Abstract
We show that the two-dimensional discrete Fourier transform DFT (2n; 2) can be transformed into a series of distinct second versions of the discrete cosine transform DCT. As a result of the minimal number of real multiplications over the field Q to compute the length 2n second version DCT, we derive the minimum number of real multiplications over the field Q necessary to compute a two-dimensional discrete Fourier transform for 2n × 2n real input data.
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