The term in the denominator is the Fourier transform of the autocorrelation of .If is the identity matrix , will be constant. This corresponds to an input with a white spectrum. If all the terms of are constant, will be non-zero only at ,and the inversion will be unstable. This corresponds to a data series containing a constant. It can be seen that is a measure of the information available at , and is a function of the uncertainty, or variance, at .The original autocorrelation matrix is the information matrix, and its inverse is the covariance matrixStrang (1986).

The expression will generally have a stabilizer in the denominator to avoid having approach infinity when gets small. Adding this stabilizer in the frequency domain corresponds to adding a small value to the diagonal of the autocorrelation matrix. In the cases discussed here, the stabilizer will seldom be needed since random noise in the data generally keeps from going to zero.

2/9/2001