B. P. Lathi, Zhi Ding - Modern Digital and Analog Communication Systems-Oxford University Press (2009)

264
SAMPLING AND ANALOG-TO-DIGITAL CONVERSION
Figure 6. 10
Illustration of
practical
sampling.
g(t)
q(t)
-+J
D P i.-
1 I
DDDDD DD
T
qr/f) = I q(t - nT,)
g(t)
g(t)
Filter impulse
response hit) T P.
.:...i 14--
1/TP I.tl_
--1
Ts
I-
Averaging
filter
g(t) = I gi(kTs)8(t - kTs)
Thus we have used the camera analogy to establish that practical samplers in fact generate
sampled signal of the form
(6.20)
We will now show the relationship between the practically sampled signal g(t) and the original
low-pass analog signal g(t) in the frequency domain.
We will use Fig. 6.10 to illustrate the relationship between g(t) and g(t) for the special
case of uniform weighting. This means that
q(t) = g itl
:s 0.5Tp
itl > 0.5Tp
As shown in Fig. 6.10, g1 (t) can be equivalently obtained by first using "natural gating" to
generate the signal snapshots
g(t) = g(t) · qTs (t) (6.21)