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Solved Example 18
(i)
Ω
0
=
π/
3, hence
T
= 6.
s
(
t
) is a linear combination of a constant and two rectangular pulse trains whose Fourier series
coeﬃcients are given by
sin(
kπ/
3)
kπ
and
sin(2
kπ/
3)
kπ
The corresponding duty factors are 1
/
3 and 2
/
3.
(ii)
We have, for

3
< t
≤
3,
x
(
t
) =
Z
t

3
s
(
τ
)
dτ
Thus
x
(
t
) is the area under the
s
(
·
) graph over the interval (

3
,t
]. This function
•
increases linearly (in
t
) for

3
≤
t
≤
2;
•
remains constant for

2
< t
≤ 
1;
•
decreases linearly for

1
< t
≤
1;
•
remains constant for 1
< t
≤
2;
•
increases linearly for 2
< t
≤
3.
(iii)
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 Spring '08
 staff

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