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Fourier space (or frequency domain or Fourier domain) is an abstract "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). Typical is to apply a Fourier transform to a function of one dimension (such as a function of time) and there are ways to apply it to functions of two or more, image processing making use of such transforms over two dimensions.
"Normal" space for a two dimensional image could be indicated by a function on x and y, consisting of a scalar value ("amplitude") at each represented point. Such a space transformed into Fourier space then consists of the amplitudes and phases of sequences of various sine functions over various directions, the sine-function characteristics being such that summing them all yields the above-mentioned function on x and y. (For the purposes of radio interferometry, the corresponding Fourier space is termed the u-v plane.) In such Fourier space, operations such as truncating (removing precision) affect an image differently than they would applying them within the normal space, offering additional means of image manipulation and analysis.