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

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.