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File:Sawtooth Fourier Animation.gif

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Sawtooth_Fourier_Animation.gif (380 × 492 pixels, file size: 226 KB, MIME type: image/gif, looped, 15 frames, 4.5 s)

This image could be re-created using vector graphics as an SVG file. This has several advantages; see Commons:Media for cleanup for more information. If an SVG form of this image is available, please upload it and afterwards replace this template with {{vector version available|new image name}}. It is recommended to name the SVG file "Sawtooth Fourier Animation.svg" - then the template Vector version available (or Vva) does not need the new image name parameter.

Summary

Description
English: Animation showing a Fourier series approximating a sawtooth wave (top), and the sinusoidal components that make up the series plotted together (bottom).
Date
Source Own work. Created from scratch in Mathematica 8. Intended to replace File:Sawtooth Fourier Analysis.JPG.
Author 4dhayman
(*Mathematica code to generate diagram and export it as an animated GIF*)
Export["Sawtooth_Fourier_Animation.gif", 
 Table[GraphicsColumn[{Show[
     Plot[2 ((1/2) - (1/Pi)*
           Sum[(1/n)*Sin[n*Pi*x*2], {n, 1, steps}]) - 1, {x, 0, 2}, 
      PlotStyle -> {Thick, Blue}], 
     Plot[2 SawtoothWave[x] - 1, {x, 0, 2}, 
      ExclusionsStyle -> {Dashing[Large], Thick, Black}, 
      PlotStyle -> {Thick, Black}], 
     Graphics[
      Text[Style["k = " <> ToString[steps], Bold, FontSize -> 18, 
        FontFamily -> "Helvetica"], {1.65, 1.1}]], 
     LabelStyle -> {FontSize -> 18, FontFamily -> "Helvetica"}, 
     AxesOrigin -> {0, -1.1}, AxesLabel -> {"x", "y"}, 
     ImageSize -> Scaled[.8], PlotRange -> {{0, 2}, {-1.1, 1.2}}], 
    Plot[Evaluate[
      2 ((1/2) - (1/Pi)*
           Table[(1/n)*Sin[n*Pi*x*2], {n, 1, steps, 1}]) - 1], {x, 0, 
      2}, PlotStyle -> ({Thick, Blue, #} & /@ 
        Table[Opacity[If[i == 1, 1, 1 - i/(steps + 1)]], {i, 1, steps,
           1}]), LabelStyle -> {FontSize -> 18, 
       FontFamily -> "Helvetica"}, AxesOrigin -> {0, -1.1}, 
     AxesLabel -> {"x", "y"}, ImageSize -> Scaled[.8], 
     PlotRange -> {{0, 2}, {-1.1, 1.2}}]}], {steps, 1, 15}], 
 "DisplayDurations" -> 0.3]

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 3.0 Unported license.
You are free:
  • to share – to copy, distribute and transmit the work
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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.

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20 February 2012

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Date/TimeThumbnailDimensionsUserComment
current22:58, 20 February 2012Thumbnail for version as of 22:58, 20 February 2012380 × 492 (226 KB)4dhayman~commonswiki

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