A Fast Algorithm Based on SRFFT for Length N = q × 2 m DFTs

In this brief, we present a fast algorithm for computing length-q × 2 discrete Fourier transforms (DFT). The algorithm divides a DFT of size-N = q × 2 decimation in frequency into one length-N/2 DFT and two length-N/4 DFTs. The length-N/2 sub-DFT is recursively decomposed decimation in frequency, and the two size-N/4 sub-DFTs are transformed into two dimension and the terms with the same rotating factor are arranged in a column. Thus, the scaled DFTs (SDFTs) are obtained, simplifying the real multiplications of the proposed algorithm. A further improvement can be achieved by the application of radix-2/8, modified split-radix FFT (MSRFFT), and Wang’s algorithm for computing its length-2 and length-q sub-DFTs. Compared with the related algorithms, a substantial reduction of arithmetic complexity and more accurate precision are obtained.