Digital Signal Processing Reference
In-Depth Information
3.7 MATLAB Exercises
Exercise M.3.1
(MATLAB file
exercise_M_3_1.m
) Generate uniform and normal
random variables
X
and
Y
using the MATLAB functions
rand
and
randn
. Deter-
mine whether or not
X
and
Y
are independent observing the plot
Y
vs.
X
.
Solution
The random variable
X
is uniform in the range [0, 1] and the variable
Y
is
a Gaussian variable with
m ¼
0 and the variance 1. The plot shown in Fig.
3.29
indicates that the variables are independent.
Exercise M.3.2
(MATLAB file
exercise_M_3_2.m
)
(a) Generate uniform random variable
X
over range [
2, 2]. Random variable
Y ¼ X
2
. Determine whether or not
X
and
Y
are correlated observing the plot
Y
vs.
X
. Estimate the coefficient of correlation.
(b) Generate uniform random variable
X
over range [0, 0.5]. Random variable
Y ¼ X
2
. Determine whether or not
X
and
Y
are correlated observing the plot
Y
vs.
X
. Estimate the coefficient of correlation.
(c) Generate uniform random variable
X
over range [5, 10]. Random variable
Y ¼ X
2
. Determine whether or not
X
and
Y
are correlated observing the plot
Y
vs.
X
. Estimate the coefficient of correlation.
(d) Generate uniform random variable
X
over range [
10,
5]. Random variable
Y ¼ X
2
. Determine whether or not
X
and
Y
are correlated observing the plot
Y
vs.
X
. Estimate the coefficient of correlation.
Solution
(a) The plot
in Fig.
3.30a
indicates that
the variables are dependent but
uncorrelated.
4
3
2
1
0
-1
-2
-3
-4
0
0.2
0.4
0.6
0.8
1
X
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