A whitening transformation or sphering transformation is a linear transformation that transforms a vector of random variables with a known covariance matrix into a set of new variables whose covariance is the identity matrix, meaning that they are uncorrelated and each have variance 1.[1] The transformation is called "whitening" because it changes the input vector into a white noise vector.
Several other transformations are closely related to whitening:
- the decorrelation transform removes only the correlations but leaves variances intact,
- the standardization transform sets variances to 1 but leaves correlations intact,
- a coloring transformation transforms a vector of white random variables into a random vector with a specified covariance matrix.[2]
- ^ Koivunen, A.C.; Kostinski, A.B. (1999). "The Feasibility of Data Whitening to Improve Performance of Weather Radar". Journal of Applied Meteorology. 38 (6): 741–749. Bibcode:1999JApMe..38..741K. doi:10.1175/1520-0450(1999)038<0741:TFODWT>2.0.CO;2. ISSN 1520-0450.
- ^ Hossain, Miliha. "Whitening and Coloring Transforms for Multivariate Gaussian Random Variables". Project Rhea. Retrieved 21 March 2016.