Method of flow graph simplification for the 16-point discrete Fourier transform

• Published in: IEEE transactions on signal processing Vol. 53; no. 1; pp. 384 - 389
• Main Authors: Grigoryan, A.M., Bhamidipati, V.S.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.01.2005; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Algorithms; Applied sciences; Chaos; Chaotic communication; Convergence; Discrete Fourier transforms; Exact sciences and technology; Fast Fourier transform; Flow graphs; Fourier transforms; Graphs; Information, signal and communications theory; Mathematical analysis; Mathematical methods; Maximum likelihood estimation; Multiplication; paired function and transform; Signal generators; Signal processing; Signal processing algorithms; Simplification; Telecommunications and information theory; Transforms; Simplification; Flow graphs; Computing method; Discrete Fourier transformation; Fast Fourier transform; paired function and transform
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2004.838970

An efficient method for the realization of the paired algorithm for calculation of the one-dimensional (1-D) discrete Fourier transform (DFT), by simplifying the signal-flow graph of the transform, is described. The signal-flow graph is modified by separating the calculation for real and imaginary parts of all inputs and outputs in the signal-flow graph and using properties of the transform. The examples for calculation of the eight- and 16-point DFTs are considered in detail. The calculation of the 16-point DFT of real data requires 12 real multiplications and 58 additions. Two multiplications and 20 additions are used for the eight-point DFT.