# Whitening transformation

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Whitening transformation

The whitening transformation is a decorrelation method that converts the covariance matrix S of a set of samples into the identity matrix I. This effectively creates new random variables that are uncorrelated and have the same variances as the original random variables. The method is called the whitening transform because it transforms the input matrix closer towards white noise.

This can be expressed as$A_w = Phi Lambda^\left\{-frac\left\{1\right\}\left\{2$ [R.O. Duda, P.E. Hart, and D.G. Stork, Pattern Classification, New York: John Wiley & Sons, 2001, pp. 34]

where $Phi$ is the matrix with the eigenvectors of "S" as its columns and $Lambda$ is the diagonal matrix of non-increasing eigenvalues.

ee also

* Decorrelation
* Randomness extractor
* Hardware random number generator

References

Wikimedia Foundation. 2010.

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