File:DIT-FFT-butterfly.svg

Summary

Description
English: Decimation in time of a length-N DFT into two length-N/2 DFTs followed by a combining stage.
Date
Source Own work
Author Yangwenbo99
Other versions A coloured version is available at File:DIT-FFT-butterfly-coloured.svg. This image is based on the PNG image File:DIT-FFT-butterfly.png.

This is the SVG version of File:DIT-FFT-butterfly.png. It it drawn by the following Latex code:

\documentclass[tikz,convert={outfile=\jobname.svg}]{standalone}
% \documentclass[tikz]{standalone}
\usetikzlibrary{automata,positioning}
\usepackage{relsize}
%\usetikzlibrary{...}% tikz package already loaded by 'tikz' option
\begin{document}
\begin{tikzpicture}% Example:
  \draw[fill=white, draw=white] (-0.5, 0.7) rectangle (8, -7.7); 
  \draw (0,0) node {$x[0]$};
  \draw (0,-1) node {$x[2]$} ;
  \draw (0,-2) node {$x[4]$} ;
  \draw (0,-3) node {$x[6]$} ;

  \draw (0,-4) node {$x[1]$} ;
  \draw (0,-5) node {$x[3]$} ;
  \draw (0,-6) node {$x[5]$} ;
  \draw (0,-7) node {$x[7]$} ;

  % arrow on the right of x's
  \foreach \n in {0,...,7} {
    \draw (0.5,-\n) circle(0.05)[fill=white]; 
    \draw [-latex] (0.55,-\n) -- (1, -\n); 
    \draw (1, -\n) -- (1.4, -\n); 
  }

  % blocks
  \draw(1.4, 0.3) rectangle (4, -3.3); 
  \draw(1.4, -3.7) rectangle (4, -7.3); 
  \draw(2.7, -1.5) node[text centered, text width=2cm] {$N/2$-point DFT};
  \draw(2.7, -5.5) node[text centered, text width=2cm] {$N/2$-point DFT};

  % E's and O's 
  \foreach \n in {0,...,7} {
    \draw [-latex] (4,-\n) -- (4.95, -\n); 
    \draw (5,-\n) circle(0.05)[fill=white]; 
  }
  \foreach \n in {0,...,3} {
    \draw (4.9,-\n + 0.3) node {$E[\n]$};
  }
  \foreach \n in {0,...,3} {
    \draw (4.9,-\n - 4 - 0.3) node {$O[\n]$};
  }

  % X's 
  \foreach \n in {0,...,7} {
    \draw (7,-\n) circle(0.05)[fill=white]; 
    \draw (7.5,-\n) node {$X[\n]$};
  }

  % Connecting X and E
  \foreach \n in {0,...,7} {
    \draw [-latex] (5.05, -\n) -- (6.95, -\n);
  }
  \foreach \n in {0,...,3} {
    \draw [-latex] (5.05, -\n) -- (6.95, -\n - 4);
  }
  \foreach \n in {0,...,3} {
    \draw [-latex] (5.05, -\n-4) -- (6.95, -\n);
  }

  % W's
  \foreach \n in {0,...,7} {
    \draw (7.1,-\n - 0.3) node {\scriptsize $W_N^{\n}$};
  }
\end{tikzpicture}
\end{document}

Licensing

I, the copyright holder of this work, hereby publish it under the following license:
w:en:Creative Commons
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Category:CC-BY-SA-4.0#DIT-FFT-butterfly.svg
Category:Self-published work Category:Discrete Fourier transform Category:FFT Category:Computational complexity theory
Category:CC-BY-SA-4.0 Category:Computational complexity theory Category:Discrete Fourier transform Category:FFT Category:Self-published work