Digital Signal Processing Chapter 7: Parametric Spectrum Estimation

3. Burg Algorithm• ACF approach: biased as a result of transient responses• covariance method: solution not imperative min. phase → unstable synthesis filter• Burg algorithm avoids both disadvantagesapproach: simultaneous minimization of the forward- and backward-prediction errorbecause both must be ideally equal:E{|E r (k)| 2 } + E{|B r (k)| 2 } ! = minestimation of E{·} by means of temporal averaging; suppression of the transient responsesbefore and after:N−1∑ [|er (k)| 2 + |b r (k)| 2] != min → ∂N−1∑ [|er (k)| 2 + |b r (k)| 2] = 0 , r = 1,...,nγ r ∂ˆγ rk=rk=rLattice equations: e r (k) = e r−1 (k) − ˆγ r · b r−1 (k − 1)b r (k) = b r−1 (k − 1) − ˆγ ∗ r · e r−1 (k)using ∂γ∗∂γ = 0→ ∂e r(k)∂ˆγ r= −b r−1 (k − 1);∂e ∗ r (k)∂ˆγ r= 0;∂b r (k)∂ˆγ r= 0;∂b ∗ r (k)∂ˆγ r= −e ∗ r−1(k)Burg algorithm Page 31