Decorrelation is a general term for any process that is used to reduce autocorrelation within a signal, or cross-correlation within a set of signals, while preserving other aspects of the signal. A frequently used method of decorrelation is the use of a matched linear filter to reduce the autocorrelation of a signal as far as possible. Since the minimum possible autocorrelation for a given signal energy is achieved by equalising the power spectrum of the signal to be similar to that of a white noise signal, this is often referred to as signal whitening. Autocorrelation is a mathematical tool used frequently in signal processing for analysing functions or series of values, such as time domain signals. ... In statistics, the term cross-correlation is sometimes used to refer to the covariance cov(X, Y) between two random vectors X and Y, in order to distinguish that concept from the covariance of a random vector X, which is understood to be the matrix of covariances between the scalar... A linear filter applies a linear operator to a time-varying input signal. ... Autocorrelation is a mathematical tool used frequently in signal processing for analysing functions or series of values, such as time domain signals. ... For other uses of the term white noise, see white noise (disambiguation). ...

Although most decorrelation algorithms are linear, non-linear decorrelation algorithms also exist.

Many data compression algorithms incorporate a decorrelation stage. For example, many transform coders first apply a fixed linear transformation that would, on average, have the effect of decorrelating a typical signal of the class to be coded, prior to any later processing. This is typically a Karhunen-Loève transform, or a simplified approximation such as the discrete cosine transform. In statistics, principal components analysis (PCA) is a technique that can be used to simplify a dataset; more formally it is a linear transformation that chooses a new coordinate system for the data set such that the greatest variance by any projection of the data set comes to lie on... 2-D DCT compared to the DFT The discrete cosine transform (DCT) is a Fourier-related transform similar to the discrete Fourier transform (DFT), but using only real numbers. ...

By comparison, sub-band coders do not generally have an explicit decorrelation step, but instead exploit the already-existing reduced correlation within each of the sub-bands of the signal, due to the relative flatness of each sub-band of the power spectrum in many classes of signals.

Linear predictive coders can be modeled as an attempt to decorrelate signals by subtracting the best possible linear prediction from the input signal, leaving a whitened residual signal.

Decorrelation techniques can also be used for many other purposes, such as reducing crosstalk in a multi-channel signal, or in the design of echo cancellers. In telecommunication, the term crosstalk (XT) has the following meanings: 1. ... An Echo canceller is a telecommunications device used to remove the echo that can result from delay on a telecommunciations circuit. ...

In image processing decorrelation techniques can be used to enhance or stretch, colour differences found in each pixel of an image. This is generally termed as 'decorrelation stretching'. It has been suggested that digital image processing be merged into this article or section. ... Depending on context, the word Stretch can refer to any of the following things: Look up Stretch on Wiktionary, the free dictionary Making something longer by stretching or pulling on it. ... Color is an important part of the visual arts. ... This example shows an image with a portion greatly enlarged, in which the individual pixels are rendered as little squares and can easily be seen. ...

The concept of decorrelation can be applied in many other fields, including neuroscience, where it can be used in the analysis of the neural networks in the human visual system, and in cryptography. Drawing of the cells in the chicken cerebellum by S. Ramón y Cajal Neuroscience is a scientific discipline that studies the structure, function, development, genetics, biochemistry, physiology, pharmacology, and pathology of the nervous system. ... Simplified view of an artificial neural network A neural network is a system of interconnecting neurons in a network working together to produce an output function. ... The German Lorenz cipher machine, used in World War II for encryption of very high-level general staff messages Cryptography (or cryptology; derived from Greek κρυπτός kryptós hidden, and γράφειν gráfein to write) is the study of message secrecy. ...

See also

• Equalization
• Whitening random signal transformations

It has been suggested that this article or section be merged with Equalization filter. ... This article is about white noise as a scientific concept, see also: White Noise (novel), a 1985 novel by Don DeLillo. ...

External links

• Non-linear decorrelation algorithms
• Associative Decorrelation Dynamics in Visual Cortex
• Provable security for block ciphers by decorrelation