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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. 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.