Digital Signal Processing Chapter 7: Parametric Spectrum Estimation

For p we insert the solution of the Wiener-Hopf-Equation and since the crosscorrelationvectorvanishesThe principle of orthogonality is:r EX = r XX − R XX [R −1XXr XX ] = 0• The prediction-error-process E(k) and the past values of the processX(k − 1),...,X(k − n) are orthogonal to each other.The ’gapped function’ for a predictor of order n is defined asg n (κ) = E{E(k) · X ∗ (k − κ)}.Since r EX = r XX − R XX [R −1XXr XX ] = 0 the gapped function has the propertyg n (κ) = 0 , 1 ≤ κ ≤ n ;Linear Prediction Page 10