Digital Communications Techniques in CTE Department - 3rd Stage
رهاط
ةزمحلا
.م :
ةداملا
سردم
2
01
8-
20
1
9
Dr.
Hussam
Dheaa
Kamel
Al-Mustafa University
Collage
CTE Department
2018-2019
Digital
Communications
CTE Department
-3
rd
stage
Reference:
Digital
Communications
Fundamentals
and
Applications,
2
nd
Addition,
by
FernardSklar
Digital
Communications
CTE Department -3
rd
stage
2-7
Differential Pulse Code Modulation
(DPCM):
Any
signal
does not change fast, so that the
value
from
present
sample to next sample does not differ
by large
amount. The
adjacent
samples
of
the signal carry
the
same information
with
little difference
as
shown
if
figure
2-11.
Figure
2-6 Redundant information
of
PCM
It
can
be
seen from figure
2-11
the samples
4𝑇
𝑠
, 5𝑇
𝑠
,
𝑎𝑛𝑑
6𝑇
𝑠
are
encoded to
the
same value
of
(110).
If
this redundancy
is
reduced, the overall bit rate
will
decrease and the number of bits required for one sample will also
be
reduced.
This
is
called
Differential Pulse Code Modulation
(DPCM).
DPCM
works on the principle
of
prediction. The value of the present sample
is
predicted from
the
past samples
as
shown in
figure
2-7.
2
Digital
Communications
CTE Department -3
rd
stage
Figure
2-7
DPCM
transmitter
The comparator fined
the
difference between the actual sample value
𝑥
(
𝑛𝑇
𝑠
)
and
predicted signal
𝑥̂(𝑛𝑇
𝑠
)
this is called
error
𝑒(𝑛𝑇
𝑠
)
:
𝑒
(
𝑛𝑇
𝑠
)
=
𝑥
(
𝑛𝑇
𝑠
)
−
𝑥̂(𝑛𝑇
𝑠
)
This
error
will
be
quantized and encoded
by
small number
of
bits.
Thus
number
of
bits
per
sample
are
reduced in DPCM.
The quantization error
can be
written
as:
𝑒
𝑞
(
𝑛𝑇
𝑠
)
=
𝑒
(
𝑛𝑇
𝑠
)
+
𝑞(𝑛𝑇
𝑠
)
The prediction filter input
is:
𝑥
𝑞
(
𝑛𝑇
𝑠
)
=
𝑥̂
(
𝑛𝑇
𝑠
)
+
𝑒
𝑞
(𝑛𝑇
𝑠
)
3
Digital
Communications
CTE Department -3
rd
stage
Substituting
by
𝑒
𝑞
(
𝑛𝑇
𝑠
)
yields
𝑥
𝑞
(
𝑛𝑇
𝑠
)
=
𝑥̂
(
𝑛𝑇
𝑠
)
+
𝑒
(
𝑛𝑇
𝑠
)
+
𝑞(𝑛𝑇
𝑠
)
We
have
𝑥
(
𝑛𝑇
𝑠
)
=
𝑒
(
𝑛𝑇
𝑠
)
+
𝑥̂(𝑛𝑇
𝑠
)
From the
last
equations;
𝑥
𝑞
(
𝑛𝑇
𝑠
)
=
𝑥
(
𝑛𝑇
𝑠
)
+
𝑞(𝑛𝑇
𝑠
)
To reconstruct the original signal
at
the receiver, the
decoder
first reconstructs the quantized error signal
as
shown
in
figure
2-8.
Figure
2-8 Reconstruction
of
DPCM
The quantized error signals are
summed
up
with prediction filter output
to
give the quantized version of
the
original signal.
The signal
at
the receiver differs from
actual
signal
by
quantization error
𝑞(𝑛𝑇
𝑠
)
.
4
Digital
Communications
CTE Department -3
rd
stage
2.8
Delta
Modulation
(DM):
DM transmit only
one
bit
per
sample. That is the present sample value
is
compared with the previous sample
of
approximated signal which confined
to
two levels
(−𝛿
𝑎𝑛𝑑
+
𝛿)
.
If the
difference
is
negative ‘0’
bit
is transmitted and ‘1’
bit is transmitted for positive difference,
as
shown in
2-9.
Figure 2.9
Delta
modulation
waveform
5
Digital
Communications
CTE
Department -3
rd
stage
-
DM
transmitter:
The block diagram
of
DM transmitter
is
shown in figure
2-10
Figure
2.10 DM
transmitter
The error between
sampled
value
of
𝑥(𝑡)
and last
approximated sample
is
given
by:
𝑒
(
𝑘𝑇
𝑠
)
=
𝑥
(
𝑘𝑇
𝑠
)
−
𝑥̂
(
𝑘𝑇
𝑠
)
From the
waveform
figure
𝑢
(
𝑘𝑇
𝑠
)
is the
present sample approximation
of
staircase output and
𝑢
[(
𝑘
−
1
)
𝑇
𝑠
]
=
𝑥̂
(
𝑘𝑇
𝑠
)
is
the last sample approximation
of
staircase output. Let the quantity
of
𝑏
(
𝑘𝑇
𝑠
)
be
define as,
𝑏
(
𝑘𝑇
𝑠
)
=
𝛿𝑠𝑖𝑔𝑛[𝑒
(
𝑘𝑇
𝑠
)
]
So
that
𝑏
(
𝑘𝑇
𝑠
)
=
+𝛿
𝑏
(
𝑘𝑇
𝑠
)
=
+𝛿
𝑖𝑓 𝑥
(
𝑘𝑇
𝑠
)
≥
𝑥̂
(
𝑘𝑇
𝑠
)
,
𝑏𝑖𝑛𝑎𝑟𝑦
′
1
′
𝑖𝑠
𝑡𝑟𝑎𝑛𝑠𝑚𝑖𝑡𝑡𝑒𝑑
𝑖𝑓 𝑥
(
𝑘𝑇
𝑠
)
<
𝑥̂
(
𝑘𝑇
𝑠
)
,
𝑏𝑖𝑛𝑎𝑟𝑦
′
0
′
𝑖𝑠
𝑡𝑟𝑎𝑛𝑠𝑚𝑖𝑡𝑡𝑒𝑑
6
Digital
Communications
CTE
Department -3
rd
stage
Where
𝑇
𝑠
is
sampling
interval.
The summer
of figure
2-7adds quantizer output
(∓𝛿)
with previous sample approximation. This gives present
sample
approximation:
𝑢
(
𝑘𝑇
𝑠
)
=
𝑢
(
𝑘𝑇
𝑠
−
𝑇
𝑠
)
+
[
∓𝛿
]
𝑜𝑟
=
𝑢
[(
𝑘
−
1
)
𝑇
𝑠
]
+
𝑏
(
𝑘𝑇
𝑠
)
The previous sample approximation
𝑢
[(
𝑘
−
1
)
𝑇
𝑠
]
is
restored
by
delayed one sample period
𝑇
𝑠
.
The sampled input
signal
𝑥
(
𝑘𝑇
𝑠
)
and
staircase approximated signal
𝑥̂
(
𝑘𝑇
𝑠
)
are
subtracted
to
get
error signal
𝑒
(
𝑘𝑇
𝑠
)
. Then
the
one
bit
quantizer
produces
+𝛿
or
–
𝛿
step
size
depending
on
the
sign
of
𝑒
(
𝑘𝑇
𝑠
)
,
‘1’
bit
is
transmitted
for
positive
values
and
‘0’
bit for
negative
values.
7
Digital
Communications
CTE
Department -3
rd
stage
-
DM
receiver:
At the receiver shown in figure
2-11,
the accumulator generates the staircase approximated signal and is delayed
by
one
sample
period
𝑇
𝑠
.
It
adds
+𝛿
step
to
the
previous
sample
if
the
input
bit
is
‘1’
and
subtract
−𝛿
for
‘0’
input
bit.
The low pass filter
with
cutoff frequency
of highest
frequency
in
𝑥(𝑡)
.
Figure
2.11 DM
receiver
-
Advantageous
of
DM:
i
-
DM transmit only
one
bit for one sample. Thus the signaling rate and transmission channel bandwidth is quite
small
for
DM.
ii-
The DM transceiver system
is very
much
simple.
8
Digital
Communications
CTE Department -3
rd
stage
-
Disadvantageous
of
DM:
i
-
Figure
12 distortion of
DM
Slop overload distortion: This distortion arises because
of
large dynamic
range of
input
signal. In
this case the
step
size
𝛿
is
too small for staircase signal
𝑢(𝑡)
to follow the steep segment
of
𝑥(𝑡)
.
Thus there is
large
error between
those signals. This error called slop overload distortion. To reduce this error the step size should
be
increased when
slop
of
signal
𝑥(𝑡)
is high. But since
the
step size
is
fixed
it is
called
Linear Delta Modulation
(LDM).
ii- Granular
Noise (Hunting):
It is
occur when
the
step size is too large compared to small variation in the input
signal
𝑥(𝑡)
which can
be
considered flat, while the staircase signal
is
oscillated
by
±𝛿
around it. The error in this case is
called
granular noise,
so
that step size should
be
small to reduce this error.
9
Digital
Communications
CTE Department -3
rd
stage
3.9
Adaptive DM:
The large step size is required
to
reduce slope overload while small steps
are
required
to
reduce granular noise.
Adaptive DM shown
in
figure
2-9
is
a
modification
of
LDM to overcome
these
errors.
Figure
2.13 Transmitter
of
adaptive DM
The step size increases
with
steep segment
of
input signal and reduces with small variation. This
called
Adaptive Delta Modulation (ADM).
At
the
receiver the logic for step size control
is
added is added
as
shown in figure
2-9.
10
Digital
Communications
CTE Department -3
rd
stage
Figure
2.14 ADM
receiver
If one
bit quantizer output is high ‘1’
the
step size may
be
doubled for next sample
and
vice versa
as
shown
in
figure
2-10.
Figure
2.15 Waveform
of
ADM
The previous input and the present input decided the step
size.
11
Explore Differential Pulse Code Modulation (DPCM) and Delta Modulation (DM) concepts in digital communications, as outlined in the 2018-2019 curriculum of the CTE Department. Learn about encoding, quantization, error prediction, reconstruction at the receiver end, and the one-bit per sample transmission method employed in DM. Gain insights into how these techniques reduce redundancy, decrease bit rates, and optimize signal transmission efficiency.
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Presentation Transcript
. : 2018-2019 Digital Communications CTE Department -3rdstage Reference: Digital Communications Fundamentalsand Applications, 2nd Addition, byFernardSklar Dr. Hussam Dheaa Kamel Al-Mustafa University Collage CTE Department 2018-2019
CTE Department -3rdstage Digital Communications 2-7 Differential Pulse Code Modulation (DPCM): Any signal does not change fast, so that the value from present sample to next sample does not differ by large amount. The adjacent samples of the signal carry the same information with little difference as shown if figure 2-11. Figure 2-6 Redundant information of PCM It can be seen from figure 2-11 the samples 4??, 5??, ??? 6??are encoded to the same value of (110). If this redundancy is reduced, the overall bit rate will decrease and the number of bits required for one sample will also be reduced. This is called Differential Pulse Code Modulation (DPCM). DPCM works on the principle of prediction. The value of the present sample is predicted from the past samples as shown in figure 2-7. 2
CTE Department -3rdstage Digital Communications Figure 2-7 DPCM transmitter The comparator fined the difference between the actual sample value ?(???) and predicted signal ? (???) this is called error ?(???): ?(???) = ?(???) ? (???) This error will be quantized and encoded by small number of bits. Thus number of bits per sample are reduced in DPCM. The quantization error can be written as: ??(???) = ?(???) + ?(???) The prediction filter input is: ??(???) = ? (???) + ??(???) 3
CTE Department -3rdstage Digital Communications Substituting by ??(???) yields ??(???)=? (???) + ?(???) + ?(???) We have ?(???) = ?(???) + ? (???) From the last equations; ??(???)=?(???) + ?(???) To reconstruct the original signal at the receiver, the decoder first reconstructs the quantized error signal as shown in figure 2-8. Figure 2-8 Reconstruction of DPCM The quantized error signals are summed up with prediction filter output to give the quantized version of the original signal. The signal at the receiver differs from actual signal by quantization error ?(???). 4
CTE Department -3rdstage Digital Communications 2.8 Delta Modulation (DM): DM transmit only one bit per sample. That is the present sample value is compared with the previous sample of approximated signal which confined to two levels ( ? ??? + ?). If the difference is negative 0 bit is transmitted and 1 bit is transmitted for positive difference, as shown in 2-9. Figure 2.9 Delta modulation waveform 5
CTE Department -3rdstage Digital Communications - DM transmitter: The block diagram of DM transmitter is shown in figure 2-10 Figure 2.10 DM transmitter The error between sampled value of ?(?) and last approximated sample is given by: ?(???) = ?(???) ? (???) From the waveform figure ?(???) is the present sample approximation of staircase output and ?[(? 1)??] = ? (???) is the last sample approximation of staircase output. Let the quantity of ?(???) be define as, ?(???) = ?????[?(???)] So that ?????? 1 ?? ??????????? ?(???) = +? ?? ?(???) ? (???), ?????? 0 ?? ??????????? ?(???) = +? ?? ?(???) < ? (???), 6
CTE Department -3rdstage Digital Communications Where ??is sampling interval. The summer of figure 2-7adds quantizer output ( ?) with previous sample approximation. This gives present sample approximation: ?(???) = ?(??? ??) + [ ?] ?? = ?[(? 1)??] + ?(???) The previous sample approximation ?[(? 1)??] is restored by delayed one sample period ??. The sampled input signal ?(???) and staircase approximated signal ? (???) are subtracted to get error signal ?(???). Then the one bit quantizer produces +? or ? step size depending on the sign of ?(???), 1 bit is transmitted for positive values and 0 bit for negative values. 7
CTE Department -3rdstage Digital Communications - DM receiver: At the receiver shown in figure 2-11, the accumulator generates the staircase approximated signal and is delayed by one sample period ??. It adds +? step to the previous sample if the input bit is 1 and subtract ? for 0 input bit. The low pass filter with cutoff frequency of highest frequency in ?(?). Figure 2.11 DM receiver - Advantageous ofDM: DM transmit only one bit for one sample. Thus the signaling rate and transmission channel bandwidth is quite i- small for DM. ii- The DM transceiver system is very much simple. 8
CTE Department -3rdstage Digital Communications - Disadvantageous ofDM: Figure 12 distortion of DM Slop overload distortion: This distortion arises because of large dynamic range of input signal. In this case the step size ? is too small for staircase signal ?(?) to follow the steep segment of ?(?). Thus there is large error between i- those signals. This error called slop overload distortion. To reduce this error the step size should be increased when slop of signal ?(?) is high. But since the step size is fixed it is called Linear Delta Modulation (LDM). ii- Granular Noise (Hunting): It is occur when the step size is too large compared to small variation in the input signal ?(?) which can be considered flat, while the staircase signal is oscillated by ? around it. The error in this case is called granular noise, so that step size should be small to reduce this error. 9
CTE Department -3rdstage Digital Communications 3.9 Adaptive DM: The large step size is required to reduce slope overload while small steps are required to reduce granular noise. Adaptive DM shown in figure 2-9 is a modification of LDM to overcome these errors. Figure 2.13 Transmitter of adaptive DM The step size increases with steep segment of input signal and reduces with small variation. This called Adaptive Delta Modulation (ADM). At the receiver the logic for step size control is added is added as shown in figure 2-9. 10
CTE Department -3rdstage Digital Communications Figure 2.14 ADM receiver If one bit quantizer output is high 1 the step size may be doubled for next sample and vice versa as shown in figure 2-10. Figure 2.15 Waveform ofADM The previous input and the present input decided the step size. 11
