Digital Signal Processing Reference
In-Depth Information
Reconstructed
Output
s
r
(t)
Sampled
Input
s(nT)
Quantizer
Encoder
Channel
Decoder
+
+
_
Delay
T
+
Delay
T
TRANSMITTER
CHANNEL
RECEIVER
FIGURE 4.7
Block diagram of Differential PCM transmitter and receiver.
The difference signal is quantized as follows:
ê
(
t
)
=
δ
if
e
(
t
)
>
0
ê
(
t
)
= -
δ
if
e
(
t
)
<
0
ê
(
t
)
=
0if
e
(
t
)
=
0
or compactly,
ê
(
t
)
= sgn
[
e
(
t
)], where sgn is the signum function and the step
size should be selected to satisfy the condition
:
δ
<<
s
(
t
)
max
. Thus the final
signal
ê
(
t
) consists of pulses with amplitude
±
Plot the quantized signal
ê
(
t
) for at least one period of the original signal
s
(
t
).
δ.
b. Channel
Model the channel as a system gain of 1.0.
c. Receiver
The receiver consists of an integrator, which sums the pulses
e
(
n
), and gen-
erates the reconstructed signal
s
r
(
t
).
i.
Plot the input and reconstructed signals on the same graph, and
determine the mean-squared error between them.
ii.
Plot the error signal between the input and the reconstructed signals.
4.4
Hardware Laboratory
Exercise 5: Design and construction of a simple Sample and Hold (S & H)
circuit
4
rapidly changing voltages that arise from the input signal
x
c
(
t
). The op-amp
acts as a high input-impedance voltage follower.
The S & H circuit using an FET switch, shown in
Figure 4.8
,
can sample
