File:Fourier transform time and frequency domains.gif

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Fourier_transform_time_and_frequency_domains.gif(500 × 400 pixels, file size: 399 KB, MIME type: image/gif, looped, 93 frames, 37 s)
Description
English: A visualization of the relationship between the time domain and the frequency domain of a function, based on its Fourier transform.

The Fourier transform takes an input function f (in red) in the "time domain" and converts it into a new function f-hat (in blue) in the "frequency domain".

In other words, the original function can be thought of as being "amplitude given time", and the Fourier transform of the function is "amplitude given frequency".

Shown here, a simple 6-component approximation of the square wave is decomposed (exactly, for simplicity) into 6 sine waves. These component frequencies show as very sharp peaks in the frequency domain of the function, shown as the blue graph.
Date
Source Own work
Author Lucas V. Barbosa
Permission
(Reusing this file)
Public domain I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
In some countries this may not be legally possible; if so:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

Other versions

Small version (to include in articles) Fourier transform time and frequency domains (small).gif

(separate files were necessary due to the awfulness of MediaWiki's thumbnail generator)

File history

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Date/TimeThumbnailDimensionsUserComment
current20:42, 23 February 2013Thumbnail for version as of 20:42, 23 February 2013500 × 400 (399 KB)LucasVB (talk | contribs)Reverted to version as of 20:31, 23 February 2013
20:38, 23 February 2013Thumbnail for version as of 20:38, 23 February 2013500 × 400 (684 KB)LucasVB (talk | contribs)Trying to circumvent MediaWiki's crappy thumbnail generator again. Completely unoptimized the animation.
20:31, 23 February 2013Thumbnail for version as of 20:31, 23 February 2013500 × 400 (399 KB)LucasVB (talk | contribs)The new GIF scaling algorithm used on MediaWiki is awful, and adds a bunch of horrible artifacts to the animated thumbs. This is an attempt at avoiding the artifacts using an alternate palette. If this doesn't work, I'll have to submit the smaller vers...
11:43, 23 February 2013Thumbnail for version as of 11:43, 23 February 2013500 × 400 (346 KB)LucasVB (talk | contribs){{Information |Description=A visualization of the relationship between the time domain and the frequency domain of a function, based on its Fourier transform. |Source={{own}} |Date=2013-02-23 |Author= Lucas V. Barbosa |Permission={{PD-...
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