File:DIT-FFT-butterfly-coloured.svg

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Summary

Description
English: Decimation in time of a length-N DFT into two length-N/2 DFTs followed by a combining stage, coloured for easier understanding.
Date
Source Own work
Author Yangwenbo99

Drawn with the following LaTeX code:

\documentclass[tikz,convert={outfile=\jobname.svg}]{standalone}
% \documentclass[tikz]{standalone}
\usetikzlibrary{automata,positioning}
\usetikzlibrary{math}
\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); 

  % arrow on the right of x's
  \tikzmath{
    int \n; 
    for \n in {0,...,3}{
      \x = int(2 * \n);
      {
        \draw[color=teal] (0,-\n) node {$x[\x]$};
        \draw[color=teal] (0.5,-\n) circle(0.05)[fill=white]; 
        \draw[color=teal] [-latex] (0.55,-\n) -- (1, -\n); 
        \draw[color=teal] (1, -\n) -- (1.4, -\n); 
      };
    };
    for \n in {0,...,3}{
      \x = int(2 * \n + 1);
      {
        \draw[color=blue] (0,-\n - 4) node {$x[\x]$};
        \draw[color=blue] (0.5,-\n - 4) circle(0.05)[fill=white]; 
        \draw[color=blue] [-latex] (0.55,-\n-4) -- (1, -\n - 4); 
        \draw[color=blue] (1, -\n - 4) -- (1.4, -\n - 4); 
      };
    };
  }

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

  % E's and O's 
  \foreach \n in {0,...,3} {
    \draw [-latex,color=teal] (4,-\n) -- (4.95, -\n); 
    \draw[color=teal] (5,-\n) circle(0.05)[fill=white]; 
  }
  \foreach \n in {0,...,3} {
    \draw [-latex,color=blue] (4,-\n  - 4) -- (4.95, -\n - 4); 
    \draw[color=blue] (5,-\n - 4) circle(0.05)[fill=white]; 
  }
  \foreach \n in {0,...,3} {
    \draw[color=teal] (4.9,-\n + 0.3) node {$E[\n]$};
  }
  \foreach \n in {0,...,3} {
    \draw[color=blue] (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,...,3} {
    \draw[color=teal] [-latex] (5.05, -\n) -- (6.95, -\n);
  }
  \foreach \n in {0,...,3} {
    \draw[color=blue] [-latex] (5.05, -\n - 4) -- (6.95, -\n - 4);
  }
  \foreach \n in {0,...,3} {
    \draw[color=teal] [-latex] (5.05, -\n) -- (6.95, -\n - 4);
  }
  \foreach \n in {0,...,3} {
    \draw[color=blue] [-latex] (5.05, -\n-4) -- (6.95, -\n);
  }

  % W's
  \foreach \n in {0,...,7} {
    \draw[color=magenta] (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
attribution share alike
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You are free:
  • to share – to copy, distribute and transmit the work
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Under the following conditions:
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Captions

Butterflydiagram of DIT-FFT

Items portrayed in this file

depicts

19 October 2021

image/svg+xml

b3888ce7b2cccc3cca9a8304451ce498efdb9cbb

80,836 byte

298 pixel

302 pixel

File history

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Date/TimeThumbnailDimensionsUserComment
current10:12, 19 October 2021Thumbnail for version as of 10:12, 19 October 2021302 × 298 (79 KB)Yangwenbo99Uploaded own work with UploadWizard
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