Double factors algorithm for computing DFT

• Published in: 2009 International Conference on Image Analysis and Signal Processing pp. 133 - 137
• Main Authors: Haijun Li, Caojun Yan, Wenbiao Peng
• Format: Conference Proceeding
• Language: English
• Published: IEEE 01.04.2009
• Subjects: Algorithm design and analysis; Discrete Fourier transforms; Doped fiber amplifiers; double factors algorithm; Educational institutions; Fast Fourier transforms; prime factor algorithm; radix-4 FFT; smaller-length DFT; splix-radix FFT; Time domain analysis
• ISBN: 9781424439874; 1424439876
• ISSN: 2156-0110
• DOI: 10.1109/IASP.2009.5054641

A fast Fourier transform algorithm for computing N=N 1 timesN 2 -point DFT, where both factors N 1 and N 2 are smaller positive integer, said to be a double factors algorithm(DFA), is developed. The DFA subdivides a DFT of length N=N 1 timesN 2 into smaller transforms of length N 1 and N 2 and takes the following steps:(1) computes N 1 N 2 -point DFTs , (2) multiplies the values of DFT by twiddle factors, (3) computes N 2 N 1 -point DFTs. The structure of the DFA is similar to those of the most simple PFA and WFTA, but N 1 and N 2 are not necessarily relatively prime. When N=2 M or 4 M , the total number of computations of DFT in the DFA is less than those in the radix-2 and radix-4 FFT algorithm but slightly more than that in the split-radix FFT algorithm. When N is other values, the total number of computations of DFT in the DFA is less than those in the PFA and WFTA.