Digital Signal Processing Reference
In-Depth Information
From
Table 4.2
, it is seen that the recovered quantized value from the
binary bit stream can be obtained easily as follows:
(
)
Quantized value
=
Decimal value of TCC
×
Peak v
alue of sample value
x
M
4.2
Problem Solving
Exercise 1: Solve the following problems, briefly outlining the important
steps.
a.
Design a uniform 8-level quantizer designed for an input signal with
a dynamic range of ± 10 volts.
i.
Calculate the quantization error vector for an input signal of
x
(
n
) = [-4.8 -2.4 2.4 4.8].
ii.
Calculate the quantization error for the same input signal if the
quantizer is preceded by a
µ
= 255 compander (compressor/ex-
pander).
b.
A continuous signal
x
c
(
t
) has a Fourier transform
X
c
(
j
Ω
), which exists
in the range
Ω
0
, and is zero elsewhere in the frequency.
This signal is sampled with sampling period
T
= 2
Ω
0
/2
≤
Ω
≤
π
/
Ω
0
to form the
discrete-time sequence
x
(
n
) =
x
c
(
nT
).
i.
.
ii. The signal
x
(
n
) is to be transmitted across a digital channel. At
the receiver, the original signal
x
c
(
t
) must be recovered. Draw a
block diagram of the recovery system and specify its character-
istics. Assume that ideal filters are available.
iii. In terms of
Sketch the Fourier transform
X
(
e
j
ω
) for
ω
<
π
Ω
0
,
for what range of values of
T
can
x
c
(
t
) be recovered
from
x
(
n
)?
c.
A TV signal has a bandwidth of 4.5 MHz. This signal is sampled,
quantized, and binary coded to obtain a PCM signal.
i. Determine the sampling rate if the signal is to be sampled at a
rate 20% above the Nyquist rate.
ii. If the samples are quantized into 1024 levels, determine the num-
ber of binary pulses q required to encode each sample.
iii. Determine the binary pulse rate (pulses/sec or bits/sec) of the
binary coded signal.
