### 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
and various Frequencies that produce the same shape.
The Fourier transform can be applied 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*)
http://en.wikipedia.org/wiki/Fourier_transform

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

http://cns-alumni.bu.edu/~slehar/fourier/fourier.html

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

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

index