Linear Prediction and the Lattice Structure

Abstract

Chapter 2 presented a derivation of the normal equations from the standpoint of minimizing the mean square prediction error. However, in that chapter no specific method was presented for solving the normal equation (2.3.5)

$$R_{NN} W_N^ * = p_N $$

((2.3.5))

for the desired linear prediction filter w ^* _N . The only topic of interest then was the nonsingularity of the autocorrelation matrix R _NN . If R _NN is nonsingular, then the inverse R^-1 _NN is nonsingular, then the inverse R ^-1 _NN exists, and the theoretical solution is given by

$$ w_{N}^{*} = R_{{NNPN}}^{{ - 1}}. $$

((2.3.6))