File:Fourier transform two ways.png
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Summary
[edit]
| Description |
Two views of the Fourier transform of a function f(t). The first shows the plot of the time domain representation of f. The second plot shows the real and imaginary parts of the Fourier transform as a function of ω (assumed real). The other two plots the magnitude (complex modulus) and phase (complex argument) of the Fourier transform. This was created by me (User:Slawekb) in Mathematica, version 9.0. The code to reproduce this is: fplot = Plot[f[x], {x, -4, 4}, AxesLabel -> {"t", "f(t)"}]
Fplot = Plot[{Re[F[s]], Im[F[s]]}, {s, -6, 6}, PlotRange -> All,
AxesLabel -> {"\[Omega]",
"Re(\!\(\*OverscriptBox[\(f\), \(^\)]\)(\[Omega])), \
Im(\!\(\*OverscriptBox[\(f\), \(^\)]\)(\[Omega]))"}]
AbsFplot =
Plot[Abs[F[s]], {s, -6, 6}, PlotRange -> All,
AxesLabel -> {"\[Omega]",
"|\!\(\*OverscriptBox[\(f\), \(^\)]\)(\[Omega])|"}]
ArgFplot =
Plot[Arg[F[s]], {s, -6, 6}, PlotRange -> All,
AxesLabel -> {"\[Omega]",
"arg(\!\(\*OverscriptBox[\(f\), \(^\)]\)(\[Omega]))"}]
GraphicsGrid[{{fplot}, {Fplot}, {AbsFplot, ArgFplot}}]
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|---|---|
| Source |
Created in mathematica 9.0 |
| Date |
2014-11-26 |
| Author | |
| Permission (Reusing this file) |
See below.
|
Licensing
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I, the copyright holder of this work, hereby publish it under the following licenses:
 | Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. |
   | This work is licensed under the Creative Commons Attribution-ShareAlike 3.0 License. |
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 | This media file is either in the public domain or published under a free license, and contains no inbound file links. If this media file is useful, then it should be transferred to the Wikimedia Commons. If this media is not useful, then please propose it for deletion or list it at files for discussion. |
File history
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 23:42, 26 November 2014 | | 648 × 610 (40 KB) | Slawekb (talk | contribs) | Made less minuscule. |
| 23:35, 26 November 2014 |  | 863 × 813 (45 KB) | Slawekb (talk | contribs) | Uploading a self-made file using File Upload Wizard |
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