Digital Signal Processing Reference
In-Depth Information
d.
Design the required parameters of the D/A circuit given in
Figure 4.6
to reconstruct the signal at the receiver. The reconstruction filter is
modeled as a low-pass filter (analog or digital) with cutoff frequency
as the sampling frequency utilized in the A/D process.
e.
Plot the reconstructed signal, compared with transmitted analog
signal, and plot the error signal.
f.
Repeat the entire simulation for a case of undersampling: choose a
sampling frequency smaller than the Nyquist rate (e.g., half the
Nyquist rate), and plot the transmitted signal, reconstructed signal,
and the error signal.
g.
Repeat the entire simulation for a case of oversampling: choose a
sampling frequency larger than the Nyquist rate (e.g., twice the
Nyquist rate), and plot the transmitted signal, reconstructed signal,
and the error signal.
Exercise 3: Simulation of A/D sample and hold (S & H) circuits with
nonuniform quantization
Repeat Exercise 2, steps a through c, however, with the following modifications:
•
Introduce a
µ
-law compressor
before the uniform quantizer, as shown
in
Figure 4.4
.
Similarly introduce a
µ
-law expander
after the uniform
quantizer. Assume
µ
= 255.
•
As in Exercise 2, repeat steps d through f, and plot the transmitted
signal, reconstructed signal, and the error signal for the cases of
undersampling, oversampling, and Nyquist sampling.
•
Compare the error in reconstruction, between the cases of uniform
quantization and nonuniform quantization.
Exercise 4: Simulation of Differential Pulse Code Modulation (DPCM)
system
Simulate the DPCM system, shown in
Figure 4.7
, using Simulink.
a. Transmitter
Assume an input signal:
s
(
t
)
=
10
sin
(5
t
). In this simulation, one
period or multiple periods of the signal can be processed. The input analog
signal
s
(
t
) is sampled at a rate much higher than the Nyquist rate (~25 to
50 times). This generates very closely spaced samples
s
(
nT
), which have a
very great degree of correlation between adjacent values. In traditional PCM,
the signal
s
(
nT
) is directly quantized and encoded. However in DPCM, the
following difference is quantized:
π
t
)
+
5
sin
(8
π
et
()
=
snT
(
)
−
sn
(
−
1
T
)
