 This eigenvector is orthogonal to each of the signal vectors .The frequency estimates may be determined by setting the frequencies equal to the angles of the roots of the eigenfilter

or the location of the peaks in the frequency estimation function

where formula_8 is the noise eigenvector and

The method was first discovered in 1911 by Caratheodory, then rediscovered by Vladilen Fedorovich Pisarenko in 1973 while examining the problem of estimating the frequencies of complex signals in white noise.He found that the frequencies could be derived from the eigenvector corresponding to the minimum eigenvalue of the autocorrelation matrix.