Digital Signal Processing Chapter 7: Parametric Spectrum Estimation
Digital Signal Processing Chapter 7: Parametric Spectrum Estimation Digital Signal Processing Chapter 7: Parametric Spectrum Estimation
• recursive expression for the foreward-prediction errore r+1 (k) = e r (k) − γ r+1 · b r (k − 1)• We need a similar expression for the backward prediction error!apply the Levinson-Durbin equation to b r+1 (k):∑r+1b r+1 (k) = x(k − 1 − r) + a ∗ r+1,µ · x(k − 1 − r + µ)= x(k − 1 − r) +µ=1r∑a ∗ r,µ · x(k − 1 − r + µ)µ=1⇐ b r (k − 1)} {{ }r∑− γr+1 ∗ · [x(k) + a r,r + 1 − µ · x(k −1} {{ } }−{{r + µ})] ⇐ e r (k)µ=1 ν−ν} {{ }• recursive expression forthe backward prediction errorb r+1 (k) = b r (k − 1) − γ ∗ r+1 · e r (k)Lattice Structure Page 20
Lattice Structure:• (r + 1)th stage:• entire (n)th order predictor using the Lattice-Structure:Lattice Structure Page 21
- 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 and 16: ecursion for the predictive coeffic
- Page 17 and 18: Levinson-Durbin Recursion• initia
- Page 19: 7.6 The Lattice-Structure7.6.1 Anal
- 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 ←
Lattice Structure:• (r + 1)th stage:• entire (n)th order predictor using the Lattice-Structure:Lattice Structure Page 21