File:Convolution Animation (Exponential and Gaussian).gif
Convolution_Animation_(Exponential_and_Gaussian).gif (360 × 222 pixels, file size: 751 KB, MIME type: image/gif, looped, 161 frames)
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DescriptionConvolution Animation (Exponential and Gaussian).gif |
English: An animation of an f(t), an exponential function and g(t), a Gaussian function.
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Date | ||||
Source | Own work | |||
Author | Inductiveload | |||
Permission (Reusing this file) |
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Mathematica Code
edit(*Function definitions*) f[t_] := Piecewise[ {{0, t < -0.5}, {0.7 Exp[-t^2], -0.5 < t < 1}, {0, t > 1}}]; g[t_] := Piecewise[ {{0, t < 0}, {0.3 Exp[t], 0 < t < 1}, {0, t > 1}}]; 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, .73}, Background -> None]}, {Blue, Text[g, {.75, .7}, Background -> None]}, {Blue, Text["g(\[Tau]-t)", {\[Tau] - .58, .4}, Background -> None]}, {Green, Text["f(t)g(\[Tau]-t)", {\[Tau] - 0.55, -0.04}, Background -> None]}, {Black, Text[Star[f, g], {.30, .15}, 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]
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 05:19, 5 March 2009 | 360 × 222 (751 KB) | Inductiveload (talk | contribs) | {{Information |Description={{en|1=An animation of an ''f''(''t''), an exponential function and ''g''(''t''), a Gaussian function.}} |Source=Own work by uploader |Author=Inductiveload |Date=2009/03/05 |Permission={{PD-self}} |other_v |
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GIF file comment | Created by Wolfram Mathematica 7.0 |
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