2. Communication System
A Communication system in the most simplest form can be defined
as any system which can help with the transmission of useful
information from one point to another.
6. Analog or Digital
Common Misunderstanding: Any transmitted signals are
(ANALOG. NO DIGITAL SIGNAL CAN BE TRANSMITTED)
The channel we transmit information through is not digital in
nature
It looks at the signal as voltage waveform as a function of time.
Analog Message: continuous in amplitude and over time
AM, FM for voice sound
Traditional TV for analog video
First generation cellular phone (analog mode)
Record player
Digital message: 0 or 1, or discrete value
VCD, DVD
2G/3G cellular phone
Data on your disk
8. Transmitter Characteristics
A carrier signal is required to carry information which
can then be transmitted over the channel.
Typically, a carrier signal would be a pure sine wave
a high frequency signal.
This process is called Modulation
Could modify the Amplitude of the carrier to get AM
Also FM or PM can be achieved by modifying the
frequency and Phase of the carrier signal
The mathematical expression for the carrier signal will
be given on the next slide as
9. Transmitter Characteristics
Change parameters of a carrier
vam ( t ) = Ac cos ( 2π f c t + θ c )
Information signal: Ac(t)
fc(t)
θ(t)
Analog Digital
Ac(t)
fc(t)
θ(t)
: amplitude modulation
: frequency modulation
: phase modulation
Ac(t) and θ(t) ⇒
QAM (Digital)
AM
FM
PM
ASK
FSK
PSK
10. Communication Channel
Physical medium
Free space
Cables
Optical fibres
Easier to work with
Relatively cleaner
Less prone to undesired effects as we face
in free space
Pair of copper wires / coaxial cables
offer larger bandwidths
A communication channel block also models
Channel
Attenuation
Noise
Distortion
11. Noise in Communication Channel
Channel is the main source of noise in communication
systems
Transmitter or Receiver may also induce noise in the
system
Noise in Communication Systems
There are mainly 2-types of noise sources
Internal noise source ( are mainly internal to
the communication system)
External noise source
External Noise Sources
Natural
Man-made
12. Noise in Communication Channel
Lightening Discharges
Biggest natural source which causes large amounts of
EM-radiation
It’s a very large magnitude waveform / impulse or A
narrow burst of large energy.
Very important because they have the potential to
interfere over a large frequency range.
Since actually it’s a pulse of finite duration
The spectrum of a pulse of finite duration is defined by
Sinc function
If the lightening discharge is of ‘Ƭ’ seconds, the
spectrum can be given by
This is always b/w +1 to -1
Sinc (f Ƭ) = Sin π f Ƭ
πfƬ
13. Noise in Communication Channel
Since this is the function of frequency, we will have
α 1 / f Also sometimes called atmospheric noise
This noise have spectrum which decays with frequency
Also this noise affect more at lower frequency bands then
at higher frequency bands
In time domain
This noise is characterised by large amplitude narrow pulses
Also called Impulsive noise
AM Broadcast Radio (550KHz to 1.6MHz)
more affected by
this noise
FM Broadcast Radio (>50MHz)
Not much affected by this
noise
14. Noise in Communication Channel
Man-made Noise Sources
High voltage power-line discharges
Electrical motor noise generated by armature and switching
taking place in the motor
Ignition noise in automobiles and aircraft
At Telephone exchanges where switching (electrical) takes
place is a source of Impulsive Noise.
Radio Frequency Interference (RFI)
Many users communicate at the same time
High density transmission environment particularly in the
context of mobile communication
A lot of wireless systems are working in parallel
Interference
RADAR communication taking place
Satellite communications / Wireless and mobile communication
etc
15. Noise in Communication Channel
Radio Frequency Interference (RFI)
Natural Source
Due to extra-terrestrial sources
Sun and stars are the sources of this noise
Internal Noise Sources
Fading effects due to multi-paths propagation b/w transmitter
and receiver.
Constructive or Destructive
Thermal Noise
Occurs due to
interference occurs at the receiver
random motion of free electrons in a
conductor or a semi-conductor.
Tx
Rx
Even when the voltage is not applied
the electrons stays in random motion.
Thermal noise is present in almost all
electrical component like diodes,
resistors, transistors etc.
Multi-path Fading
effect
16. Noise in Communication Channel
Since there are thousands of these components used
overall effect of the thermal noise is quite significant.
the
Shot Noise
Random arrival of charged carriers in semiconductor devices i.e. transistor / diodes
All active devices have charged carriers
The move between junction (PN junctions)
This random motion generates Shot Noise
Collectively Thermal and Shot Noise can significantly
degrade the performance of a communication system
17. Signal Analysis
Signal
analysis
is
very
important
in
communication theory and system and circuit
design.
In order to predict and understand electronic
system and circuit behavior, we use the results of
mathematical analysis.
The most common representation of signals and
waveforms is in the time domain. However,
most signal analysis techniques work only in the
frequency domain.
18. Time & Frequency Domains…
In a digital communications link design, a good
grounding is needed in the relationship between
the shape of a digital waveform in the time
domain and its corresponding spectral content in
the frequency domain.
Time domain
signal as a function of time.
Analog signal
signal’s amplitude varies
continuously over time, i.e. no discontinuities.
Digital signal
data represented by sequence of
0’s and 1’s (e.g., square wave).
19. Time / Frequency Domains
The performance of a digital communications link
is constrained by two primary factors:
Channel Bandwidth
how much of the frequency spectrum do we give
each user?
System Noise
both thermal (kTB) and man made!
Both of these effects are more evident in
frequency domain
20. Time / Frequency Domains
A grasp of the frequency content of various
types of time domain data signals is key to
understand the interaction between:
System data / Symbol rate
Modulation type
Pulse shape
and
Channel bandwidth
It is difficult to extract the above information
from the time domain waveform but frequency
domain waveform gives all this information.
21. Time domain – Sine Wave
zero crossing
amplitude
(volts)
period t
time
(seconds)
frequency = 1/t
if t = 1 ms, f= 1 kHz
22. Frequency Domain
Signal consists of components of different
frequencies.
Spectrum of signal: Range of frequencies
a signal contains.
Absolute bandwidth: Width of signal’s
spectrum or spectrum occupied by the
signal
Bandwidth also refers to the information
transmission capability
24. Frequency Domains
The frequency domain is simply another
way of representing a signal. For example,
consider a simple sinusoid
25. Frequency Domain
The time - amplitude axes on which the
sinusoid is shown define the time plane.
If an extra axis is added to represent
frequency, then the sinusoid would be
26. Frequency Domain Analysis
The frequency - amplitude axes define the frequency
plane in a manner similar to the way the time plane is
defined by the time - amplitude axes.
The frequency plane is orthogonal to the time plane,
and intersects with it on a line which is the amplitude
axis.
The actual sinusoid can be considered to be as
existing some distance along the frequency axis away
from the time plane.
This distance along the frequency axis is the
frequency of the sinusoid, equal to the inverse of the
period of the sinusoid.
27. Frequency Analysis
• Fast & efficient insight on signal’s building blocks.
• Simplifies original problem –
• Powerful & complementary to time domain analysis techniques.
• Several transforms in DSPing: Fourier, Laplace, z, etc.
• Based primarily on Fourier series & Transform
analysis
time, t
General Transform as
problemproblem-solving tool
frequency, f
F
S(f) = F[s(t)]
s(t)
synthesis
s(t), S(f) :
Transform Pair
31. The Phasor: Definition
The Phasor is a complex number that carries the amplitude
and phase angle information of a sinusoidal function.
Euler’s
identity
1 jθ
e + e − jθ
2
1 jθ
sin θ = − j e − e − jθ
2
e jθ = cosθ + j sin θ
e ± jθ = cosθ ± j sin θ
cos θ = ℜ{e jθ }
jθ
sin θ = ℑ{e }
cosθ =
[
]
[
Real
e − jθ = cosθ − j sin θ
Imaginary
v = Vm cos( t +φ) = Vmℜ{e
ω
]
j (ωt +φ )
jωt jφ
} = Vmℜ{e e }
32. The Phasor
v = ℜ{Vm e jφ e jωt }
Complex number that carries the amplitude and
phase angle of the given sinusoidal function.
Phasor Transform
V = Vm e jφ = Ρ{Vm cos(ωt + φ )}
(polar form)
Phasor transform of Vmcos(ωt+φ)
ω φ
The Phasor transform transfers the sinusoidal function from the
time domain to the complex-number domain (the frequency
domain), since the response depends on ω.
V = Vm cos φ + jVm sin φ
(rectangular form)
36. Phasor Signals and Spectra (cont.)
A sinusoid is usually represented by a complex
exponential or Phasor form
Euler’s Theorem: e ± j θ = c o s θ ± j s i n θ
Theorem:
−1 and θ is an arbitrary angle
where j
θ = ω0t + φ , then any sinusoid can be written
Let
as the real part of a complex exponential:
exponential:
e j (ω0t +φ )
A cos(ω0t + φ ) = A Re
Ae jφ e jω0t
= Re
37. Phasor Signals and Spectra (cont.)
The diagram shows a Phasor representation of a signal
because the term inside the brackets may be viewed as a
rotating vector in a complex plane whose axes are the real
and imaginary parts.
The phasor has length A, rotate
countercounter-clockwise at a rate f0 revolution
per second, and at time t = 0 makes an
angle φ with respect to the positive
real axis.
The three parameters that completely
specifies a phasor:
phasor:
1)
Amplitude;
Amplitude;
2)
Phase angle; and
angle;
3)
Rotational frequency
Phasor
representation
38. Phasor Signals and Spectra (cont)
To describe the same phasor in the frequency domain, the
domain,
corresponding amplitude and phase must be associated
with the particular frequency, f0, giving us the LINE
SPECTRA.
SPECTRA. (Line spectra have great conceptual value when
extended to more complicated signals)
Amplitude Spectrum
Phase Spectrum
41. Fourier Series and Fourier
Transform
Fourier series representation for periodic
signals
Fourier transform for general periodic and
nonnon-periodic signals
42. Fourier Series and Fourier Transform
Defined for periodic signals.
Periodic signals repeats
themselves over time and
given by property x (t+To) = x(t)
for all values of T0
43. Reading Assignment
Go through Time and frequency domain
concepts
Fourier Transforms and FFTs in your own
time.
Check Bruce Carlson or Haykin’s books for
further reading
