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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)
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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
DescriptionSawtooth Fourier Animation.gif |
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:
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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.
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 22:58, 20 February 2012 | ![]() | 380 × 492 (226 KB) | 4dhayman~commonswiki |
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GIF file comment | Created by Wolfram Mathematica 8.0 |
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