Digital Signal Processing Chapter 7: Parametric Spectrum Estimation

7.6.3 Minimal Phase – Stability• synthesis filter (receiver/decoder) is recursive → demand of stability• analysis filter (transmitter/coder) must be minimum phase• necessary and sufficient condition for minimum phase: |γ r | < 1(verification using the Schur-Cohn Test, see Proakis, Manolakis: Digital Signal Processing, Maximillian Pub. 1992)It hast been shown that the solution of the Wiener-Hopf (Yule-Walker) equation usingthe exact ACF *) has generally minimum phase.properties of a predictor using the lattice-structure:• The transfer function from the input to the upper output (foreward predictionerror) A(z) has minimum phase.• The transfer function form the input to the lower output (backward predictionerror) z −n A(1/z ∗ ) has maximum phase.*) if the ACF is estimated minimum phase cannot be guaranteed!Lattice Structure Page 23