Chapter 5 : Digital Communication Systems
Chapter contents
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5.1 Overview of Digital Communication Systems
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5.2 Digital Transmission – Pulse Modulation
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PCM operation, sampling, quantization
5.4 Information Capacity, Bits, Bit Rate, Baud, M-ary encoding
5.5 Digital Modulation
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Pulse modulation method PWM, PAM, PPM, PCM
5.3 Pulse Code Modulation
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Transmission schemes, communication link, Adv vs. Disadv
ASK, FSK. PSK
5.6 Applications of Digital Communication Systems
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5.1 Overview
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Digital communications is the transfer of information (voice, data etc) in
digital form.
Basic diagram of digital/data communications
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5.1 Overview
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If the information is in the analog form, it is converted to a digital form for
transmission. At the receiver, it is re-converted to its analog form.
In some case, data needs to be changed to analog form to suit the transmission line
(ex : internet/point-to-point data communication through the public switching
telephone network) – the use of modem
Modem (from modulator-demodulator) is a device that modulates an analog
carrier signal to encode digital information, and also demodulates such a carrier
signal to decode the transmitted information
Function of modem at transmitter – converts digital data to analog signal that are
compatible to the transmission line characteristics.
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5.1 Overview
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Transmission schemes for analog and digital signals
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5.1.1 Communication links in digital transmission
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Basic protocol of transmission : simplex, half-duplex, full duplex
Classification of communication link
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Synchronous Channel – the transmitted and received data clocks are locked
together. This requires that the data contains clocking information (self-clocking
data).
Asynchronous Channel – the clocks on the transmitter and the receiver are not
locked together. The data do not contain clocking information and typically
contains start and stop bits to lock the systems together temporarily.
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5.1.2 Digital vs Analog Communication Systems
Advantages
 Noise immunity
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Signal processing capability
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Digital signals are less susceptible than analog signals to interference caused by
noise
Simple determination is made whether the pulse is above or below the prescribed
reference level
Digital signals are better suited than analog signals for processing and combining
for multiplexing purpose.
Much simpler to store digital signals compare to analog signals
Transmission rate of digital signals can be easily changed to suit different
environments and to interface with different types of equipment.
Can also be sample instead of continuously monitored
A regenerative repeater along the transmission path prevent accumulation of
noise along the path. It can detect a distorted digital signal and transmit a new
clean signal
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5.1.2 Digital vs Analog Communication Systems
Advantages
 Simpler to measure and evaluate than analog signals
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Easier to compare the error performance of one digital system to another digital
system.
Transmission error can be detected and corrected more easily and more
accurately (error bit check). This gives very low error rate and high fidelity.
Digital hardware implementation is flexible and permits the use of
microprocessors and digital switching.
Ability to carry a combination of traffics, e.g. telephone signals, data, coded
video and teletext, if the medium has enough capacity.
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5.1.2 Digital vs Analog Communication Systems
Disadvantages
 Bandwidth
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Circuit complexity
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Transmission of digitally encoded analog signals requires significantly more
bandwidth than simply transmitting the original analog signal.
Analog signals must be converted to digital pulses prior to transmission and
converted back to their original analog form at the receiver – additional
encoding/decoding circuitry.
Requires precise time synchronization between the clocks in the transmitter
and receiver.
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5.2 Digital Transmission – Pulse Modulation
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Mostly used modulation technique in digital transmission
Consists of several processes:
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Sampling analog information signals
Converting those samples into discrete pulse
Transporting the pulses from a source to a destination over a physical transmission
medium
Predominant method of pulse modulation – pulse width modulation (PWM),
pulse position modulation (PPM), pulse amplitude modulation (PAM), pulse
code modulation (PCM)
Pulse Width Modulation (PWM)
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The width (active portion of the duty cycle) of a constant amplitude pulse is varied
proportional to the amplitude to the amplitude of the analog signal at the time the
signal is sampled.
Maximum analog signal amplitude produces the widest pulse, and the minimum
analog signal amplitude produces the narrowest pulse.
All pulses have the same amplitude.
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5.2 Digital Transmission – Pulse Modulation
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Pulse Position Modulation (PPM)
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The position of a constant-width pulse within a prescribed time slot is varied
according to the amplitude of the sample of the analog signal.
The higher the amplitude of the sample, the farther to the right the pulse is
positioned within the prescribed time slot.
The highest amplitude sample produces a pulse to the far right, and the lowest
amplitude sample produces a pulse to the far left.
Pulse Amplitude Modulation (PAM)
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the amplitude of a constant-width constant-position pulse is varied according to the
amplitude of the sample of the analog signal.
The amplitude of a pulse coincides with the amplitude of the analog signal
PAM wave resemble the original analog signal more than the waveforms for PWM
or PPM.
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5.2 Digital Transmission – Pulse Modulation
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Pulse Code Modulation (PCM)
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
Analog signal is sampled and then converted to a serial n-bit binary code for
transmission.
Each code has the same number of bits and requires the same length of time for
transmission.
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Figure : Comparing between Pulse modulations:
(a) analog signal; (b) sample pulse; (c) PWM; (d)
PPM; (e) PAM; (f) PCM
5.2 Digital Transmission – Pulse Modulation
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5.3 Pulse Code Modulation (PCM)

Preferred method of communication within the public switched telephone
network (PSTN).
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with PCM it is easy to combine digitized voice and digital data into a single, highspeed digital signal and propagate it over either metallic or optical fiber cables.
Refer to figure of simplified block diagram of PCM system.
At the transmitter
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The bandpass filter limits the frequency of the analog input signal to the standard
voice-band frequency range of 300 Hz ~ 3000 Hz.
The sample-and-hold circuit periodically samples the analog input signal and
converts those samples to a multilevel PAM signal.
The analog-to-digital converter (ADC) converts the PAM samples to parallel PCM
codes, which are converted to serial binary data in the parallel-to-serial converter.
The output to the transmission line is a serial digital pulses.
The transmission line repeaters are placed at prescribed distances to regenerate the
digital pulses.
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5.3 Pulse Code Modulation (PCM)
At the receiver
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The serial-to parallel converter converts serial pulses received from the
transmission line to parallel PCM codes.
The digital-to-analog converter (DAC) converts the parallel PCM codes to
multilevel PAM signals.
The hold circuit is basically a low pass filter that converts the PAM signals back to
its original analog form
An integrated circuit that performs the PCM encoding and decoding is called a
codec (coder/decoder)
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5.3 Pulse Code Modulation (PCM)
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Block diagram of a single channel, simplex PCM transmission channel :
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5.3.1 PCM Sampling
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The function of the sampling circuit :
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to periodically sampled the continually changing analog input and convert those
samples to a series of constant-amplitude pulse that easily be converted to binary
PCM code
2 basic techniques for the sampling function :
1) Natural sampling
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Tops of the sample pulses retain their natural shape during the sample interval.
Difficult for an ADC to convert the sample to a PCM code due to un-constant
voltage.
2) Flat-top sampling

Most common method, used in the sample-and-hold circuit – periodically sample
the continually changing analog input voltage and converts those samples to a
series of constant-amplitude PAM voltage levels.
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5.3.1 PCM Sampling
Natural sampling
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Flat-top sampling
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5.3.2 Sampling Rate
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Sampling is a process of taking samples of information signal at a rate based
on the Nyquist Sampling Theorem.
Nyquist Sampling Theorem – the original information signal can be
reconstructed at the receiver with minimal distortion if the sampling rate in
the pulse modulation signal is equal or greater than twice the maximum
information signal frequency.
fs  2 fm (max)
where fs = minimum Nyquist sampling rate/frequency
fm(max) = maximum information signal frequency
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5.3.2 Sampling Rate

If fs is less than 2 times fm(max) an impairment called as alias or fold-over
distortion occurs.
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5.3.3 Quantization
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Quantization – process of assigning the analog signal samples to a predetermined discrete level.
The number of quantization levels, L depends on the number of bits per
sample, n where
n
L2

where L = number of quantization level
n = number of bits in binary to represent the value of the samples
The quantization levels are separated by a value of ΔV that can be defined as
V max  V min
V 
L 1

ΔV is the resolution or step size of the quantization level.
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5.3.3 Quantization
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Ex :
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5.3.3 Quantization
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Ex (continue) :
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5.3.3 Quantization
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Quantization error/Quantization noise – error that is produced during the
quantization process due to the difference between the original signal and
quantized signal magnitudes.
Since a sample value is approximated by the midpoint of the sub-internal of
height ΔV, in which the sample value falls, the maximum quantization error is
± ΔV/2.
Thus, the quantization error lies in the range (- ΔV/2, + ΔV/2).
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5.3.4 Dynamic Range
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the number of PCM bits transmitted per sample determined by determined by
several factors – maximum allowable input amplitude, resolution and dynamic
range.
Dynamic range (DR) – the ratio of the largest possible magnitude to the
smallest possible magnitude (other than 0 V) that can be decoded by the DAC
converter in the receiver.
mathematically expressed
V max
V max
DR 

V min resolution
where DR = dynamic range (unitless ratio)
Vmin = the quantum value (resolution)
Vmax = the maximum voltage magnitude that can be discerned by the
DAC’s in the receiver
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5.3.4 Dynamic Range

Dynamic range is generally expressed as a dB value
V max
DR  20 log
V min
where DR = dynamic range (unitless ratio)
Vmin = the quantum value (resolution)
Vmax = the maximum voltage magnitude that can be discerned by the
DAC’s in the receiver

the number of bits used for a PCM code depends on the dynamic range. The
relationship between dynamic range and the number of bits in a PCM code is
2n 1  DR
and for a minimum number of bits 2n – 1 = DR
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5.3.4 Dynamic Range

Ex : For a PCM system with the following parameters, determine (a)
minimum sample rate (b) minimum number of bits used in the PCM code (c)
resolution (d) quantization error
Maximum analog input frequency = 4 kHz
Maximum decode voltage at the receiver = ±2.55V
Minimum dynamic range = 46 dB
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5.3.4 Coding Efficiency
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Coding efficiency – ratio of the minimum number of bits required to achieve a
certain dynamic range to the actual number of PCM bits used.
min_ number _ of _ bits
coding _ efficiency 
100
actual _ number _ of _ bits

number of bits should include the sign bit !
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5.3.5 Signal-to-Quantization Noise Ratio
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Generally, the quantization error or distortion caused by digitizing an analog
sample expressed as an average signal power-to-average noise power ratio.
For a linear PCM codes (all quantization intervals have equal magnitudes), the
signal power-to-quantizing noise power ratio is determined by
v2 / R
SQR (dB)  10 log 2
q / 12 / R



where R = resistance (ohms)
v = rms signal voltage (volts)
q = quantization intervals (volts)
v2/R = average signal power (watts)
(q2/12)/R = average quantization noise power (watts)
if R is assume to be equal
v2
v
SQR (dB)  10 log 2
 20 log
q / 12
q

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5.3.6 Companding
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Companding is the process of compressing and expanding to improve the
dynamic range of a communication system.
a companding process is done by firstly compressing signal samples and then
using a uniform quantization. The input-output characteristics of the
compressor are shown below.
the compressor maps input signal
increments Δx into larger increments
Δy for a large input signals.
2 compression laws recognized by
CCITT :
μLaw : North America & Japan
A-Law : Europe & others
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5.3.7 Line speed / Transmission bit rate
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Line speed is the transmission bit rate at which serial PCM bits are clocked
out of the PCM encoder onto the transmission line.
Line speed/transmission bit rate can be expressed as
Line speed = samples/seconds x bits/sample
line speed = transmission rate (bps)
samples/second = sampling rate fs
bits/sample = no of bits in the compressed PCM code
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5.4 Parameters in Digital Modulation
5.4.1 Information Capacity
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Information capacity – a measure of how much information can be propagated
through a communication systems and is a function of bandwidth and
transmission time.
represents the number of independent symbols that can be carried through a
system in a given unit of time
the most basic digital symbol used to represent information is the binary digit, or
bit.
Bit rate – the number of bits transmission during one second and is expressed in
bits per second (bps).
Bit rate is used to express the information capacity of a system.
mathematically expressed, information capacity I
IB  t

refer to slides of chapter 1 !
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5.4.2 M-ary encoding
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in an M-ary encoding, M represents a digit that corresponds to the number of
conditions, levels, or combination possible for a given number of binary
variables.
the number of bits necessary to produce a given number of conditions is
expressed mathematically as
N  log 2 M

where N = number of bits necessary
M = number of conditions, levels, or combination possible with N bits
from above, the number of conditions possible with N bits can be expressed as
2N  M

Ex : with 1 bit → 21 = 2 conditions
2 bits → 22 = 4 conditions
3 bits → 23 = 8 conditions
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5.4.3 Baud and Minimum Bandwidth
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Bit rate – refers to the rate of change of digital information, which is usually
binary.
Baud – refers to the rate of change of a signal on a transmission medium after
encoding and modulation have occurred.
Baud can be expressed as
1
B
ts
where Baud = symbol rate (baud per second)
ts = time of one signaling element (seconds)
signaling element = symbol

for a given bandwidth B, the highest theoretical bit rate is 2B. Using the
multilevel signaling, the Nyquist formulation for channel capacity is
fb  2 B log 2 M
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5.4.3 Baud and Minimum Bandwidth

where fb = channel capacity (bps)
B = minimum Nyquist bandwidth (Hertz)
M = number of discrete signal or voltage levels
above formula can be rearranged to solve for the minimum bandwidth necessary
to pass M-ary digitally modulated carrier as follow

fb
B
 log 2 M






since N = log2M above formula can be expressed as
 fb 
B

N
where N is the number of bits encoded into each signaling element (symbol).
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5.5 Digital Modulation
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Given an information signal which is digital and a carrier signal represented
as follow :

A digitally modulated signal is produced as follow :
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If the amplitude (V) of the carrier is varied proportional to the information signal,
ASK (Amplitude Shift Keying) is produced.
If the frequency (f) of the carrier is varied proportional to the information signal,
FSK (Frequency Shift Keying) is produced.
If the phase (θ) of the carrier is varied proportional to the information signal, PSK
(Phase Shift Keying) is produced.
If both amplitude and phase are varied proportional to the information signal,
QAM (Quadrature Amplitude Modulation) is produced.
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5.5.1 Amplitude Shift Keying
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digital information signal directly modulates the amplitude of the analog carrier.
mathematically, the modulated carrier signal is expressed as follow :
A

vask (t )  1  vm (t ) cos(ct ) 
2

(5.5-1)
where vask(t) = amplitude-shift keying wave
vm(t) = digital information (modulating) signal (volts)
A/2 = unmodulated carrier amplitude (volts)
ωc = analog carrier radian frequency

in the above (5.5-1), modulating signal vm(t) is a normalized binary waveform,
where +1V = logic 1 and -1V = logic 0.
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5.5.1 Amplitude Shift Keying

for a logic 1 input, vm(t) = +1V, and (5.5-1) reduces to
A

vask (t )  1  1 cos(ct )   A cos(ct )
2


and for logic 0 input, vm(t) = -1V, and (5.5-1) reduces to
A

vask (t )  1  1 cos(ct )   0
2


so the modulated wave vask(t), is either Acos(ωct) or 0, means the carrier is either
“on” or “off”. ASK is sometimes referred as on-off keying (OOK).
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5.5.1 Amplitude Shift Keying
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5.5.2 Frequency Shift Keying

general expression for FSK :
vfsk(t )  Vc cos2  fc  vm(t )f t 
(5.5-2)
where vfsk(t) = binary FSK waveform
Vc = peak analog carrier amplitude
fc = analog carrier center frequency (Hz)
vm(t) = binary input (modulating signal)
Δf = peak change (shift) in the analog carrier frequency



from (5.5-2), the peak shift in the carrier frequency (Δf) is proportional to the
amplitude of the binary input signal vm(t).
the direction of the shift is determined by the polarity of signal ( 1 or 0 ).
the modulating signal vm(t) is a normalized binary waveform where a logic 1 =
+1V and a logic 0 = -1V.
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5.5.2 Frequency Shift Keying

for logic 1 input, vm(t) = +1, equation (5.5-2) becomes
vfsk(t )  Vc cos2  fc  f t 

for logic 0 input, vm(t) = -1, equation (5.5-2) becomes
vfsk(t )  Vc cos2  fc  f t 

the carrier center frequency fc is shifted (deviated) up and down in the
frequency domain by the binary input signal as shown below.
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5.5.2 Frequency Shift Keying
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5.5.2 Frequency Shift Keying


mark (fm) = logic 1 frequency
space (fs) = logic 0 frequency
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5.5.3 Phase Shift Keying



modulation technique that alters the phase of the carrier.
in a binary phase-shift keying (BPSK), where N (number of bits) = 1, M
(number of output phases) = 2, one phase represents a logic 1 and another
phase represents a logic 0.
as the input digital signal changes state (i.e. from 1 to 0 or 0 to 1), the phase of
the output carrier shifts between two angles that are separated by 180º.
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5.5.3 Phase Shift Keying
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