Chapter 2
Sampling & Pulse Code Modulation
1
Sampling
•
Suppose we wish to sample an analog signal
v
(
t
)
at a
sam-
pling rate
f
0
given by
1
/T
0
. That is, we wish to take snap-
shots of
v
(
t
)
every
T
0
seconds.
This may be achieved by multiplying
v
(
t
)
with the rectangular
pulse train
ψ
(
t
) =
∞
n
=
−∞
p
(
t
−
nT
0
)
where
p
(
t
) =
1 : 0
≤
t < T
0
/
2
0 :
otherwise.
The resulting signal
v
s
(
t
) =
v
(
t
)
ψ
(
t
) =
v
(
t
)
∞
n
=
−∞
p
(
t
−
nT
0
)
consists of pulses (or snapshots of
v
(
t
)
) of duration
T
0
/
2
and
amplitudes corresponding to
v
(
t
)
at the sampling instances.
Note that the duration of the pulses is given by the duration
of
p
(
t
)
.
1

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