The separating decomposition of discrete Fourier transform and vectorization of its calculation

Abstract

The transfer to the parallel calculations gives new possibilities for digital signal processing. However, for the realization of these possibilities, it is necessary to use efficiently high-speed parallel processors and vector computers. For that one needs algorithms orientated on parallel calculating procedures. We propose the method of the separating decomposition of discrete Fourier transform (DFT) orientated to the creation of the DFT algorithms with a flexible structure characterized by the parametrical adjustability to different forms of parallel processing. We consider the recursive vector DFT algorithms based on the separating decomposition of DFT in which both the algorithm of the standard fast Fourier transform (FFT) and the mixed-radix FFT algorithm can be used. The proposed algorithms are characterized by the natural succession of the samples of both the input signal and its spectrum and provide the effective application of the vector arithmetic instructions in DFT calculations with a wide range of lengths.