Frequency-domain bias decomposition for LMS and LS adaptive filters

Frequency-domain analysis is presented for the bias distribution in a reduced-order modeling experiment using either LMS (least mean square) or LS (least square)-type algorithms. The authors develop and prove a new theorem that allows the exact decomposition of the bias into a sum of components related to the eigenfilters of the input autocorrelation matrix. The new bias decomposition theorem allows accurate prediction of the bias as a function of the input power spectral density beyond results previously obtained for the case of large filter order. Furthermore, for low-order adaptive filters, eigenvalues and eigenfilters are shown to be fundamental tools for extracting the essential features of the filter input spectrum.<>