File:DIT-FFT-butterfly.svg

Original file(SVG file, nominally 302 × 298 pixels, file size: 78 KB)

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
attribution share alike
This file is licensed under the Creative Commons Attribution-Share Alike 4.0 International license.
You are free:
  • to share – to copy, distribute and transmit the work
  • to remix – to adapt the work
Under the following conditions:
  • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
  • share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

Captions

Butterflydiagram of DIT-FFT

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File history

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Date/TimeThumbnailDimensionsUserComment
current08:42, 19 October 2021Thumbnail for version as of 08:42, 19 October 2021302 × 298 (78 KB)Yangwenbo99Uploaded own work with UploadWizard
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