Digital Signal Processing Chapter 7: Parametric Spectrum Estimation

7.6.2 Synthesis Filter using the Lattice Structureanalysis filter:A n (z) = 1 + a n,1 · z −1 + a n,2 · z −2 + . .. + a n,n · z −nsynthesis filter:1A n (z)→ recursiveLattice-Predictor: step-by-step calculation from the output e n (k) to the input x(k)e r+1 (k) = e r (k) − γ r+1 · b r (k − 1)backward prediction unchanged→e r (k) = e r+1 (k) + γ r+1 · b r (k − 1)b r+1 (k) = b r (k − 1) − γ ∗ +r1 · e r (k)Lattice Structure Page 22