Continuous and Discrete Time Signals and Systems Mandal Asif Solutions Chap11
Chapter 1: Introduction to Signals
Problem 1.1:
i) z [m ,n ,k ] is a three dimensional (3D) DT signal. The independent variables are given by m , n , and k ,
while z is the dependent variable. Digital video is an example of a 3D DT signal of the form z [ m ,n,k ]. The
intensity z of the pixels in a frame is a function of the spatial coordinates (m ,n ) and frame number k .
ii) I (x , y , z ,t ) is a four dimensional (4D) CT signal. The independent variables are given by x , y , z, and t ,
while I is the dependent variable. Atmo spheric pressure is an example of a 4D DT signal of the form
I(x , y , z , t) if recorded continuously in time and space. The atmospheric pressure I is a function of the spatial
coordinates (x , y , z ) and time t . ▌
Problem 1.2:
The CT signals can be plotted using the following MATLAB code. The CT signals are plotted in Fig.
S1.2. The students should also try plotting them by hand. ▌
-1 -0.5 0 0.5 1 1.5 2
-1
-0.5
0
0.5
1
t
x1(t)
cos(3
Ï€
t/4 +
Ï€
/8)
-1 -0.5 0 0.5 1 1.5 2
-1
-0.5
0
0.5
1
t
x
2
(t)
sin(-3
Ï€
t/8 +
Ï€
/2)
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2
2
4
6
8
10
12
14
t
x
3
(t)
5t + 3exp(-t)
-1 -0.5 0 0.5 1 1.5 2
0
0.2
0.4
0.6
0.8
1
t
x
4
(t)
(sin(3
Ï€
t/4+
Ï€
/8))
2
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3
-2
-1
0
1
2
t
x
5
(t)
cos(3
Ï€
t/4) + sin(
Ï€
t/2)
-2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3
-150
-100
-50
0
50
t
x
6
(t)
t exp(-2t)
Fig S1.2: CT signals plotted for Problem 1.2.
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