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)

Summary

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.

Licensing

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File history

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Date/TimeThumbnailDimensionsUserComment
current20:36, 6 January 2017Thumbnail for version as of 20:36, 6 January 2017300 × 240 (265 KB)127.0.0.1 (talk)A visualization of the relationship between the time domain and the frequency domain of a function, based on its Fourier transform. <p>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". </p> <p>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". </p> 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.
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