Frequency domain methods

Image processing, in common with other branches of signal processing, has a well-developed literature covering image manipulation in the frequency domain. An image is a two-dimensional array of pixels and is referred to as being in the spatial domain. (In signal processing, the corresponding domain is usually the time domain, the signals, such as audio, being functions of time.) It is possible, however, to transform an image into the spatial frequency domain using, for example, a Fourier transform, and manipulate the frequency domain representation of the image. In the spatial domain, the image is represented as the variation of luminance and/or chrominance with position in the pixel array (corresponding to the imaging plane in the camera or other acquisition device), whereas in the frequency domain, the image is represented by its spatial frequency components, each having a magnitude and phase. This representation has it roots in the mathematical technique of Fourier Series analysis, whereby a periodic function or signal may be decomposed into a series of sinusoidal components, or alternatively, viewed as a superposition or summation of the sinusoidal components. The frequency domain representation of the image is usually referred to as its ‘spectrum’.