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File:Fourier transform time and frequency domains (small).gif

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Fourier_transform_time_and_frequency_domains_(small).gif ‎(300 × 240 pixels, file size: 265 KB, MIME type: image/gif, looped, 93 frames, 37 s)

Description
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
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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.
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23 February 2013

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Date/TimeThumbnailDimensionsUserComment
current20:44, 23 February 2013Thumbnail for version as of 20:44, 23 February 2013300 × 240 (265 KB)LucasVB{{Information |Description={{en|1=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 con...
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