Digital Signal Processing Reference
In-Depth Information
h
(
t
)
1
0.5
0
0
2
4
6
8
10
t
(a)
h
(
t
1)
1
0.8
0.6
0.4
0.2
0
0
1
2
3
4
5
6
7
8
9
10
t
(b)
x
(
t
)
0.1
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
t
(c)
y
(
t
)
1.5
1
0.5
0
Figure 3.2
Impulse responses for
the system of Example 3.1.
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
t
(d)
If the time shift between impulses approaches zero, then discrete time variable becomes
a continuous-time variable (which we denote by the symbol ), the time increment
becomes the time-differential
k¢
t
¢
dt,
and the summation becomes an integral [1], so that
q
¢:0
q
k=-
q
y(t) =
lim
v(k¢)h(t - k¢)¢=
3
v(t)h(t - t)dt.
-
q
In addition, the input signal becomes
q
q
k=-
q
x(t) =
lim
¢:0
v(k¢)d(t - k¢)¢=
3
v(t)d(t - t)dt.
(3.12)
-
q
