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.

(*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]

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