Digital Signal Processing Chapter 7: Parametric Spectrum Estimation

N−1∑k=rN−1∂ ∑N−1∑[e r (k) · e ∗∂ˆγr(k) + b r (k) · b ∗ r(k)] = − [b r−1 (k − 1) · e ∗ r(k) + b r (k) · e ∗ r−1(k)] = 0rk=rk=r[][b r−1 (k − 1) · [e ∗ r−1(k) − ˆγ r ∗ · b ∗ r−1(k − 1)] + e ∗ r−1(k)[b r−1 (k − 1) − γr ∗ · e r−1 (k)] = 0transform to ˆγ → estimation of the PARCOR-coefficients of the rth stage(based on the state variables of the (r − 1)th stage):ˆγ r =∑N−1k=r2 · N−1 ∑k=re r−1 (k) · b ∗ r−1(k − 1)(|e r−1 (k)| 2 + |b r−1 (k − 1)| 2 )scalar product: 2|e · b|euclidean norm: ||e|| 2 + ||b|| 2 < 1|ˆγ| < 1→ the Burg Algorithm guarantees a solution with minimum phase!Burg algorithm Page 32