### Fourier space

**(Fourier domain, frequency domain)**
(domain into which the Fourier transform maps a function)

**Fourier space** (or **frequency domain** or **Fourier domain**)
is a space into which the Fourier transform maps a function,
consisting of the amplitude and phase of the sine function
at various frequencies that sum to produce the same shape.
For a function that is periodic or is over a finite domain,
the frequencies generally chosen are with periods 1/2, 1/3, 1/4,
(and so forth) of the repeating period (or domain extent).
There are ways to apply the Fourier transform to a function
of one or more dimensions, two dimensions being commonly
used for processing images.

"Normal" space for, say, a two dimensional image could
be X and Y, with a function consisting of the amplitude at each
such point.
Fourier space is two corresponding frequencies (periods),
with the transformed function mapping the frequencies them into an
amplitude and a phase of a sine wave (a complex number) such that
if all were summed over the fourier space, the same surface
is produced.

Operations such as truncating (removing precision)
affect an image differently than would applying it
to the normal space, offering more means of
manipulation and analysis.

(*mathematics*)
**Further reading:**

http://en.wikipedia.org/wiki/Fourier_transform

http://math.stackexchange.com/questions/1189142/are-frequency-domain-and-fourier-space-the-same-thing

http://medical-dictionary.thefreedictionary.com/Fourier+space

https://homepages.inf.ed.ac.uk/rbf/HIPR2/fourier.htm

https://web.iit.edu/sites/web/files/departments/academic-affairs/academic-resource-center/pdfs/Fourier_Space_and_image.pdf

**Referenced by pages:**

Fourier series expansion

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