Digital Signal Processing Reference
In-Depth Information
h
(
t
)
1
Figure 6.47
Impulse response of a data-
0
T
t
hold circuit.
The output signal is given by
s(t) = h(t) * m
s
(t) = h(t) * m(t)
q
n=-
q
d(t - nT
s
).
The frequency spectrum of the output signal can be determined by finding the
Fourier transform of the last equation by the convolution property:
2p
M(v) *
q
1
B
R
S(v) = H(v)
v
s
d(v - nv
s
)
n=-
q
q
n=-
q
1
T
S
B
R
=
H(v)
M(v - nv
s
)
q
n=-
q
T
T
s
sinc(vT/2)
B
R
e
-jvT/2
.
=
M(v - nv
s
)
This frequency spectrum is illustrated in Figure 6.48. The reader is encouraged to
compare the frequency spectrum of the
flat-top
PAM signal with that of the
natural-
top
PAM signal shown in Figure 6.43(c).
M
( )
M
M
0
(a)
M
s
( )
3
2
s
s
2
3
0
(b)
s
s
s
s
T
T
s
S
( )
sinc (
T
/2)
s
3
2
2
s
3
s
0
(c)
s
s
s
Figure 6.48
Frequency spectra for flat-top
PAM.
