**Definition:**Pre-whitening removes autocorrelations from the residuals in preparation of data for analysis with the general linear model (GLM) and whitens the frequency content of the signal. Due to the inherent properties of fNIRS, signals are autocorrelated and reflect 1/f properties (i.e. the noise power is inversely proportional to the frequency). Pre-whitening the fNIRS signal can help minimize errors, particularly the False Discovery Rate, that may arise with certain statistical models (such as a General Linear Model). In particular, pre-whitening makes the distribution of the noise uniform (thus, “white”), by applying a whitening filter W, selected such that the new error term W*e is spherical. The whitening matrix W can be obtained by iteratively fitting the GLM and examining the residuals. Based on the residuales, a W matrix is estimated, usually by fitting an autoregressive model to the residuals’ vector. The AR model will remove the noise structure to the autocorrelation of the samples. The coefficients of the AR model are then used to build the W matrix.The extent to which the whitening matrix is able to effectively reduce the autocorrelation of the residuals depends on the AR model order, i.e. the duration of the autocorrelation.

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**References:**https://doi.org/10.1117/1.jbo.22.5.055002 https://doi.org/10.1002/1097-0193(200102)12:2%3C61::AID-HBM1004%3E3.0.CO;2-W DOI:10.1364/BOE.4.001366

**Related terms:**noise, pre-colouring, General Linear Model