Digital Communication, 3rd year, Chapter 2
Assist. Prof. Dr. Asmaa H. Majeed
CHAPTER TWO
Digitization Techniques and Baseband Transmission
2.1 Elements of Digital Communication Systems:
a. Information Source and Input Transducer:
The source of information can be analog or digital, e.g. analog: audio or video
signal, digital: like teletype signal. In digital communication the signal produced
by this source is converted into digital signal which consists of 1′s and 0′s. For this
we need a source encoder.
b. Source Encoder:
In digital communication we convert the signal from source into digital signal as
mentioned above. The point to remember is we should like to use as few binary
digits as possible to represent the signal. In such a way this efficient representation
of the source output results in little or no redundancy. This sequence of binary digits
is called information sequence.
Source Encoding or Data Compression: the process of efficiently converting the
output of whether analog or digital source into a sequence of binary digits is known
as source encoding.
c. Channel Encoder:
The information sequence is passed through the channel encoder. The purpose of
the channel encoder is to introduce, in controlled manner, some redundancy in the
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Digital Communication, 3rd year, Chapter 2
Assist. Prof. Dr. Asmaa H. Majeed
binary information sequence that can be used at the receiver to overcome the effects
of noise and interference encountered in the transmission on the signal through the
channel.
For example, take k bits of the information sequence and map that k bits to unique
n bit sequence called code word. The amount of redundancy introduced is measured
by the ratio n/k and the reciprocal of this ratio (k/n) is known as rate of code or
code rate.
d. Digital Modulator:
The binary sequence is passed to digital modulator which in turns convert the
sequence into electric signals so that we can transmit them on channel (we will see
channel later). The digital modulator maps the binary sequences into signal wave
forms, for example if we represent 1 by sin x and 0 by cos x then we will transmit
sin x for 1 and cos x for 0. (a case similar to BPSK)
e. Channel:
The communication channel is the physical medium that is used for transmitting
signals from transmitter to receiver. In wireless system, this channel consists of
atmosphere, for traditional telephony, this channel is wired, there are optical
channels, under water acoustic channels etc. We further discriminate these
channels on the basis of their property and characteristics, like AWGN channel etc.
f. Digital Demodulator:
The digital demodulator processes the channel corrupted transmitted waveform and
reduces the waveform to the sequence of numbers that represents estimates of the
transmitted data symbols.
g. Channel Decoder:
This sequence of numbers then passed through the channel decoder which attempts
to reconstruct the original information sequence from the knowledge of the code
used by the channel encoder and the redundancy contained in the received data.
Note: The average probability of a bit error at the output of the decoder is a
measure of the performance of the demodulator – decoder combination.
h. Source Decoder:
At the end, if an analog signal is desired then source decoder tries to decode the
sequence from the knowledge of the encoding algorithm. And which results in the
approximate replica of the input at the transmitter end.
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Digital Communication, 3rd year, Chapter 2
Assist. Prof. Dr. Asmaa H. Majeed
i. Output Transducer:
Finally, we get the desired signal in desired format analog or digital.
2.1.1 Advantages of digital communication
1. The effect of distortion, noise and interference is less in a digital communication
system. This is because the disturbance must be large enough to change the pulse
from one state to the other.
2. . Since the transmission is digital and the channel encoding is used, therefore the
noise does not accumulate from repeater to repeater in long distance
communications
3. Digital circuits are simpler and cheaper compared to analog circuits because of the
advances made in the IC technologies
4. Using data encryption, only permitted receivers may be allowed to detect the
transmitted data. This property is of its most importance to maintain the secrecy of
the information in military applications.
5. It has excellent processing techniques are available for digital signals such as data
compression, image processing, channel coding and equalization etc.
6. In digital communication, the speech, video and other data may be merged and
transmitted over a common channel using multiplexing. Combining digital signals
using TDM is simpler than combining analog signals using FDM.
7. Since in digital communication, channel coding is used, therefore, the errors may
be detected and corrected in the receivers thus improve the system performance by
reducing the probability of error.
2.1.2 Disadvantages of Digital Communication
1.Due to analog to digital conversion, the data rate becomes high. Therefore, more
transmission bandwidth is required for digital communication.
2. It has sampling error.
3. High power consumption
4. Digital communication needs synchronization in case of synchronous modulation
2.2 Digital Transmission of Analogue Signals:
2.2.1 Pulse Code Modulation (PCM):
Pulse-code modulation (PCM) is used to digitally represent sampled analog signals. It
is the standard form of digital audio in computers, CDs, digital telephony and other digital
audio applications. The amplitude of the analog signal is sampled at uniform intervals at
sampler then the sampled signal passes through quantizer where each sample is quantized
to its nearest value within a predetermined range of digital levels. Quantization is
representing the sampled values of the amplitude by a finite set of levels, which means
create a series of digital values out of the given analog signal)
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Digital Communication, 3rd year, Chapter 2
Assist. Prof. Dr. Asmaa H. Majeed
It is widely used in digital transmissions. Its block diagram is as shown below:
ADC: Analogue to digital converter.
DAC: Digital to Analogue converter.
• The output of the sampler f𝑠(𝑘𝑇𝑠)(𝐴𝐷𝐶).
• Assuming that 𝑓(𝑡) has 𝑓(𝑡) has fp voltage level, (ADC full scale),
(Note: the range of f(t) may extend beyond (- fp, + fp) in some cases.)
• The quantizer divide the range (-fp, +fp) into L uniformly spaced intervals. The
number of intervals is L and the separation between two adjacent representation
levels is called a quantum or step-size and is given by:
The kth sample point of f(t) is designated as f(kTS) and is assigned a value equal to the
midpoint between two adjacent levels. Define:
f(kTS) = kth sample’s value, and
fq(kTS) = kth quantized sample’s value.
• The quality of a Quantizer output depends upon the number of quantization levels
used.
• The discrete amplitudes of the quantized output are called as representation
levels or reconstruction levels.
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Digital Communication, 3rd year, Chapter 2
Assist. Prof. Dr. Asmaa H. Majeed
There are two types of Quantization:
• Uniform Quantization
• Non-uniform Quantization.
The type of quantization in which the quantization levels are uniformly spaced is
termed as a Uniform Quantization.
The type of quantization in which the quantization levels are unequal and mostly
the relation between them is logarithmic, is termed as a Non-uniform Quantization.
Since the quantization process introduces some fluctuations about the true
value, these fluctuations can be regarded as noise. As the number of quantization
levels L increases, the quantization noise decreases.
2.2.1.2 Encoding:
• ADC will then encode the quantized values according to a certain binary code.
The uniform PCM with equal step size mostly uses the signed binary code of n
bits. For 16 quantization levels, 4 bits are required. PCM can use a binary
representation of value.
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Digital Communication, 3rd year, Chapter 2
Assist. Prof. Dr. Asmaa H. Majeed
For n=4, then the ±m𝑝 values will be encoded as shown above, this is called transfer
characteristic of the PCM encoder. The relation between number of quantizing levels and
number of bits of encoder is:
𝐿 = 2𝑛
or
𝑁 = 𝑙𝑜𝑔2𝐿
Note:
If n for a given value of L is not integer number,
Then n is computed using
𝑛 = 𝑖𝑛𝑡(𝑙𝑜𝑔2𝐿) + 1,
and L is corrected using
𝐿 = 2𝑛
6
… (3)
Digital Communication, 3rd year, Chapter 2
Assist. Prof. Dr. Asmaa H. Majeed
2.2.1.3 The output SNR:
= 1.76 + 20 𝑙𝑜𝑔 𝐿 = 1.76 + 6.02 𝑛
... (6)
2.2.1.4 Bandwidth Requirement of PCM
The information rate of PCM channel is 𝑛𝑓𝑠 bits/sec, if message bandwidth is
m𝑚𝑎𝑥 and the sampling rate is f𝑠 (≥ 2f𝑚𝑎𝑥) then 𝑛𝑓𝑠 binary pulses must be transmitted
per second.
Assuming the PCM signal is a low-pass signal of bandwidth 𝐵𝑊𝑃𝐶𝑀, the
required minimum sampling rate is 2𝐵𝑊𝑃𝐶𝑀. Thus:
2𝐵𝑊𝑃𝐶𝑀 = 𝑛f𝑠
𝐵𝑊𝑃𝐶𝑀 =
𝑛
2
f𝑠 ≥ 𝑛f𝑚𝑎𝑥
𝐵𝑊𝑃𝐶𝑀𝑚𝑖𝑛𝑖𝑚𝑢𝑚 = 𝑛f𝑚𝑎𝑥
Hz
... (7)
Hz
... (8)
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Digital Communication, 3rd year, Chapter 2
Assist. Prof. Dr. Asmaa H. Majeed
Ex -1:
In a binary PCM system, the output signal-to-quantization ratio is to be hold
to aminimum of 40dB. If the message is a single tone with fm=4 kHz.
Determine:
1- The number of required levels, and the corresponding output signal-to-quantizing
noiseratio.
2- Minimum required system bandwidth.
Solution:
H.W:
Consider a single tone signal of frequency 3300 Hz. A PCM is generated with a
sampling rate of 8000 sample/sec. the required output signal-to-quantizing noiseratio
is 30dB.
1) What the minimum number of uniform quantizing levels needed? And what the
minimum number of bits per sample needed?
2) Calculate minimum system bandwidth required.
Ans: (a) 26.5 (b) 20 kHz
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Digital Communication, 3rd year, Chapter 2
Assist. Prof. Dr. Asmaa H. Majeed
Delta Modulation:
Delta Modulation is a sampling way to convert analog signal into digital with
reduced bandwidth.
Delta modulation produces information about the difference between successive
samples.
The sampler with rate (𝑓𝑠 ≫ 𝑁𝑦𝑞𝑢𝑖𝑠𝑡 𝑟𝑎𝑡𝑒) produces pulse train 𝑑q(𝑡) where
𝑑q(𝑡) represents the derivative of m(𝑡).
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Digital Communication, 3rd year, Chapter 2
Assist. Prof. Dr. Asmaa H. Majeed
The demodulator will integrate 𝑑(𝑡) to produce 𝑓𝑠(𝑘𝑇𝑠) smoothed by LPF with
𝐵𝑊 of 𝑓𝑚𝑎𝑥
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Digital Communication, 3rd year, Chapter 2
Assist. Prof. Dr. Asmaa H. Majeed
Slope overload problem:
To avoid slope overload, the step size must be kept such that:
𝑑𝑓(𝑡)
𝑑𝑡
< ∆𝑉. 𝑓𝑠
... (9)
Delta modulation transmits the derivative of signal f(t). Suppose the
message signal is the sinusoidal signal Am cos(2fmt), then
where fm < B. Slope overload means mq(t) can’t follow m(t). We then have
the condition, mAm< V. fS or mAm TS <V.
... (10)
𝑓
For speech signal, the typical frequency analysis
shows that about 70% of totalenergy lies between 600
and 1000 Hz indicating that peak energy is located that
almost at frequency of 800 Hz called response
frequency 𝑓𝑟=800 Hz, then we could assume ∆𝑉𝑚𝑖𝑛 for
speech to be:
2𝜋(800)𝐴
𝑓
... (11)
where 𝑓𝑝 in the maximum amplitude of the speech signal.
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Digital Communication, 3rd year, Chapter 2
Assist. Prof. Dr. Asmaa H. Majeed
12
Digital Communication, 3rd year, Chapter 2
Assist. Prof. Dr. Asmaa H. Majeed
Quantizing Error:
Assuming quantizing error is equally likely in the interval (-∆V, ∆V)
…………………(12)
where B is the preconstruction filter bandwidth
Output Signal to Noise Ratio:
……………………. (13)
For single tone message𝑓(𝑡) = 𝐴𝑚𝑐𝑜𝑠𝜔𝑚𝑡
𝑁
=
3𝑓𝑠2
... (14)
2
8𝜋 𝑓 𝐵
Ex -2:
A DM has sampling frequency of 64 kHz is used to encode speech signal of ±1volt:
1- Find minimum step size to avoid step overloading.
2- Find 𝑆𝑁𝑅𝑞 assuming speech has uniform probability density function (PDF)over
the interval [-1, 1] volt.
Solution:
Note:
Compare this result of 35 dB with PCM at 64000 bps (𝑓𝑠 = 8 𝑘𝐻𝑧. 𝑛 =8
𝑏𝑖𝑡𝑠⁄𝑠𝑎𝑚𝑝𝑙𝑒) then 𝑆𝑁𝑅𝑞 ≅ 48 𝑑𝐵. i.e. PCM is better than DM for the same bit rate.
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Digital Communication, 3rd year, Lect 2
Assist. Prof. Dr. Asmaa H. Majeed
H.W:
A DM system is designed to operate at 3 times the Nyquist rate for the signal with a3 kHz
bandwidth. The quantization step size is 250 mV. Determine:
a) Maximum amplitude of a 1 kHz input sinusoid for which the delta modulatordoes not
show slop over load.
b) The post filter output signal-to-quantizing noise ratio for the signal in part a.
Problems
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