Digital Signal Processing Reference
In-Depth Information
a
b
4
0.25
3.5
0.2
3
2.5
0.15
2
0.1
1.5
1
0.05
0.5
0
0
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
0
0.1
0.2
0.3
0.4
0.5
X
X1
c
d
100
100
90
90
80
80
70
70
60
60
50
50
40
40
30
30
20
20
5
6
7
8
9
10
-10
-9
-8
-7
-6
-5
X2
X3
Fig. 3.30
Uncorrelated and correlated variables
The coefficient of correlation is estimated using the MATLAB file
corrcoef.m.
The estimated coefficient of correlation is
0.0144.
(b) The variables are correlated as shown in Fig.
3.30b
.
The estimated coefficient of correlation is 0.9679.
(c) The variables are correlated as shown in Fig.
3.30c
.
The estimated coefficient of correlation is 0.9964.
(d) The variables are negative correlated as shown in Fig.
3.30d
.
The estimated coefficient of correlation is
0.9964.
Exercise M.3.3
(MATLAB file
exercise_M_3_3.m
) Generate uniform random
variables
X
1
and
X
2
using
rand.m
.
(a) Determine whether or not
X
1
and
X
2
are independent observing the plot
X
2
vs.
X
1
.
(b) Plot the sum
Y ¼ X
1
þ X
2
:
(3.331)
and estimate the PDF of the sum.
(c) Find the mathematical PDF of
Y
as the convolution of the corresponding PDFs,
f
Y
ðyÞ¼f
X
1
ðx
1
Þf
X
2
ðx
2
Þ:
(3.332)
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