Discrete transform
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In signal processing, discrete transforms are mathematical transforms, often linear transforms, of signals between discrete domains, such as between discrete time and discrete frequency.[1]
Mant common integral transforms used in signal processing have their discrete counterparts. For example, for the Fourier transform the counterpart is the discrete Fourier transform.
In addition to spectral analysis of signals, discrete transforms play important role in data compression, signal detection, digital filtering and correlation analysis.[2]
There is a subtle difference between the terms "discrete transform" and "discrete-time transform". Both work over the discrete time domain, however the latter ones are represented by means of (infinite) series, which are a closer counterparts of the integral used in integral transform formulae, so they are also referred to as "series transforms".[citation needed]
Classical signal processing deals with one-dimensional discrete transforms. Other application areas, such as image processing, computer vision, high definition television, visual telephony, etc. make use of two-dimensional and in general, multidimensional discrete transforms.