Digital Signal Processing Reference
In-Depth Information
4
3
u
(
t
)
2
tu
(
t
)
0
1
2
3
4
t
(s)
(
t
1)
u
(
t
1)
2
4
5
u
(
t
2)
(a)
f
(
t
)
4
2
0
1
2
3
4
t
(s)
2
(b)
Figure 2.25
Signal for Example 2.11.
Using these functions and (2.43), we can write the equations for
f
(
t
) (as the sum of four
terms) over each different range:
t 6 0,
f(t) = 0 + 0 - 0 - 0 = 0 ;
0 6 t 6 1,
f(t) = 3 + t - 0 - 0 = 3 + t ;
0 6 t 6 2,
f(t) = 3 + t - (t - 1) - 0 = 4 ;
2 6 t,
f(t) = 3 + t - (t - 1) - 5 =-1 .
The graph of
f
(
t
) given in Figure 2.25(b) is correct.
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