Random Processes - Random Signals and Processes Primer with MATLAB - page 420

Exercise M.6.3 (MATLAB file exercise_M_6_3.m ). Generate a random process
X ( t ) with N ¼ 2,000 realizations where each realization has M ¼ 2,000 elements.
Observe the process at three different points:

M 1 ¼ 100 ; M 2 ¼ 450 ; and M 3 ¼ 900 : (6.246)

(a) Denote the corresponding random variables as X 1 , X 2 , and X 3 and plot their
plots.
(b) Estimate the mean values of variables X 1 , X 2 , and X 3 .
(c) Estimate the variances of variables X 1 , X 2 , and X 3 .
(d) Estimate the PDFs of variables X 1 , X 2 , and X 3 .
(e) Is this process stationary?

Solution The process is generated using the MATLAB file: X_E_6_3.m

(a) The random variables are shown in Fig. 6.21 for the first n ¼ 1,000 samples.
(b) The mean values are estimated using the MATLAB file mean.m. The following
mean values are obtained:

m 1 ¼ 100 : 0067 m 2 ¼ 450 : 0204 m 3 ¼ 900 : 0040 : (6.247)

; ;

All estimated mean values are different.
(c) The variances are estimated using the MATLAB file var.m . The following
values for the variances are obtained:

s 1 ¼ 0 s 2 ¼ 0 s 3 ¼ 0

: 0331 : 3245 : 0321 : (6.248)

; ;

100.5

100

99.5

0 200 400 600 800 1000

n

451

450

449

0 200 400 600 800 1000

n

900.5

900

899.5

0 200 400 600 800 1000

n

Fig. 6.21 Random variables X 1 , X 2 , and X 3 in Exercise M.6.3