Title: Chapter 3: Data Transmission
1COE 341 Data Computer Communications Dr.
Radwan E. AbdelAal
 Chapter 3 Data Transmission
2Remaining Six Chapters
Chapter 7 Data Link Flow and Error
control, Link management
Data Link
Chapter 8 Improved utilization Multiplexing
Chapter 6 Data Communication Synchronization,
Error detection and correction
Physical Layer
Chapter 4 Transmission Media
Transmission Medium
Chapter 5 Encoding From data to signals
Chapter 3 Signals, their representations, their
transmission over media, Resulting impairments
3Agenda
 Concepts Terminology
 Signal representation
Time and Frequency domains  Bandwidth and data rate
 The decibels notation for signal strength
(Appendix 3A)  Fourier Analysis (Appendix B)
 Analog Digital Data Transmission
 Transmission Impairments
 Channel Capacity
4Terminology (1)
 Transmission system Components
 Transmitter
 Receiver
 Medium
 Guided media
 e.g. twisted pair, coaxial cable, optical fiber
 Unguided media
 e.g. air, water, vacuum
5Terminology (2)
 Link Configurations
 Direct link
 No intermediate communication devices
 (these exclude repeaters/amplifiers)
 Two types
 Pointtopoint (AB)
 Only 2 devices share link
 Multipoint (CB)
 More than two devices share the same link,
e.g. Ethernet bus segment
C
Amplifier
A
B
6Terminology (3)
 Transmission Types (ANSI Definitions)
 Simplex
 Information flows only in one direction all the
time  e.g. Television, Radio broadcasting
 Duplex
 Information flows in both directions
 Two types
 Half duplex
 Only one direction at a time
 e.g. WalkiTalki
 Full duplex
 In both directions at the same time
 e.g. telephone
7Frequency, Spectrum and Bandwidth
 Time domain concepts
 Analog signal
 Varies in a smooth, continuous way in both time
and amplitude  Digital signal
 Maintains a constant level for sometime and then
changes to another constant level
(i.e.
amplitude takes only a finite number of discrete
levels)  Periodic signal
 Same pattern repeated over time, e.g. sine wave
or a square wave  Aperiodic signal
 Pattern not repeated over time
8Analogue Digital Signals
All values on the time and amplitude axes are
allowed
Analogue
Only a few amplitude levels allowed  Binary
signal 2 levels
Digital
9PeriodicSignals
T
Temporal Period
t
t1T
t2T
For any periodic wave S (tnT) S (t) 0 ? t
? T Where t is time over first period T is the
waveform period n is an integer
Signal behavior over one period describes
behavior at all times
10Aperiodic (non periodic) Signals in time
s(t)
11Continuous Versus Discrete
Availability of the signal over the horizontal
axis
(Time or Frequency)
Continuous Signal is defined at all points on
the horizontal axis
Sampling with a train of very narrow pulses
(delta function)
Discrete Signal is defined Only at certain
points on the horizontal axis
12Sine Wave s(t) A sin(2?f t ?)
T (Period)
A sin (F)
A (Amplitude)
w
 Peak Amplitude (A)
 Peak strength of signal, volts
 Repetition Frequency (f), Cycles/s Hz
 Measures how fast the signal varies with time
 Number of cycles per second (Hz)
 f 1/ T(xx sec/cycle) yy cycles/sec yy Hz
 Angular Frequency (w), Radians/s
 w radians per second 2? f 2? /T
 Temporal (time) Period, T 1/f
 Phase Angle (?), Radians
 Determines relative position in time, radians
(how to calculate?)
13Varying one of the three parameters of a sine
wave carriers(t) A sin(2?ft ?) A
sin(wtF)
Can be used to convey information!
M o d u l a t I o n
AM
Varying A
Varying ?
FM
PM
Varying f
14Sine Wave Traveling in the ive x directions(t)
A sin (k x  ? t)
? Angular Frequency 2? f 2? / T
k Wave Number 2? / ?
 Spatial Period
 Wavelength
?
 For point p on the wave
 Total phase at t 0 kx  ? (0) kx
 Total phase at t ?t k(x ?x)  ? (?t)
 Same total phase,
 kx k(x ?x)  ? (?t)
 k ?x ? ?t
 Wave propagation velocity v ?x / ?t
 v ?/k ?/T ?f
?x
p
x
Distance, x
t 0
t ?t
ive x direction
Direction of wave travel, at velocity v
? Show that the wave s(t) A sin (k x ?
t travels in the negative x direction
V is constant for a given wave type (e.g. sound)
and medium (e.g. air)
v ?f
15Wave Propagation Velocity, v m/s
 Constant for
 A given wave type (e.g. electromagnetic, seismic,
ultrasound, ..)  and a given propagation medium (air, water,
optical fiber)  For all types of waves
 v l f
 For a given wave type and medium (given v)
higher frequencies correspond to shorter
wavelengths and vise versa  Electromagnetic waves
 long wave radio (km), short wave radio (m),
microwave (cm) light (nm)  For electromagnetic waves
 In free space, v ? speed of light in vacuum
 v ? c 3x108 m/sec
 Over other guided media (coaxial cable, optical
fiber, twisted pairs) v is always lower than c
Shorter wavelength ? Higher frequency
16Wavelength, l (meters)
 Is the Spatial period of the wave
i.e. distance between two points
in space on the wave propagation path where the
wave has the same total phase  Also Distance traveled by the wave during one
temporal (time) cycle  dT v T (l f) T l
17Frequency Domain Concepts
 Response of systems to a sine waves is easy to
analyze  But signals we deal with in practice are not all
sine waves, e.g. Square waves  Can we relate waves we deal with in practice to
sine waves? YES!  Fourier analysis shows that any signal can be
treated as the sum of many sine wave components
having different frequencies, amplitudes, and
phases (Fourier Analysis Appendix B)  This forms the basis for frequency domain
analysis  For a linear system, its response to a complex
signal will be the sum of its response to the
individual sine wave components representing that
signal.  Dealing with functions in the frequency domain is
simpler than in the time domain
18Addition of Twofrequency Components
Fundamental
A 1(4/?) frequency f
1/3 rd the Amplitude 3 times the frequency
3rd harmonic
A (1/3)(4/?) frequency 3f
Frequency Spectrum
Approaching a square wave
Fourier Series
t
3
f
Frequency Domain S(f) vs f
Time Domain s(t) vs t
Fourier Series
Discrete Function in f
Periodic function in t
19Asymptotically approaching a square wave by
combining the fundamental an infinite number of
odd harmonics at prescribed amplitudes
Topic for a programming assignment
Adding more of the higher harmonics
What is the highest Harmonic added?
20 More Frequency Domain Representations A single
square pulse (Aperiodic signal)
Sinc(f) sin(f)/f
Fourier Transform
X
To ?
To ?
To ?
frequency
1/X
Fourier Transform
Frequency Domain S(f) vs f
Time Domain s(t) vs t
Continuous Function in f
Aperiodic function in t
 What happens to the spectrum as the pulse gets
broader ? DC ?
 What happens to the spectrum as the pulse gets
narrower ? spike ?
21Spectrum Bandwidth of a signal
 Spectrum of a signal
 Range of frequencies contained in a signal
 Absolute (theoretical) Bandwidth (BW)
 Is the full width of spectrum fmax fmin
 But in many situations, fmax ?!
 (e.g. a square wave), so
 Effective Bandwidth
 Often called just bandwidth
 Narrow band of frequencies containing most of the
signal energy  Somewhat arbitrary what is most?
 ? e.g. that contains say 95 of the energy of
the signal
S(f)
.
f
5f
7f
3f
f
22Signals with a DC Component
NO DC Component, Signal average over a period 0
_
t
1V DC Level
t
1V DC Component
DC Component ? is the component at zero
frequency ? Determines if fmin 0 or not
23Bandwidth for these signals
(fmax fmin)
fmin fmax Absolute BW Effective BW
1f 3f 2f 2f
0 3f 3f 3f
0 ? ? 1/X ?
24Bandwidth of a transmission system
 Is the Range of signal frequencies that are
adequately passed by the system  Effectively, the transmission system
(TX, medium, RX) acts as
a filter  Poor transmission media, e.g. twisted pairs, have
a narrow bandwidth  This effectively cuts off higher frequency signal
components  ? poor signal quality at receive
 ? limit the signal frequencies (Hz) that can be
used for transmission  ? this limits the data rates that can be used
(bps), examples  Twisted pair 4 KHz BW ? 100 Kbps
 Optical fiber 4 THz BW ? 10 Gbps
25Limiting Effect of System Bandwidth
Received Waveform
1,3
Better reception requires larger BW
BW 2f
More difficult reception with smaller BW
f
3f
1
1,3,5
BW 4f
5f
f
3f
2
Varying System BW
1,3,5,7
BW 6f
7f
f
5f
3f
3
BW ?
1,3,5,7 ,9,?
?
f
5f
7f
3f
4
Fourier Series for a Square Wave
26System Bandwidth and Achievable Data Rates
 Any transmission system supports only a limited
range of frequencies (bandwidth) for satisfactory
transmission  For example, this bandwidth is largest for
expensive optical fibers and smallest for cheap
twisted pair wires  So, bandwidth is money ? Economize in its use
 Limited system bandwidth degrades higher
frequency components of the signal transmitted ?
poorer received waveforms ? more difficult to
interpret the signal at the receiver (especially
with noise) ? Data Errors  More degradation occurs when higher data rates
are used (signal will have higher frequency
components)
27Maximum Data Rate ( link channel
capacity)Considerations
 Bandwidth of transmission system
 Signal to noise ratio (SNR)
 Receiver type
 Specified acceptable error performance
28Bandwidth and Data Rates
Data Element Signal Element
Period T 1/f
T/2
Data rate 1/(T/2) (2/T) bits per sec 2f bps
B
0
0
1
1
Data
B 4f
Given a bandwidth B, Data rate 2f B/2
To double the data rate you need to double f Two
ways to do this
1. Double the bandwidth, same received waveform
quality (same RX conditions error rate)
2B 4f
2B
1
1
1
1
0
0
0
0
1
1
1
0
0
1
0
0
New bandwidth 2B, Data rate 2f 2(2f) 4f B
X 2
f
3f
5f
2. Same bandwidth, B, but tolerate poorer
received waveform (needs better receiver, higher
S/N ratio, or tolerating more errors in data)
1
B 2f
1
1
1
0
0
0
0
B
X 2
Bandwidth B, Data rate 2f 2(2f) 4f B
5f
3f
f
29Bandwidth Data Rates Tradeoffs Compromises
 Increasing the data rate (bps) while keeping BW
the same (to economize) means working with
inferior (poorer) waveforms at the receiver,
which may require  Ensuring higher signal to noise ratio (SNR) at RX
 Larger transmitted power (may cause interference
to others!)  Limited (shorter) link distances
 Use of more enroute repeaters/amplifiers
 Better shielding of cables to reduce noise, etc.
 More sensitive ( costly!) receiver
 Suffering from higher bit error rates
 Tolerate them?
 Add more efficient means for error detection and
correction this also increases overhead!.
30Appendix 3A Decibels and Signal Strength
 The decibel notation (dB) is a logarithmic
measure of the ratio between two signal power
levels  NdB number of decibels
 P1 input power level (Watts)
 P2 output power level (Watts)
 e.g. ? Amplifier gain
 ? Signal loss
 (attenuation) over a link
 Example
 A signal with power level of 10mW is inserted
into a transmission line  Measured power some distance away is 5 mW
 Power loss in dBs is expressed as
 NdB 10 log (5/10)10(0.3) 3 dB
  ive dBs P2 lt P1 (Loss),
 ive dBs P2 gt P1 (Gain)
P2
P3
P1
Lossy Link
Amplifier
31Relationship Between dB Values and Power ratio
(P2/P1)
Power Ratio dB Power Ratio dB
1 0
101 10 101 10
102 20 102 20
103 30 103 30
104 40 104 40
105 50 105 50
106 60 106 60
2 3 1/2 3
32Decibels and Signal Strength
 Decibel notation is a relative, not absolute,
measure  A loss of 3 dB halves the power (could be 100 to
50, 16 to 8, )  A gain of 3 dB doubles the power (could be 5 to
10, 7.5 to 15, )  Will see shortly how we can handle absolute
levels  Advantages of using dBs
 The log allows replacing
 Multiplication with Addition
 C A B
 Log C Log A Log B
 and Division with Subtraction
 A C / B
 Log A Log C  Log B
33Decibels and Signal Strength
 Example Transmission line with an intermediate
amplifier
(/10)
(/15.6)
(3162)
 Net power gain over transmission path
 35 12 10 13 dB ( ive means there is
net gain)
?
 Received signal power (4 mW) log101(13/10) 4
x 101.3  4 x 101.3 mW 79.8 mW
Still we use some multiplication!
34How to represent absolute power
levels?DecibelWatt (dBW) and DecibelmW (dBm)
WK 4
 As a ratio relative to a fixed reference power
level  With 1 W used as a reference ? dBW
 With 1 mW used as a reference ? dBm
 Examples
 Power of 1000 W is 30 dBW, 1 W ? dBW
 10 dBm represents a power of 0.1 mW,
 1 mW ? dBm X dBW (X ?) dBm
Caution! Must be same units at top and bottom
Caution! Must be same units at top and bottom
35dBs dBms are added algebraically
P2
P1
G
G is ? Positive for gain ? Negative for
loss (attenuation)
G power ratio
G dBs 10 log10 G
Similarly for dBs dBWs
36Decibels and Signal Strength
 Example Transmission line with an intermediate
amplifier
 If all ratios are in dBs and all levels are in
dBm ? solve by algebraic addition Same for
dBs and dBWs (No need for
any multiplication/division)
4 mW
?
Gain 35 dB
Transmitted Signal
Received Signal
Loss 10 dB
Loss 12 dB
Amplifier
 Net power gain over transmission path
 35 12 10 13 dB ( ive means actual
net gain)
TX Signal Power in dBm 4 mW 10 log (4/1)
6.02 dBm
 RX signal power (dBm) 6.02 13 19.02 dBm
 Check 19.02 dBm 10 log (RX signal in mW/1 mW)
 ? RX signal log1 (19.02/10) 79.8 mW
As on Slide 33
37Decibels Voltage ratios
 Power decibels can also be expressed in terms of
voltage ratios  Power P V2/R, assuming same R
 ? Relative
 ? Absolute dBV and dBmV
 Decibelmillivolt (dBmV) is an absolute unit,
with 0 dBmV being equivalent to 1mV.
dBV is similarly defined
38Pitfalls with the Decibel Notation
 Wrong to multiply dBs dBs x dBs !
 35 dBs x 5 dBs (what would be the units of
the result!)  Wrong to divide dBs dBs / dBs !
 (caution dBs / (dBs/km) is OK)
 Wrong to mix numerical levels with dBs
 3.5 W 24 dBs ..
 OK to mix dBs with dBms
 35 dBm 12 dBs 18 dBs .
 But wrong to use dBm and dBW in the same
expression  35 dBm 12 dBs X dBs 3 dbW
39Appendix B Fourier Analysis
Signals in Time
Aperiodic
Periodic
Discrete Continuous
Discrete Continuous
DFS
FS
FT
DFT
Use Fourier Series
Use Fourier Transform
FS Fourier Series DFS Discrete Fourier
Series FT Fourier Transform DFT Discrete
Fourier Transform
40Fourier Series for periodic continuous signals
 Any periodic signal x(t) of period T and
repetition frequency f0 (f0 1/T) can be
represented as an infinite sum of sinusoids of
different frequencies and amplitudes its
Fourier Series. Expressed in Two forms  1. The sine/cosine form
Frequencies are multiples of the
fundamental frequency f0
f0 fundamental frequency 1/T
Where
DC Component
f(n)
Two components at each frequency
All integrals over one period only
If A0 is not 0, x(t) has a DC component
f(n)
41Fourier Series 2. The AmplitudePhase form
 Previous form had two components at each
frequency (sine, cosine i.e. in quadrature) An,
Bn coefficients  The equivalent AmplitudePhase representation has
only one component at each frequency Cn, qn  Derived from the previous form using
trigonometry  cos (a) cos (b)  sin (a) sin (b) cos a b
Now we have Only one component at each
frequency nf0
Now components have different amplitudes,
frequencies, and phases
The Cs and ?s are obtained from the previous
As and Bs using the equations
42Fourier Series General Observations
Fourier Series Expansion
Function
Odd Function
Even Function
DC
Function Function Series
No DC A0 0
Even Function x(t) x(t) Symmetric about Y axis Bn 0 for all n
Odd Function x(t)  x(t) Symmetric about the origin An 0 for all n
43Correction
44Fourier Series Example
x(t)
Note (1) x( t)x(t) ? x(t) is an even
function (2) f0 1 / T ½ Hz
Note A0 by definition is 2 x the DC content
45Contd
0 for n even
(4/n?) sin (n?/2) for n odd
f0 1/2
a function of n only
? Replace t by t ? Swap limits in the first
integral
 sin(2pnf t)
 dt
Then Bn 0 for all n
x(t), since x(t) is an even function
46Contd
f0 ½, so 2? f0 ?
A0 0, Bn 0 for all n, An 0 for n
even 2, 4, (4/n?) sin (n?/2) for n
odd 1, 3,
Original x(t) is an even function!
Amplitudes, n odd
Cosine is an even function
2 p 3 (1/2) t
2 p (1/2) t
3rd Harmonic
Fundamental
f0 ½ ?
47Another Example
Previous Example
x1(t)
1
1
1
2
2
1
T
Note that x1(t) x1(t) ? so, x(t) is an odd
function
Also, x1(t)x(t1/2)
This waveform is the previous waveform shifted
right by 1/2
48Another Example, Contd
Sine is an odd function
As given before for the square wave on slide 25.
Because
49Fourier Transform
 For aperiodic (nonperiodic) signals in time, the
spectrum consists of a continuum of frequencies
(not discrete components)  This spectrum is defined by the Fourier Transform
 For a signal x(t) and a corresponding spectrum
X(f), the following relations hold
Imaginary
1
nf0 ? f
T/2 ? ?
Inverse FT (from frequency to time )
Forward FT (from time to frequency)
Real
? Express sin and cos
 X(f) is always complex (Has both real Imaginary
parts), even for x(t) real.
50(Continuous in Frequency)
(nonperiodic in time)
Sinc function
Sinc2 function
51Fourier Transform Example
x(t)
A
Sin (x) / x i.e. sinc function
Area of pulse In time domain
52Fourier Transform Example, contd.
Sin (x) / x sinc function
Lim x?0 (sin x)/x (cos x)x0/1 1
First zero in the Frequency spectrum
sin pft 0 pft p f 1/t
Study the effect of the pulse width ?
53The narrower a function is in one domain, the
wider its transform is in the other domain
The Extreme Cases
0
54Power Spectral Density (PSD) Bandwidth
 Absolute bandwidth of any timelimited signal is
infinite  But luckily, most of the signal power will be
concentrated in a finite band of lower
frequencies  Power spectral density (PSD) describes the
distribution of the power content of a signal as
a function of frequency  Effective bandwidth is the width of the spectrum
portion containing most of the total signal power  We estimate the total signal power in the time
domain
55Signal Power in the time domain
 Signal is specified as a function s(t)
representing signal voltage or current  Assuming resistance R 1 W,
 Instantaneous signal power (t) v(t)2/1
i(t)21 s(t)2  Signal power can be obtained as the average of
the instantaneous signal power over a given
interval of time constant  For periodic signals, this averaging is taken
over one period, i.e.  This measure in the time domain gives the total
signal power  Effective BW is then determined such that it
contains a specified portion (percentage) of this
total signal power
(1)
s
56Signal Power in the Frequency Domain Periodic
signals
 For periodic signal we have a discrete spectrum
(the F Series)  For a DC component, Power Vdc2
 For AC components Power Vrms2 Vpeak 2 (use
eqn. 1 on prev. slide)  Power spectral density (PSD) is a discrete
function of frequency  Where ?(f) is the Dirac delta function
 Total signal power (watts) up to the j th
harmonic is
(A function of frequency)
(A quantity, summation of PSD components not a
function of a frequency)
57Example
 Consider the following signal
 The PSD is (A function of Frequency)
 The signal power is (A quantity)
(No DC)
58Signal Power in the Frequency Domain Aperiodic
signals
Watts/Hz
 Continuous (not discrete) frequency spectrum
 PSD (Power spectrum density) function, in
Watts/Hz, is a continuous function of frequency
S(f),  Total signal power contained in the frequency
band f1lt f lt f2 (in Watts) is given by  (Integration, instead of summation, over
frequency)
Components exist in both negative and positive
frequencies
59Complete Fourier Analysis Example
 Consider the halfwave rectified cosine signal,
Figure B.1 on page 793  Write a mathematical expression for s(t) over its
period T  Compute the Fourier series for s(t) (Amplitude
Phase form)  Get an expression for the power spectral density
function for s(t)  Find the total power of s(t) from the time domain
 Find the order of the highest harmonic n such
that the Fourier series for s(t) contains at
least 95 of the total signal power  Determine the corresponding effective bandwidth
for the signal
60Example (Cont.)
 Mathematical expression for s(t)
T/2
Where f0 is the fundamental frequency, f0
(1/T)
61Example (Cont.)
 2. Fourier series
 Before we start what to expect?
 DC Component?
 Even or odd function?
 A0 ?
 An ?
 Bn ?
Sine/cosine form of the Fourier Series
To get to the amplitudephase form of the Fourier
series, we must first obtain the sinecosine form
62Example (Cont.)
f0 (1/T)
DC ?
63Example (Cont.)
f0 (1/T)
n 1 will be treated Separately later
From integral tables
64Example (Cont.)
 Fourier Analysis (cont.)
 n ? 1
, for n even
65Example (Cont.)
 Fourier Analysis (cont.)
 For n 1, A1 is obtained separately
Note cos2q ½(1 cos 2q)
66Example (Cont.)

67Example (Cont.)
 Fourier Analysis (cont.)
 For n 1, B1 is obtained separately
i.e. Bn 0 for all n (our function is even!)
68Example (Cont.)
Note qn are not required for PSD and power
calculations
69Example (Cont.)
 3. Power Spectral Density function (PSD)
n Even
n 1
n 0 (DC)
For large n, power decays ? (1/n4) Good or bad?
70Example (Cont.)
 4. Total Power
 (From the time domain)
Note cos2q ½(1 cos 2q)
0.25 A2
Zero
Half the power of a full sine wave
71Example (Cont.)
 5. Finding n such that we get at least 95 of the
total power
(Only the DC component)
Power
of total power in this component
72Example (Cont.)
 Finding n such that we get at least 95 of the
total power, contd.
(DC first harmonic)
Power
of total power in these two components
73Example (Cont.)
 Finding n such that we get at least 95 of the
total power, Contd.
(DC first harmonic second harmonic)
Power
OK! ? 95
 n 2, and
 6. the effective bandwidth is
 Beff fmax fmin
 Beff 2f0 0 2f0
Beff
?
f
2f0
0
f0
3f0
DC
74Bandwidth about a Center Frequency
 So far we have considered signals in their base
band form (without modulation)  Data is often sent as variations in a high
frequency carrier signal having a frequency fc
(modulation)  So, bandwidth (BW) of this signal occupies a
range of frequencies centered about fc 
 The larger fc, the larger the BW obtainable
 Largest BW obtainable for a given center
frequency fc is 2 fc
Carrier
With Amplitude Modulation, For each component of
the modulating signal
75Analog and Digital Data Transmission
WK5
 Data
 Entities that convey meaning
 Signals
 Electric or electromagnetic representations of
data  Data Transmission
 Communication of data
through propagation and processing of
signals that represent them
76Data types in nature Analog and Digital Data
 Analog Data
 Continuous values within some interval
 Examples audio, video
 Typical bandwidths
 Speech 100Hz to 7kHz
 Voice over telephone 300Hz to 3400Hz
 Video 4MHz
 Digital Data
 Discrete values (not necessarily binary)
 Examples integers, text characters, mixture
 2347, text, SDR054
77Analog and Digital Signals
 Means by which data get transmitted over various
media, e.g. wire, fiber optic, space  Analog signal
 Continuously variable in time and amplitude
 Digital signal
 Uses a few (two or more) DC levels
78Analog Signal Example 1 Speech Data
 Frequency range for human hearing 20Hz20kHz
 Almost fully utilized by music
 Human speech 100Hz7kHz
 Telephone voice channel Spectrum is further
limited to 3003400Hz (why?)  Mechanical sound waves (data) are easily
converted into electromagnetic signal for
processing and transmission  Mechanical waves (Sound) of varying pitch and
loudness (Data)  is represented as
 Electromagnetic signals of different frequencies
and amplitudes (Signal)
79Analog Example 1. The Acoustic Spectrum
Dynamic range of the human ear can be as high as
120 dBs!
dBs
Source Data
Hearing Spectrum
Dynamic Range of Signal Power
SPEECH
Frequency Range
70
Log Scale
80Conventional Telephony Analog data Analog
Signal
 Telephone mouthpiece converts mechanical voice
analog data into electromagnetic analog
electrical signal  Signal travels on telephone lines
 At receiver, speaker reconverts received
electrical signal to voice
81Analog Signal Example 2. Video Data
 Electrical signal proportional to the brightness
of image spot on a rasterscanned phosphor screen
Interlaced Scan
11 ms
52.5 ms (Active)
Line Scan
Frame Scan
82Bandwidth of a Black White Video Signal
 USA Specification 525 lines per frame scanned at
the rate of 30 frames per second  525 lines 483 active scan lines 42 lost
during vertical retrace  So 525 lines x 30 frames/second 15750 lines per
second  Line scan interval 1/15750 63.5?s
 11?s go for horizontal retrace, so 52.5 ?s for
active video per line  Effective vertical resolution 0.7 x 483 338
lines  Horizontal resolution 338 x aspect ratio
 338 x (4/3) 450 dots
 Max frequency is when black and white dots
alternate  450 picture dots correspond to 225 cycles in 52.5
?s ? Time period 52.5/225 ?s ? fmax 1/Period
4.2 MHz  fmin (DC) 0 ? Bandwidth fmax  fmin 4.2 MHz
83Digital Signals
 Advantages
 Cheaper and easier to generate No extra
processing needed  Less susceptible to noise
 (The threshold effect)
 Disadvantages
 When noise is above threshold ? Total data
reversal (Bit error) (1? 0, 0 ?1)  Greater attenuation
 Line capacitances make pulses rounded and smaller
in amplitude, leading to loss of information  More so at higher data rates and longer distances
 So, use at low data rates over short distances
84Attenuation of Digital Signals
1 1 1 1 . . .
0 0 0 0 . . .
Pulse shaping Due to line capacitances Worse
over longer distances
Worse at higher data rates (narrower pulses)
Effect of line capacitances
85Digital Binary Signal
 Example Between keyboard and computer
 Two bipolar dc levels ( and Why?)
 Bandwidth required depends on the signal
frequency, which depends on  The data rate (bps) and
 The actual data sequence transmitted
_
Data

 Data rate ?
  Maximum f ?
  Minimum f ?
Data element
Signal
86Data and Signal combinations
 We have seen above (data and signal of same
type)  Analog signals carrying analog data Telephony,
Video  Digital signals carrying digital data Keyboard
to PC  Simple one only needs a transducer/transceiver
 But we may also have (data and signal of
different types)  Analog signal representing digital data Data
over telephone wires (using a modem)  Digital signal representing analog data CD
Audio, PCM (pulse code modulation) (using a
codec)  More complex We Need a converter
 So, all the four datasignal combinations are
possible!
87Analog Signals can carry Analog Data or Digital
Data
(Base band)
i.e. in its original form
(Transducer)
(Converter)
We need a converter when the signal type is
different from the data type
88Digital Signals can carry Analog Data or Digital
Data
Digitized Analog Samples
e.g. using PCM (Pulse Code Modulation)
CoderDecoder
(Converter)
TransmitterReceiver
We need a converter when the signal type is
different from the data type
89Four Data/Signal Combinations
Signal Signal
Analog Digital
Data Analog Two ways Signal has Same spectrum as data (base band) e.g. Telephony to exchange Different spectrum (through modulation) e.g. AM Radio, FDM Use a (converter) codec, e.g. for PCM (pulse code modulation)
Data Digital Use a (converter) modem e.g. the V.90 standard Simple two signal levels e.g. NRZ code Special Encoding e.g. Manchester code (Chapter 5)
90Two Modes of Transmitting Signals 1. The Analog
Mode (associated with FDM)
 Treats the signal as analog regardless of what
it represents (Not interested in the data content
of signal)  Following attenuation over distance, signal level
is boosted using amplifiers  Unfortunately, this also amplifies inband noise
 With cascaded amplifiers (i.e. one after the
other at locations along the link), effect on
noise and distortion is cumulative, i.e. they get
amplified again and again  Effect of noise and distortion on analog systems
may be tolerated, e.g. with telephony you can
still manage to get it! (Humans are good at
fillingin gaps!)  But digital systems are more sensitive to the
effects of excessive noise and distortion ?
unacceptable errors  So Do not transmit digital signals the analog
way!
91Two Modes of Transmitting Signals 2. The
Digital Mode (Associated with TDM)
 Concerned with the data content of the signal
 It assumes that the signal carries digital data
 Uses repeaters (not amplifiers), which
 Receive the signal
 Extract the data bit stream from it
 Retransmit a fresh, strong signal representing
the extracted bit stream  This way
 Effect of attenuation is overcome
 Noise and distortion are not cumulative
92Four Signal/Transmission Mode Combinations
Transmission mode Transmission mode
Analog Uses amplifiers Not concerned with what data the signal represents Noise and distortion are cumulative  Associated with FDM Digital Uses repeaters Assumes signal represents digital data, recovers this data and represents it as a new outbound signal This way, noise and distortion are not cumulative Associated with TDM
Signal Analog OK Makes sense only if the analog signal represents digital data! (Ask yourself What data is the repeater going to extract?!)
Signal Digital Avoid OK
Which transmission mode is more versatile and
useful for integrating different signal types?
FDM Frequency Division
Multiplexing TDM Time Division
Multiplexing
93Advantages of Digital Mode of Transmission
 Use of digital technology
 Lower cost, smaller size, and high speed VLSI
technology  Higher data integrity (reliability) as noise
effects are not cumulative (fresh signal
restoration enroute)  Cover longer distances, at higher data rate, at
low error rates, over lower quality lines  Easier to implement multiplexing for improved
utilization of link capacity  High bandwidth links are now economical (Fiber,
Satellite)  To utilize them efficiently we need to do a lot
of multiplexing  This is done more efficiently using digital (TDM)
rather than analog (FDM) (Chapter 8)  Encryption for data security
 and confidentiality is digital
 Easier to integrate different data types
 Convert analog data to digital signalsand use
one system to handle all voice, video, and data,
e.g. one network for all types of traffic
Frequency Division Multiplexing
Time Division Multiplexing
94Transmission Impairments
 Signal received is often a degraded form of the
signal transmitted  Why? What happens enroute?... Impairments
 Attenuation
 Limits the bandwidth of the received signal
 Inband signals arrive weaker
 Attenuation distortion (Attenuation is not
uniform over bandwidth)  Delay
 Delay distortion
 Noise and interference (including crosstalk)
 Effect
 On analog data  Some degradation in signal
quality  On digital data Fatal bit errors (total bit
reversals)
95Attenuation
 Signal strength falls off with distance traveled
 Nature of loss in signal power depends on medium
 Guided (Wires, etc.)
 Exponential drop is signal power with distance
Pd P0 ead  10 ln (Pd/P0) ad
 10 log (Pd/P0) ad
 ? Loss a dBs per km (a depends on medium
type e.g. fiber, twisted pair, cable)  Unguided (Open space)
 Inverse square law spread with distance P ? P0
/d2  ? Loss 6 dBs for each distance doubling
 Absorption, scattering
 May also depend on weather, e.g. rain, sunspots,
Signal power after traveling distance d
96Effects of Attenuation
 Received signal strength must be
 Sufficiently Large enough to be detected
 Sufficiently higher than noise to be interpreted
correctly (without error)  To overcome these problems
 Use amplifiers (analog transmission mode)
 or repeaters (digital transmission mode)
enroute  Amplifier gains should not be too large as this
may cause signal distortion due to saturation
(nonlinearities)  Problem with networks distance actually traveled
(hence attenuation) will depend on actual route
taken through the network!
97Attenuation Distortion
 Attenuation usually increases with frequency
 This causes bandwidth limitation (understood)
 Moreover, over the transmitted bandwidth itself
 Different frequency components of the signal get
attenuated differently ? Signal distortion  Affects analog signals more
 To overcome this problem
 Use Equalizers that reverse the effect of
frequencydependent attenuation distortion  Passive e.g. loading coils in telephone circuits
 Active Amplifier gain designed specifically for
this purpose
98Attenuation Distortion
Equalization To Reduce Attenuation Distortion
Q. What is the signal ?
99Delay Distortion
 Happens only on guided media
 Wave propagation velocity varies with frequency
 Highest at the center frequency (minimum delay)
 Lower at both ends of the bandwidth (larger
delay)  Effect Different frequency components of the
signal arrive at slightly different times!
(Dispersion in time)  Affects digital data more due to bit spillover
(timing is more critical here than for analog
data)  Again, equalization can help overcome the problem
100Delay Distortion
Equalization To Reduce Delay Distortion
Without Equalizer
With Equalizer
101Noise (1)
 Definition Any additional unwanted signal
inserted between transmitter and receiver  The most limiting factor in communication systems
 Noise Types
 Thermal Noise
 Intermodulation Noise
 Crosstalk Noise
 Impulse Noise
102Noise (2)
PSD
 Thermal (White) Noise
 Due to thermal agitation of electrons
 (Increases with temperature)
 Uniformly distributed over frequency (White
noise)  ? Difficult to eliminate
 (exists even in the same bandwidth as your
signal!)  Effect is more significant on weak received
signals, e.g. from satellites
f
103Thermal Noise, Contd.
 Thermal noise power density in 1 Hz of bandwidth,
N0 (Constant, Independent of frequency)  k Boltzmanns constant 1.38?1023 J/K
 T temperature in degrees Kelvin ( 273 t ?C)
 Thermal noise power in a bandwidth of B Hz
PSD
N0
B
1 Hz
f
Can you see some disadvantage now in having a
larger BW?
10 log k
Example at t 21 ?C (T 294 ?K) and for a
bandwidth of 10 MHz N 228.6 10 log 294
10 log 107  133.9 dBW
104Noise (3)
WK 6
 Intermodulation Noise
 Signals having the sum and difference (frequency
mixing) of original frequencies sharing a
transmission system  (e.g. in FDM systems)
 f1, f2 ? (f1f2) and (f1f2)
 Caused by nonlinearities in the medium and
equipment, e.g. due to overdrive and saturation
of amplifiers  Danger Resulting new frequency components may
fall within valid signal bands, thus causing
interference
Linear System
A cos q1 B cos q2
A cos q1 B cos q2
Output
K(A cos q1 B cos q2)
A cos q1 B cos q2 f(2q1)f(2q2)f(q1q2)f(q
1q2)
NonLinear System
Input
A cos q1 B cos q2
K(A cos q1 B cos q2) K(A cos q1 B cos q2)2
Intermodulation components
Input
New spurious components can fall within genuine
signal bands causing interference
105Noise (4)
 Crosstalk Noise
 A signal from one channel picked up by another
channel in close proximity  Examples
 Physical proximity coupling between adjacent
twisted pair channels  ? Shield cables properly
 Directional proximity antenna pick up from other
directions ? Use directional antennas  Spectral proximity leakage between adjacent
channels in frequency division multiplexing (FDM)
systems  ? Use guard bands between adjacent channels
106Noise (5)
 Impulse Noise
 Pulses (spikes) of irregular shape and high
amplitude lasting short durations  Causes External electromagnetic interference due
to switching large currents, car ignition,
lightning,  Minor effect on analog signals (e.g. crackling
noise in voice channels)  Major effect on digital signals Bit reversal
error!  More damage at higher data rates
 (a noise pulse of a given width can destroy a
larger block of bits)
107Effect of Impulse Noise on a Digital Signal
Impulse
RX
Q What is the effect of the same noise at 10
times the data rate?
108Channel Capacity
 Channel capacity Maximum data rate usable under
a given set of communication conditions  How channel BW (B), signal level, noise and
impairments, and the amount of data error that
can be tolerated limit the channel capacity?  In general, Max possible data rate, C, on a given
channel  Function (B, Signal wrt noise, Bit error rate
allowed)  Max data rate Max rate at which data can be
communicated on the channel, bits per second
(bps)  Bandwidth BW of the transmitted signal as
constrained by the transmission system, cycles
per second (Hz)  Signal relative to Noise, SNR signal
power/noise power ratio (Higher SNR ? better
communication conditions ? higher C)  Bit error rate (BER) allowed in (bits received
in error)/(total bits transmitted). Equal to
the bit error probability.
e.g. Higher allowed ? higher usable data
rates ? higher C
109Channel Capacity, C
 So, in general C bps F(B, SNR, BER)
 Three Formulations under different assumptions
Idealistic
Assumptions Formulation
Ideal Noisefree, Errorfree C F(B) Nyquist
Noisy, Errorfree C F(B, SNR) Shannon
Practical Noisy, Error C F(B, SNR, BER) Eb/N0 Vs Error Rate
Realistic
110Bandwidth (or Spectral) Efficiency (BE)
 Measures how well we are utilizing a given
bandwidth to send data at a high rate.  Can be greater than 1 (not like engineering
efficiencies)  The larger the better
1111. Nyquist Channel capacity (Noisefree,
Errorfree)
 Idealized, theoretical
 Assumes a noisefree ? errorfree channel
 Nyquist showed that (without noise, without
errors) If rate of signal transmission is 2B
then a signal with frequency components up to B
Hz is sufficient to carry that signalling rate  In other words Given bandwidth B, highest
signalling rate possible is 2B signal elements/s  How much data rate does this represent?
 (depends on how many bits are represented by
each signal element!)  Given a binary signal (1,0), data rate is same as
signal rate ? Data rate supported by a BW of
B Hz is 2B bps ? C 2B  For the same B, data rate can be increased by
sending one of M different signals (symbols) as
each signal level now represents log2M bits  Generalized Nyquist Channel Capacity, C 2B
log2M bits/s (bps)  Bandwidth efficiency C/B 2 log2M
 (bits/s)/Hz Dimensionless quantity
bits/signal
Signals/s
112Nyquist Bandwidth Example
 C 2B log2M bits/s
 C Nyquist Channel Capacity
 B Bandwidth
 M Number of discrete signal levels (symbols)
used  Data on telephone Channel
B 3400300 3100 Hz  With a binary signal (M 2 symbols, e.g. 2
amplitudes)  C 2B log2 2 2B x 1 6200 bps
 With a quadnary signal (M 4 symbols)
 C 2B log2 4 2B x 2 4B 12,400 bps
 Channel capacity increased, but
 disadvantage Larger number of signal levels (M)
makes it more difficult for the receiver to
determine data correctly in the presence of noise
Signal Element
1
0
11
10
2 bits/Symbol i.e. 2 bits /signal
element
01
00
1132. Shannon Capacity Formula (Noisy, ErrorFree)
 Highest errorfree data rate in the presence of
noise  Signal to noise ratio SNR signal / noise levels
 SNRdB 10 log10 (SNR ratio)
 Errors are less likely with lower noise (larger
SNR ratios). This allows higher errorfree data
rates i.e. larger Shannon channel capacities  Shannon Capacity C B log2(1SNR)

 Highest data rate transmitted errorfree with a
given noise level  For a given BW, the larger the SNR the higher the
data rate I can use without introducing errors  C/B Spectral (bandwidth) efficiency, BE,
(bps/Hz) (gt1)  Larger BEs mean better utilization of a given
bandwidth B for transmitting data fast.
Caution! Log2 Not Log10
Caution! Ratio Not dBs
114Shannon Capacity Formula Comments
 Formula says for data rates ? calculated C, it
is theoretically possible to find an encoding
scheme that achieves errorfree transmission at
the given SNR But it does not say how!  Also
 It is a theoretical approach based on thermal
(white) noise only. But in practice, we also have
impulse noise, attenuation and delay distortions,
etc  So, maximum errorfree data rates measured in
practice are expected to be lower than the C
predicted by the Shannon formula due to the
greater noise  However, maximum errorfree data rates can be
used to compare practical systems The higher
that rate the better the system
115Shannon Capacity Formula Comments Contd.
 Formula suggests that changes in B and SNR can be
done arbitrarily and independently but  ? In practice, this may not be the case!
 Higher SNR obtained through excessive
amplification may also introduce nonlinearities ?
increased distortion and intermodulation noise
which reduces SNR!  High Bandwidth B opens the system up for more
thermal noise (kTB), and therefore reduces SNR!
116Shannon Capacity Formula Example
 Spectrum of communication channel extends from 3
MHz to 4 MHz  SNR 24dB
 Then B 4MHz 3MHz 1MHz
 SNRdB 24dB 10 log10 (SNR)
 SNR (ratio) log110 (24/10) 1024/10 251
 Using Shannons formula C B log2 (1 SNR)
 C 106 log2(1251) 106 8 8 Mbps
 Based on Nyquists formula, determine M that
gives the above channel capacity  C 2B log2 M
 8 106 2 (106) log2 M
 4 log2 M
 M 16
1173. Eb/N0 Vs Error Rate Formulation
(Noise and Error are both specified Together)
 Handling both noise and a quantified error rate
simultaneously  We introduce Eb/N0 A standard quality measure of
three channel parameters (B, SNR, R) and can also
be independently related to the error rate  R is the data rate. Max value of R is the
channel capacity C  It expresses SNR in a manner related to the data
rate, R  Eb Signal energy in one bit interval (Joules)
 Signal power (Watts) x bit interval Tb
(second)  S x (1/R) S/R
 N0 Noise power (watts) in 1 Hz kT. Two
formulations
Tb 1/R
SNR/BE
118Eb/N0 (Cont.)
BER vs Eb/N0 curve for a given encoding scheme
Lower Error Rate larger Eb/N0
 Bit error rate for digital data is a decreasing
function of Eb/N0 for a given signal encoding
scheme  Analysis ? For a given system (SNR, B, R) ?
(Eb/N0), determine error rate BER  Design ? Given a desired error rate BER, get
Eb/N0 to achieve it, then determine other
parameters from formula, e.g. S, SNR, R, etc.  Effect of S, R, T on error performance
 Which encoding scheme is better A
or B?
B
A
Better Encoding
SNR
BE
Max R C, BE C/B
119Example
 Given
 The effective noise temperature, T, is 290oK
 The data rate, R, is 2400 bps
 Would like to operate with a bit error rate of
104 (e.g. 1 error in 104 bits)  What is the minimum signal level required for the
received signal?  From curve, a minimum Eb/No needed to achieve a
bit error rate of 104 8.4 dB  8.4 S(dBW) 10 log 2400 228.6 dBW 10
log290  S(dBW) (10)(3.38) 228.6
(10)(2.46)  S 161.8 dBW
Design or Analysis?
120Eb/N0 in terms of BE, assuming Shannon channel
capacity
 From Shannons formula

 C B log2(1SNR)

 We have
 From the Eb/N0 formula



 C/B (bps/Hz) is the spectral (bandwidth)
efficiency BE based on Shannon channel capacity
121Example
 Find the minimum Eb/N0 required to achieve a
Shannon bandwidth efficiency (BECShannon/B)
of 6 bps/Hz  Substituting in the equation above
 Eb/N0 (1/6) (26  1) 10.5 10.21 dB