On the fast computation of cross-covariance and auto-covariance sequences
C.J. Demeure, C.T. Mullis · 2003
A simple linear procedure is given to compute the cross-variance sequence associated with the outputs of two rational digital filters that are driven by the same white noise sequence. Such a computation appears in the study of digital filters, Wiener filters, noise-variance estimation, low order approximations, and in the study of multichannel systems. Fast algorithms based on Euclid's algorithm are introduced to solve the linear systems of equations involved. The special case of the autocovariance computation is reviewed. Alternate polynomial representations are shown to share the same properties as the matrix equations.>