File:From Continuous To Discrete Fourier Transform.gif
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From_Continuous_To_Discrete_Fourier_Transform.gif (800 × 242 pixels, file size: 15 KB, MIME type: image/gif)
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[edit]DescriptionFrom Continuous To Discrete Fourier Transform.gif |
English: Relationship between the (continuous) Fourier transform and the discrete Fourier transform.
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Date | |
Source | Own work |
Author | Sbyrnes321 |
(* Source code written in Mathematica 6.0, by Steve Byrnes, 2011. I release this code into the public domain. *) ClearAll["Global`*"] SetOptions[Plot, Frame -> True, FrameTicks -> None, Axes -> False, PlotRange -> {{-8, 8}, All}]; SetOptions[ListPlot, Frame -> True, FrameTicks -> None, Axes -> False, Filling -> Axis, PlotStyle -> None, PlotRange -> {{-8, 8}, All}]; f[x_] := Exp[-(4/3)*\[Pi] x^2]; g[x_] := Exp[-(3/4)*\[Pi] x^2]; repeatedf[x_, p_] := Sum[f[x + n*p], {n, -10, 10}]; repeatedg[x_, p_] := Sum[g[x + n*p], {n, -10, 10}]; plotf = Plot[f[x], {x, -10, 10}, PlotStyle -> Darker[Blue]]; plotg = Plot[g[x], {x, -10, 10}, PlotStyle -> Darker[Red]]; plotrepeatedf = Plot[repeatedf[x, 5], {x, -10, 10}, PlotStyle -> Darker[Blue]]; discreteg = Table[{x, g[x]}, {x, -10, 10, 1/5}]; plotdiscreteg = ListPlot[discreteg, FillingStyle -> Darker[Red]]; discretef = Table[{x, f[x]}, {x, -10, 10, 1/3}]; plotdiscretef = ListPlot[discretef, FillingStyle -> Darker[Blue]]; plotrepeatedg = Plot[repeatedg[x, 3], {x, -10, 10}, PlotStyle -> Darker[Red]]; discreterepeatedf = Table[{x, repeatedf[x, 11/4]}, {x, -12, 12, 1/4}]; plotdiscreterepeatedf = ListPlot[discreterepeatedf, FillingStyle -> Darker[Blue]]; discreterepeatedg = Table[{x, repeatedg[x, 4]}, {x, -12, 12, 4/11}]; plotdiscreterepeatedg = ListPlot[discreterepeatedg, FillingStyle -> Darker[Red]]; finalimg = Show[GraphicsGrid[{{plotf, plotrepeatedf, plotdiscretef, plotdiscreterepeatedf}, {plotg, plotdiscreteg, plotrepeatedg, plotdiscreterepeatedg}}], ImageSize -> 800] SetDirectory["C:\\Users\\Steve\\Desktop"]; Export["test.gif", finalimg]
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[edit]I, the copyright holder of this work, hereby publish it under the following license:
This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. | |
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current | 18:18, 5 December 2011 | 800 × 242 (15 KB) | Sbyrnes321 (talk | contribs) |
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