From the (12.3.6) and (12.3.9) we note that an AR(p) stationary random process satisfies the equation Where
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From the (12.3.6) and (12.3.9) we note that an AR(p) stationary random process satisfies the equation
Where ap 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+
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Proof is by contradiction a Assume the km 1 Since Em 1 k ...View the full answer
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Related Book For
Digital Signal Processing
ISBN: ?978-0133737622
3rd Edition
Authors: Jonh G. Proakis, Dimitris G.Manolakis
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