PRACTICAL MATLAB® FOR ENGINEERS PRACTICAL MATLAB

408 Practical MATLAB® Applications for Engineers

Example 4.10

Analyze by hand and using MATLAB (include pretty) the block box system diagram

shown in Figure 4.55, and obtain

a. Analytical expressions of

i. X(w)

ii. H(w)

iii. Y(w)

iv. y(t)

b. Create the script fi le syst_anal that returns the following plots:

i. X(w) versus w (numerical)

ii. H(w) versus w (numerical)

iii. Y(w) versus w (numerical)

iv. |H(w)| versus w, and verify that its spectrum consists of two impulses, located at

w = ± 3 rad/s

v. x(t) versus t, h(t) versus t, and y(t) versus t

vi. X(w) versus w (symbolic)

vii. Y(w) versus w (symbolic)

ANALYTICAL Solution

Part a: From Table 4.1, the following transforms are obtained:

ℑ

ℑ

[() ()] ( )

()

()

[() ] ( )

xt t Xw

w

w

ht e H w

w

Y

t

 




pul

sin







2

6

9

3

2



(() () ()

sin( )

()( )

() () ()

wXwHw

w

ww

yt xt ht



⋅

⋅

⊗

12

(^29)


where
yt()
x ht( ) ( )d xt() ht()


−
∞
∞
∫ (convolution of with )
MATLAB Solution
[part(b)]
% Script file: syst _ anal
echo off;
w =-2pi:0.01:2pi;
w =w+eps;
h(t) = e−^3 [t]
−π +π
x(t)
t y(t)
1
FIGURE 4.55
Block box system diagram of Example 4.10.