2 butterflies calculated at [D.sub.n] is N x [2.sup.n]/4.
As mentioned in Section 2, a 2 x 2 butterfly needs two CM's and six [C.sub.A]'s, and the VR-2 x 2 SFFT requires [N.sup.2]-N CM's and 3([N.sup.2] - N) [C.sub.A]'s for N x N input data.
The 2D MFFT , SFFT , and 2D SDFT  are chosen for the existing fast DFT/FFT algorithms.
We investigated the stability of the proposed VR-2 x 2 SFFT algorithm using a complex test signal, which was zero-mean Gaussian noise with a standard deviation of one.
The measured [E.sub.n] values of the 1D mSDFT + 1D FFT, 1D gSDFT + 1D FFT, and VR-2 x 2 SFFT are presented in Figure 9.
In this letter, a new stable SFFT based on the VR-2 x 2 FFT algorithm was presented for 2D input data.