Experiment 1: Using the autocorrelation coefficients from Table 1, compute Gp2 for p = 1.2..... 20 through the Levinson-Durbin algorithm. Plot G₁² as a function of p. What do you observe?
Experiment 2 (Computation of AR spectrum from autocorrelation coefficients): Using the autocorrelation coefficients from Table 1, compute AR power spectrum for p=4, 6, 8 and 10. Plot them. What do you observe as you increase p? You can use Levinson-Durbin algorithm developed in earlier experiment to compute AR parameters.
Experiment 3 (AR spectral estimation using Yule-Walker method): Your lab demonstrator will provide you a finite data record {r(n), n = 0, 1,..., N-1} of N=240 samples of speech signal. Speech signal is digitized at 8 kHz sampling frequency. Compute AR spectrum for p=4, 6, 8 and 10 using the Yule-Walker method. Plot them. On each plot, also plot periodogram spectrum. What do you observe?
Experiment 4 (AR spectral estimation using covariance method): Repeat Experiment 3 for the covariance method of linear prediction.
Experiment 5 (AR spectral estimation using forward-backward linear prediction method): Repeat Experiment 3 for the forward-backward method of linear prediction. (Optional) Experiment 6 (AR spectral estimation using Burg method of linear predic- tion): Repeat Experiment 3 for the Burg method of linear prediction.
Table 1: Autocorrelation coefficients of the process x(n).
Index Autocorrelation coefficient
0 7687.5127
1 -549.9650
2 -2026.8005
3 2749.4333
4 1879.6405
5 1204.4525
6 -1226.9852
7 -6.9493
8 3313.3511
9 888.9630
10 -2409.3477
11 1484.6106
12 2550.4963
13 -1353.7297
14 197.0582
15 444.5435
16 241.0369
17 1030.9800
18 -1392.1342
19 13.7750
20 1090.0167