Digital Signal Processing Reference
In-Depth Information
Electrical
network
h
(
t
)
x
(
t
)
y
(
t
)
(a)
1
RC
e
t
/
RC
u
(
t
)
h
(
t
)
1
RC
1
RC
0
t
(b)
x
(
t
)
Vu
(t)
V
t
(c)
y
(
t
)
V
1
RC
0
t
(d)
Figure 5.29
Illustrations for Example 5.17.
From Table 5.2, the Fourier transforms of
h(t)
and
x(t)
are found to be
1
1 + jvRC
(1/RC)e
-t/RC
u(t)
H(v) = f
5
6
=
and
1
jv
+ pd(v)
X(v) = f
5
Vu(t)
6
= V
B
R
.
Therefore,
pd(v)
1 + jvRC
1
1 + jvRC
1
jv
+ pd(v)
1
jv(1 + jvRC)
+
B
RB
R
B
R
Y(v) = V
= V
.
