Random Processes - Random Signals and Processes Primer with MATLAB - page 417

X1

300

200

100

0
- 1 - 0.5 0 0.5 1

X2

300

200

100

0

- 1 - 0.5 0 0.5 1

X3

300

200

100

0

- 1 - 0.5 0 0.5 1

Fig. 6.17 Histograms for random variables X 1 , X 2 , and X 3 in Exercise M.6.1

(e) The estimated PDFs shown in Fig. 6.18 indicate that they estimate the uniform
PDFs:

1 = 2 for 1 x 1

f X ðxÞ¼ : (6.242)

0 otherwise

(f) The process is stationary of the first and second order.

Exercise M.6.2 (MATLAB file exercise_M_6_2.m ). Generate a normal random
process with N ¼ 1,000 realizations where each realization has M ¼ 10,000
elements. The mean and the variance are 0 and 1, respectively.

(a) Observe the process at three different points:

M 1 ¼ 91 ; M 2 ¼ 780 ; and M 3 ¼ 900 : (6.243)

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