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In this paper, a new decimation-in-time vector-radix-22 × 22 fast Fourier transform (VR-22 × 22-FFT) algorithm for computing the two dimensional discrete Fourier transform (2-D DFT) is presented. The algorithm is derived by applying a two-stage decomposition approach and by introducing an efficient technique for grouping the twiddle factors. The arithmetic complexity of the proposed algorithm is analyzed and the number of real multiplications and additions are computed for different transform sizes. Moreover, a comparison with the existing 2-D vector-radix FFT algorithms has shown that the presented algorithm can be considered as a good compromise between the structural and computational complexities.