From the (12.3.6) and (12.3.9) we note that an AR(p) stationary random process satisfies the equation

Where a_p are the prediction coefficients of the linear predictor of order p and ?²_? is the minimum mean-square prediction error. If the (p + 1) x (p + 1) autocorrelation matrix ?_xx?in (12.3.9) is positive definite, prove that:

(a) The reflection coefficients |Km|

(b) The polynomial has all its roots inside the unit circle (i.e., it is minimum phase).

Transcribed Image Text:

SarYxz (m – k), k=1 Yıx (m) = (12.3.6) -EakYzx (m - k) + o, %3D k=1 Yir(-m), Yax (0) Yer (1) Yxx(-1) Yır (0) Yxr (-p) 1 Yex (-p+ 1) aj ... (12.3.9) LYax (p) Yx (p– 1) Yzx (0) ... m = 0, >a, (k)Yaz (m – k) = Yu (m) + 1< m < p. (b) Σ a,(k): A,(z) = 1+