NEW INSIGHTS INTO THE HIGH-ORDER YULE-WALKER EQUATIONS

Presented in this correspondence are some new analytical results on the high-order Yule-Walker (HOYW) equations. First, we have found a simple singularity condition for the high-order autocorrelation matrix. This allows us to determine situations where application of the HOYW equations could be specially unsuitable. We have also shown that using the HOYW equations is equivalent to performing conventional noise compensation in the main diagonal of the low-order autocorrelation matrix. This is in connection with the possibility of matching a given set of (the first) 2M + 1 autocorrelation estimates to a noisy AR process of order M. © 1990 IEEE