Vector-radix FFT algorithm: Difference between revisions

Revision as of 16:25, 5 August 2017

Revision as of 20:32, 21 December 2017

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We suppose the 2-D DFT

:<math>X(k_1,k_2) = \sum_{n_1=0}^{N_1-1} \sum_{n_2=0}^{N_2-1} x[n_1, n_2] \cdot W_{N_1}^{k_1 n_1} W_{N_2}^{k_2 n_2}, </math>

where <math>k_1 = 0,\dots,N_1-1</math>,and <math>k_2 = 0,\dots,N_2-1</math>, and <math>x[n_1, n_2]</math> is a <math>N_1 \times N_2</math> matrix, and <math>W_N^{k n} = \exp(-j 2\pi /N)</math>.

For simplicity, let us assume that <math>N_1=N_2=N</math>, and radix-<math>(r\times r)</math>(<math>N/r</math> are integers).