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Learning Outcomes
After studying this chapter, you should be able to:
Digital Transmission
Digital Communications - PRELIM
ECE 502
 Compare analog and digital communication techniques and discuss the advantages
of each.
 Calculate the minimum sampling rate for a signal and explain the necessity for
sampling at that rate or above.
 Describe the common types of analog pulse modulation.
 Describe pulse-code modulation and calculate the number of quantizing levels, the
bit rate, and the dynamic range for PCM systems.
 Explain companding, show how it is accomplished, and explain its effects.
 Describe the coding and decoding of a PCM signal.
 Describe differential PCM and explain its operation and advantages.
 Describe delta modulation and explain the advantages of adaptive delta
modulation.
 Distinguish between lossless and lossy compression and provide examples of each.
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Digital communications
electronic communications is the transmission, reception, and
processing of information with the use of electronic circuits.
Digital Modulation
Or
Digital Radio
Information is defined as knowledge or intelligence that is
communicated (i.e., transmitted or received) between two or more
points.
the carrier facility could
be a physical cable, or
it could be free space.
Digital Transmission
require a physical facility between the
transmitter and receiver, such as a
metallic wire pair, a coaxial cable, or
an optical fiber cable.
Kurose, J and Ross, K, Computer Networking, 6th ed, ©2013
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Definition
digital transmission is the transmittal of digital signals between two
or more points in a communications system. The
Advantages of Digital Transmission
 noise immunity
 ease of processing,
a physical facility, such as a pair of wires, coaxial cable, or an optical
fiber cable, is required to interconnect the various points within the
system.
 ease of multiplexing,
TRUE OR FALSE:
Digital pulses cannot be propagated through a wireless transmission
system, such as Earth’s atmosphere or free space (vacuum).
 transmission errors can be detected and corrected more easily
and more accurately
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Disadvantages of Digital Transmission
 simpler to measure and evaluate
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PULSE MODULATION
 requires significantly more bandwidth
*Bandwidth is one of the most important aspects of any communications system
because it is costly and limited.
 additional encoding and decoding circuitry
Pulse modulation consists essentially of sampling analog information
signals and then converting those samples into discrete pulses and
transporting the pulses from a source to a destination over a physical
transmission medium.
 requires precise time synchronization between the clocks in the
transmitters and receivers
 incompatible with older analog transmission systems
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PULSE WIDTH MODULATION (PWM)
PULSE MODULATION
ANALOG
DIGITAL
PULSE AMPLITUDE
MODULATION
PULSE CODE
MODULATION
PULSE POSITION
MODULATION
DELTA MODULATION
PULSE DURATION
MODULATION
ADAPTIVE DELTA
MODULATION
PWM is sometimes called pulse
duration modulation (PDM) or
pulse length modulation (PLM), as
the width (active portion of the
duty cycle) of a constant
amplitude
pulse
is
varied
proportional to the amplitude of
the analog signal at the time the
signal is sampled.
Differential PCM
Tomasi,Wayne, Advanced Electronic Communication System, 6th ed, © 2014
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PULSE POSITION MODULATION (PPM)
PPM, 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
PULSE AMPLITUDE MODULATION (PAM)
PAM, the amplitude of a
constant width, constantposition pulse is varied
according
to
the
amplitude of the sample of
the analog signal.
Tomasi,Wayne, Advanced Electronic Communication System, 6th ed, © 2014
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Tomasi,Wayne, Advanced Electronic Communication System, 6th ed, © 2014
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PULSE CODE MODULATION (PCM)
PULSE CODE MODULATION (PCM)
The term pulse code modulation is somewhat of a misnomer, as it is not really a
type of modulation but rather a form of digitally coding analog signals.
Alex H. Reeves is credited with inventing PCM in 1937 while
working for AT&T at its Paris laboratories.
PCM is the only digitally encoded modulation technique
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PCM PROCESS
Discrete Signal
Analog Signal
SAMPLING
Digital Signal
QUANTIZATION
Time: Continuous
Amplitude: Continuous
Time: Discrete
Amplitude: Continuous
Example: 𝑥 𝑡 = 𝑠𝑖𝑛(2𝜋𝑓𝑡)
@ t = 0.1, 0.11, 0.115,……
Example: 𝑥(𝑛) = 𝑠𝑖𝑛(2𝜋𝑓𝑛𝑇𝑠)
@ Ts = 0.1, 0.2, 0.3,……
ENCODING
101101
Time: Discrete
Amplitude: Discrete
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SAMPLING
SAMPLING RATE
In 1928, Harry Nyquist showed mathematically that it is possible to
reconstruct a band-limited analog signal from periodic samples, as
long as the sampling rate is at least twice the frequency of the
highest-frequency component of the signal.
If the sampling rate is too low, a form of distortion called aliasing or
foldover distortion is produced
Blake, Roy, Electronics Communication System, 2 nd ed
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Aliasing or Foldover Distortion
Example
Find the Nyquist rate and Nyquist interval for the following signals:
𝑖. ) 𝑚 𝑡 =
sin 500𝜋𝑡
𝜋𝑡
𝑖𝑖. ) 𝑚 𝑡 =
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Blake, Roy, Electronics Communication System, 2 nd ed
𝑓𝑠 = 500𝐻𝑧, 𝑇𝑠 = 2𝑚𝑠𝑒𝑐
1
cos 400𝜋𝑡 cos(1000𝜋𝑡)
2𝜋
𝑓𝑠 = 5000𝐻𝑧, 𝑇𝑠 = 0.2𝑚𝑠𝑒𝑐
cosAcosB =1/2 [cos(A+B)+cos(A-B]
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Quantization
Quantization
Quantization is the process of converting
an infinite number of possibilities to a finite
number of conditions
Assigning PCM codes to absolute
magnitudes is called quantizing
The codes currently used for PCM are signmagnitude codes, where the most
significant bit (MSB) is the sign bit and the
remaining bits are used for magnitude.
Tomasi,Wayne, Advanced Electronic Communication System, 6th ed, © 2014
Quantization and the Folded Binary Code in PCM
Quantization and the Folded Binary Code
Tomasi,Wayne, Advanced Electronic Communication System, 6th ed, © 2014
Tomasi,Wayne, Advanced Electronic Communication System, 6th ed, © 2014
The magnitude difference between adjacent steps is called the quantization interval or quantum.
This type of code is called a folded binary code because the codes on the bottom half of the
table are a mirror image of the codes on the top half, except for the sign bit.
The magnitude of a quantum is also called the resolution.
n = number of bits in a PCM code, excluding the sign bit
The smaller the magnitude of a quantum, the better (smaller) the resolution and the more
accurately the quantized signal will resemble the original analog sample.
The leftmost bit is the sign bit (1=+ and 0= - ), and the two rightmost bits represent
magnitude.
 The 0-V codes each have an input range equal to only one-half a quantum.
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Example
Example
maximum quantization error
Quantized Level (𝒙𝒒 )
𝒔𝒂𝒎𝒑𝒍𝒆 𝒗𝒐𝒍𝒕𝒂𝒈𝒆 (𝒙)
= round
Input Signal Subrange (V)
Quantization Level 𝒙𝒒
𝒓𝒆𝒔𝒐𝒍𝒖𝒕𝒊𝒐𝒏
Binary Code
≤𝒙<
≤𝒙<
Sampled Analog Value
𝒙
Quantized Level
𝒙𝒒
<𝒙 <
Binary Equivalent Code
𝒊
≤𝒙<
Quantization error
𝒒𝒆
0
0.6
0.95 0.95
0.6
0
-0.6 -0.95 -0.95 -0.6
0
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Dynamic Range
The number of PCM bits transmitted per sample is determined by several variables,
including maximum allowable input amplitude, resolution, and dynamic range.
Dynamic Range (DR) is the ratio of the largest possible magnitude to the smallest
possible magnitude (other than 0 V) that can be decoded by the digital-toanalog converter in the receiver.
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Quantization Error or Noise
 any round-off errors in the transmitted
signal are reproduced when the code is
converted back to analog in the
receiver. This error is called the
quantization error (Qe).
 The quantization error is equivalent to
additive white noise as it alters the
signal amplitude
Tomasi,Wayne, Advanced Electronic Communication System, 6th ed, © 2014
 quantization error is also called quantization noise (Qn).
 The maximum magnitude for the quantization error is equal to one-half a quantum
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Coding Efficiency
 Coding efficiency is a numerical indication of how efficiently a PCM
code is utilized.
Line Codes
 Line Codes are electrical representation
of a binary data stream
 Coding efficiency is the ratio of the minimum number of bits
required to achieve a certain dynamic range to the actual number
of PCM bits used.
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Haykin,S., Communication Systems, 4th ed,
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BiPolar nonreturn-to-zero (BPNRZ) signaling
symbola 1 and 0 are represented by transmitting pulses of amplitude +A and –A,
respectively. This line code is relatively easy to generate but its disadvantages is that
the power spectrum of the signal is large near zero frequency.
 Unipolar nonreturn-to-zero (UPNRZ) signaling
In this line code, symbol 1 is represented by transmitting a pulse of
amplitude A for the duration of the symbol, and symbol 0 is
represented by switching off pulse. The line code is also referred to as
on-off signaling. Disadvantages of on-off signaling are the waste of
power due to the transmitted DC level and the fact that the power
spectrum of the transmitted signal does not approach zero at zero
frequency.
 UniPolar Return-to-Zero (UPRZ)
Symbol 1 is represented by a rectangular pulse of amplitude A and half-symbol
width, and symbol 0 is represented by transmitting no pulse. An attractive feature of
this line code is the presence of delta functions at 𝑓 = 0, ±1/𝑇𝑏 in the power
spectrum of the transmitted signal, which can be used for bit-timing recovery at the
receiver. However, its disadvantages is that it requires 3 dB more power than polar
return-to-zero signaling for the same probability of symbol errors
 BiPolar Return-to-Zero (UPRZ)
This line code uses three amplitude levels. Specifically, positive and negative pulses
of equal amplitude (+A and –A) are used alternate for symbol 1, with each pulse
having a half-symbol width; no pulse is always used for symbol 0. A useful property
of BPRZ signaling is that power spectrum of the transmitted signal has no DC
component and relatively insignificant low-frequency components for the case
when symbols 1 and 0 occur with equal probability.
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 Split-Phase (Manchester)
symbol 1 is represented by a positive pulse amplitude A followed by a negative
pulse of amplitude –A, with both pulses being half-symbol wide. For symbol 0, the
polarities of these two pulses are reversed. The Manchester code suppresses the
DC component and has relatively insignificantl low-frequency components,
regardless of signal statistics.
SIGNAL-TO-QUANTIZATION NOISE RATIO
LINEAR VERSUS NONLINEAR PCM CODES
 The maximum quantization noise is half the resolution (quantum value).
The worst possible signal voltage-to-quantization noise voltage ratio
(SQR) occurs when the input signal is at its minimum amplitude
the signal power-to-quantizing noise power ratio (also called signal-to-distortion
ratio or signal-to-noise ratio) is determined by the following formula:
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COMPANDING
ANALOG COMPANDING
 Companding is the process of
compressing
and
then
expanding.
 With companded systems, the
higher-amplitude analog signals
are compressed (amplified less
than the lower-amplitude signals)
prior to transmission and then
expanded (amplified more than
the lower-amplitude signals) in
the receiver.
 Companding is a means of
improving the dynamic range of a
communications system.
ANALOG COMPANDING
𝜇 − 𝐿𝑎𝑤
United States and
Japan
𝑨 − 𝑳𝒂𝒘
Europe
The most recent PCM systems use an
eight-bit code and a μ=255, A=87.6
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DIGITAL COMPANDING
Determine the 12-bit
linear code, the eight-bit
compressed code, the
decoded 12-bit code,
the quantization error,
and the compression
error for a resolution of
0.01V
and
analog
sample voltages of (a)
+0.053 V, (b) -0.318 V,
and (c) +10.234 V
EXAMPLE
DIGITAL COMPANDING
The most recent digitally compressed PCM systems use a 12-bit linear PCM code
and an eight-bit compressed PCM code.
Digital Compression Error
The segment number in the eight-bit code is determined by counting the number of
leading 0s in the 11-bit magnitude portion of the linear code beginning with the most
significant bit. Subtract the number of leading 0s (not to exceed 7) from 7. The result
is the segment number, which is converted to a three-bit binary number and inserted into
the eight-bit compressed code as the segment identifier.
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DELTA MODULATION PCM
PCM LINE SPEED
 Line speed is simply the data rate at which serial PCM bits are clocked
out of the PCM encoder onto the transmission line.
 Line speed is dependent on the sample rate and the number of bits
in the compressed PCM code.
Delta modulation uses a single-bit PCM code to achieve digital transmission of analog
signals. If the current sample is smaller than the previous sample, a logic 0 is
transmitted. If the current sample is larger than the previous sample, a logic 1 is
transmitted.
EXAMPLE For a single-channel PCM system with a sample rate fs 6000 samples per
second and a seven-bit compressed PCM code, determine the line speed:
two problems associated with delta modulation
Slope overload
Granular noise
 happens when the analog input signal
changes at a faster rate than the DAC
can maintain
 The slope of the analog signal is greater
than the delta modulator can maintain
and is called slope overload.
 Increasing the clock frequency and
increase the magnitude of the minimum
step size reduces the probability of slope
overload occurring
 when the original analog input signal has
a relatively constant amplitude, the
reconstructed signal has variations that
were not present in the original signal.
 Granular noise in delta modulation is
analogous to quantization noise in
conventional PCM.
 Granular noise can be reduced by:
 decreasing the step size
 a small resolution is needed
ADAPTIVE DELTA MODULATION PCM
Adaptive delta modulation is a delta modulation system where the step size of the DAC
is automatically varied, depending on the amplitude characteristics of the analog
input signal .
A common algorithm for an adaptive delta modulator is when three consecutive 1s
or 0s occur, the step size of the DAC is increased or decreased by a factor of 1.5
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Differential PCM
 Differential pulse code modulation (DPCM) is designed
specifically to take advantage of the sample-to-sample
redundancies in typical speech waveforms.
 With DPCM, the difference in the amplitude of two successive
samples is transmitted rather than the actual sample.
 Because the range of sample differences is typically less than
the range of individual samples, fewer bits are required for
DPCM than conventional PCM.
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