File:Convolution Animation (Boxcar).gif
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Convolution_Animation_(Boxcar).gif (360 × 222 pixels, file size: 542 KB, MIME type: image/gif, looped, 161 frames)
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DescriptionConvolution Animation (Boxcar).gif |
English: An animation of the convolution of two boxcar functions, f(t) (red) and g(t) (blue)
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Date | ||||
Source | Own work | |||
Author | Inductiveload | |||
Permission (Reusing this file) |
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Mathematica Code
[edit](*Function definitions*) boxcar[x_, {a_, b_}] := UnitStep[x - a] - UnitStep[x - b] f[t_] := boxcar[t, {-1/2, 1/2}]; g[t_] := boxcar[t, {-1/4, 1/4}]/2; h[y_] := Module[ {t}, Convolve[f[t], g[t], t, y] ]; (*Parts of the drawing that only need to be computed once*) constplots = Plot[ {f[t], g[t], h[t]}, {t, -2, 2}, PlotStyle -> {Red, {Blue, Dashed}, Black}, ClippingStyle -> False, Axes -> False, Exclusions -> False ]; anim = Table[Show[ { (*The plots we generated earlier*) constplots, (*Plot the time reversed g[t], g[\[Tau]-t]*) Plot[g[\[Tau] - t], {t, -5, 5}, PlotPoints -> 100, ClippingStyle -> False, PlotStyle -> Blue, Exclusions -> False, Axes -> False], (*Plot the product of the f[t] and g[\[Tau]-t]*) Plot[f[t]*g[\[Tau] - t], {t, -5, 5}, PlotPoints -> 100, ClippingStyle -> False, Filling -> Axis, FillingStyle -> Directive[Green, Opacity[0.2]], PlotStyle -> Green, Exclusions -> False, Axes -> False], (*Plot the embellishments*) Graphics[ {{Blue, Line[{{\[Tau], -0.05}, {\[Tau], 1.1}}]}, {Red, Text[f, {.2, .96}, Background -> None]}, {Blue, Text[g, {.2, .55}, Background -> None]}, {Blue, Text["g(\[Tau]-t)", {\[Tau] - 0.45, .4}, Background -> None]}, {Green, Text["f(t)g(\[Tau]-t)", {\[Tau] - 0.35, -0.04}, Background -> None]}, {Black, Text[Star[f, g], {0, .22}, Background -> None]}, {Blue, Text["\[Tau]", {\[Tau], -0.1}, Background -> White]} }] }, PlotRange -> {{-1.9, 1.9}, {-.2, 1}}], {\[Tau], -2, 2, .025}(*Table index is the time delay*) ]; ListAnimate[anim] Export["anim2.gif", anim]
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 04:19, 5 March 2009 | ![]() | 360 × 222 (542 KB) | Inductiveload (talk | contribs) | {{Information |Description={{en|1=An animation of the convolution of two boxcar functions, ''f(t)'' and ''g(t)''.}} |Source=Own work by uploader |Author=Inductiveload |Date=2009/03/05 |Permission={{PD-self}} |other_versions= }} ==Ma |
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GIF file comment | Created by Wolfram Mathematica 7.0 |
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5 March 2009
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94e06153936d927a87acf2e8ec1c6e8e00be57a8
555,384 byte
222 pixel
360 pixel
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