Digital Signal Processing Chapter 7: Parametric Spectrum Estimation

Br B q (0) = σ2 ∑q+1rγ rν=1a q,q+1−ν[ 1σ 2 r−1g r−1 (ν − 1) − 1 σ 2 r]g r (ν − 1)applying: g r (ν − 1) ={0, ν = 2, ...,r + 1σ 2 r, ν = 1; g r−1 (ν − 1) ={0, ν = 2,...,rσ 2 r−1, ν = 1q < rq = r∑≤rν=1∑r+1ν=1a q,q+1−ν[ 1σ 2 r−1a q,q+1−ν[ 1σ 2 r−1g r−1 (ν−1)− 1 σ 2 rg r−1 (ν−1)− 1 σ 2 r]g r (ν−1)]g r (ν−1)[ ] σ2= a r−1q,qσr−12 − σ2 rσr2= g r−1(r)σ 2 r−1= 0= g r−1(r)g r−1 (0) = γ rr Br B q(0) = E{B r (k)·B ∗ q(k)} ={ σ2 rγ r · γ r = σr2 for r = q0 for r ≠ qLattice Structure Page 25