Digital Signal Processing Reference
In-Depth Information
F
()
A
0
(a)
F
s
()
T
s
2
s
0
2
s
s
s
(b)
H
()
T
s
s
s
2
2
(c)
Figure 6.24
The frequency spectrum of a sampled-data signal.
ideal sampling function (5.39), the frequency spectrum of the sampled-data signal is
shown in Figure 6.24(b). Since, as shown in Figure 6.24(b), the sampled signal fre-
quency spectrum is made up of an infinite number of copies of the frequency spec-
trum of the original continuous signal, modified only in magnitude, the information
contained in the original signal can, theoretically, be recovered from the sampled
signal by filtering the sample data signal, with an ideal low-pass filter. The fre-
quency response of such a filter is shown in Figure 6.24(c). The effect of this filter is
to multiply the frequency components of the input signal that fall into the filter's
pass band by the factor and to eliminate all frequency components that fall outside
the passband. The output of the filter is then a baseband continuous signal contain-
ing all the information of the original signal.
f
S
(t),
T
S
