Digital Signal Processing Chapter 7: Parametric Spectrum Estimation

Burg Algorithm• initialization: e 0 (k) = b 0 (k) = x(k) ; k = 0,...,N − 1a 0 = 1; ˆσ 0 2 = 1 N−1∑|x(k)| 2N• 1st iteration:ˆγ 1 =2 · N−1 ∑∑N−1k=1k=1k=0x(k) · x ∗ (k − 1)(|x(k)| 2 + |x(k − 1)| 2 )e 1 (k) = x(k) − ˆγ 1 x(k − 1) ; k = 1, ...,N − 1b 1 (k) = x(k − 1) − ˆγ ∗ x(k) ; k = 1,...,N − 1[ ] [ ] ]1 1a 1,1 0=− ˆγ 1[01→ â 1,1 = −ˆγ 1Â 1 (z) = 1 − ˆγ 1 · z −1 ; ˆσ 2 1 = (1 − |ˆγ 1 | 2 ) · ˆσ 2 0Burg algorithm Page 33