Digital Signal Processing Chapter 7: Parametric Spectrum Estimation

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comparison of the coefficients left and right of ∗) (left side: separation of 2 terms):∑r+1ν=0r∑a r+1,ν r XX (κ − ν) = r XX (κ) + a r+1,r+1 r XX (κ − (r + 1)) + a r+1,ν r XX (κ − ν)= r XX (κ)−γ r+1 r XX (κ − (r + 1)) +ν=1r∑[a r,ν − γ r+1 · a ∗ r,r+1−ν] · r XX (κ − ν)ν=1a r+1,ν = a r,ν − γ r+1 · a ∗ r,r+1−ν(for ν = 1 ,...,r)a r+1,r+1 = −γ r+1vectorized expression:⎡ ⎤ ⎡1 1a r+1,1a r+1,2.=.⎢⎣ a r+1,r⎥ ⎢⎦ ⎣a r+1,r+1 0a r,1a r,2a r,r⎤⎥⎦⎡− γ r+1 ⎢⎣0a ∗ r,ra ∗ r,r−1.a ∗ r,11⎤⎥⎦Levinson-Durbin Recursion Page 16
Levinson-Durbin Recursion• initialization (r = 0): a 0,0 = 1σ0 2 = r XX (0)• 1st iteration (r = 1) :γ 1 = r XX (1)/r XX (0)[ ] [ ] [ ]1 1 0= − γ 1a 11 0 1→ a 11 = −γ 1σ 2 1 = [1 − |γ 1 | 2 ] · σ 2 0 .• rth iteration (r = 2, ...,n) :γ r =r−1 ∑ν=0a r−1,ν r XX (r − ν)σ 2 r−1Levinson-Durbin Recursion Page 17
Page 1 and 2: transparencies - lecture: Digital S
Page 3 and 4: 7.2 Markov Process as an Example fo
Page 5 and 6: Past values x(k − 1), · · · ,x
Page 7 and 8: Conjugating all elements yields inI
Page 9 and 10: 7.4.2 The Principle of Orthogonalit
Page 11 and 12: 7.4 Linear Prediction (Overview)app
Page 13 and 14: 7.5 Levinson-Durbin Recursion∑A r
Page 15: ecursion for the predictive coeffic
Page 19 and 20: 7.6 The Lattice-Structure7.6.1 Anal
Page 21 and 22: Lattice Structure:• (r + 1)th sta
Page 23 and 24: 7.6.3 Minimal Phase - Stability•
Page 25 and 26: Br B q (0) = σ2 ∑q+1rγ rν=1a q
Page 30 and 31: 2. Covariance Method• disadvantag
Page 32 and 33: N−1∑k=rN−1∂ ∑N−1∑[e r
Page 34 and 35: • rth iteration:⎡⎢⎣1â r,1
Page 36 and 37: 7.8 Examples for Parametric Spectru
Page 38 and 39: • application for speech codingso
Page 40 and 41: example 3:vowel ”a”, german mal
Page 42: example 5:comparison parametric ←

Digital Signal Processing Chapter 7: Parametric Spectrum Estimation

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