Digital Signal Processing Chapter 7: Parametric Spectrum Estimation

7.2 Markov Process as an Example for a 1st Order AR-Modelx(k) = q(k) − a 1 · x(k − 1) ⇒ H(z) =11+a 1 z −1a 1 = −0.5a 1 = +0.5r xx (κ) →1.510.50-0.5a) Beispiel 1: AKF-1-10 -5 0 5 10κ →S xx (e jΩ ) →b) Beispiel 1: LDS43.532.521.510.50-1 -0.5 0 0.5 1Ω/π →e) Beispiel 3: komplexe AKFa 1 = −0.5e jπ/2 o ˆ= Re{r xx }10.5x ˆ= Im{r xx }0-0.5-1-10 -5 0 5 10r xx (κ) →1.5κ →S xx (e jΩ ) →4r xx (κ) →1.510.50-0.5c) Beispiel 2: AKF-1-10 -5 0 5 10κ →f) Beispiel 3: unsymm. LDS3.532.521.510.50-1 -0.5 0 0.5 1Ω/π →S xx (e jΩ ) →d) Beispiel 2: LDS43.532.521.510.50-1 -0.5 0 0.5 1Ω/π →• limited by model order!• for a 1 ∈ IR ⇒ onlylow- or highpassprocesses producibleMarkov Process Page 3