Transcript Signal - 5th Semester Notes

CE-308 Communication System
Engr. Muhammad Noman Ali Khan
Lecturer
Computer Engineering Department
SSUET
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Communication Systems
Course Objectives
To develop the basic concepts of communication systems
Text Books
• Modern Digital and Analog Communication Systems. 3rd Edition by B.P.Lathi
• Digital communication Fundamentals and Application 2nd Edition by Bernald
Sklar
Reference books
• Communication Systems by Bruce Carlson
• Communication Systems 4th ed. By Simon Haykin
Marks Distribution
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Assignment + Quizzes
Attendance+ Discipline+Register
Lab Work
Mid Term Exam
Final Term Exam
05 Marks
05 Marks
15 Marks
15 Marks
60 Marks
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Course Outline
• Week 1-3
– Introduction to Communication System
– Basic concepts and definitions, Overview of Signals and Systems,
Nyquist an Shannon's Law
• Week 4-5
– Review of Fourier Series and Fourier Transform
• Week 6-8
– Formatting and Baseband Modulation
• Week 10-13
– Signal Space, Minimum distance detection
• Week 13-16
– Bandpass modulation, Coherent and non-coherent detection
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WEEK 1-3
• Introduction to Commuynication systemns
• Signals
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Mathematical expression of a signal
Signal parameters
Sinusoid waves concepts
Classifications of signals
Operation on signals
Time and Frequency Domain
Fourier analysis
Signal energy and power
Nyquist and Shannon’s Law
Communication System
• Communications involves transfer of information over a distance
OR
• Communication is a process by which information is exchanged
between individuals through a common system of symbols, signs,
or behaviour
• Communications had its beginning in 1837 with the
• invention of the telegraph by Samuel Morse, followed by
• the invention of the telephone in 1876.
• Communication systems are reliable, economical and efficient
means of communications
• Public switched telephone network (PSTN), mobile telephone
communication (GSM, 3G, ...), broadcast radio or television,
navigation systems, ...
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Communication System(Cont..)
Signal
–
The actual entity (electrical, optical, mechanical, etc.) that is
transmitted from sender to receiver.
Message
–
knowledge that is transmitted
Information
–
Knowledge communicated or received concerning some fact or
circumstance
Message and information are quite closely related.
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Communication System(Cont..)
scheme of a simplified communication system
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source: originates a message
transmitter: converts the message into a signal that can be
transmitted over a channel
• Channel: transport of the signal over a certain medium (e.g.
wire, optical fiber or a radio link)
• Receiver: converts the received signal back into a readable
message
• Sink/destination: end user
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Communication System
scheme of a (nearly) complete digital communication system
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adc (analog/digital converter): converts the physical analog signal into a digital electronic
signal
• source encoder: encodes the data in a format that removes redundancy and irrelevant
information
• modulator: adaptation of the frequency according to the channel characteristics
on the receiver side all transformation steps must be reversed
• channel encoder: encodes the signal pulses in a format that is required by the channel
• protocol: controls start, end of transmission and error recovery by adding additional bits for
error detection and/or correction
• noise: inside the channel the signal is disturbed by noise
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Communication System(Cont..)
• In a realistic channel a signal is disturbed by:
•noise: random and unpredictable modifications of the signal amplitude
•thermal noise, caused by random movements of electrons in conductors
•external noise, caused e.g. by interference with other channels
•attenuation: the amplitude of the signal decreased caused by the resistance
of the channel
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the maximum length is restricted; amplifiers are required in certain distances!
distortion: the distortion depends on the frequency, different signal frequencies
suffer different signal distortion.
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SIGNALS
• A signal is the form in which data is transmitted. Its
describes the behavior of data
Mathematical representation of a signal
• Signal can be Mathematically represented by a
dependent variable and independent variable
x(t) = t2 + 1
• Also a signal could be represented by sinusoidal
wave x(t) = Asin(2πft + θ )
• Parameters of the signal are: amplitude, phase and
frequency
• Deterministic and random signals
Signal parameters
•Sine Wave
•Amplitude ,Frequency Phase
The sine wave or sinusoid
•
The sine wave or sinusoid is a
mathematical function that describes a
smooth repetitive oscillation. It occurs
often in pure mathematics, as well as
physics, signal processing, electrical
engineering and many other fields. Its
most basic form as a function of time (t)
is:
•
•
where:
A, the amplitude, is the peak deviation of
the function from its center position.
ω, the angular frequency, specifies how
many oscillations occur in a unit time
interval, in radians per second
φ, the phase, specifies where in its cycle
the oscillation begins at t = 0.
– When the phase is non-zero, the
entire waveform appears to be
shifted in time by the amount φ/ω
seconds. A negative value represents
a delay, and a positive value
represents a "head-start".
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A cosine wave is said to be "sinusoidal",
because cos(x) = sin(x + π / 2), which is
also a sine wave with a phase-shift of π/2.
Occurrences of Sinusoids
Three sine waves with the same amplitude and frequency,
but different phases
Phase describes the position of the waveform relative to time 0.
•Time and Frequency Domain
•Composite Signals
The time-domain and frequency-domain plots of a sine wave
A complete sine wave in the time domain can be represented by one single
spike in the frequency domain.
The time domain and frequency domain of three sine waves
A single-frequency sine wave is not useful in data communications;
we need to send a composite signal, a signal made of many simple sine
waves.
Fourier Analysis
According to Fourier analysis, any composite
signal is a combination of
simple sine waves with different frequencies,
amplitudes, and phases.
If the composite signal is periodic, the
decomposition gives a series of signals
with discrete frequencies;
if the composite signal is nonperiodic, the
decomposition gives a combination of
sine waves with continuous frequencies.
A composite periodic signal
Decomposition of a composite
periodic signal in the time and
frequency domains
The time and frequency domains of a nonperiodic signal
Bandwidth
The bandwidth of periodic and nonperiodic composite signals
The bandwidth of a composite signal is the difference between the
.
highest and the lowest frequencies contained in that signal
Classifications of Signals
• Continuous-Time vs. Discrete-Time
– determined by whether or not the time axis (x-axis) is
discrete (countable) or continuous
– A continuous-time signal will contain a value for all real
numbers along the time axis.
– In contrast to this, a discrete-time signal is often created by
using the sampling theorem to sample a continuous signal,
so it will only have values at equally spaced intervals along
the time axis.
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Analog versus Digital
• The difference between analog and digital is similar to the
difference between continuous-time and discrete-time.
• Analog corresponds to a continuous y-axis, while digital
corresponds to a discrete y-axis. An easy example of a digital
signal is a binary sequence, where the values of the function
can only be one or zero.
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Analog versus Digital Communication
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Analog messages are characterized by data with values from a
continuous range.
they have an indefinite number of values
there is an indefinite number of possible waveforms in a time
interval.
• Digital messages are constructed from a finite number of
symbols.
• Mostly only a binary message is used.
Different kinds of digital signal are treated
identically.
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Analog versus Digital communication (Cont’d)
• Analog example:
• Digital example: (k=2)
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Analog versus Digital communication (Cont’d)
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In a binary digital signal a "1" can be transmitted by an electric pulse of amplitude
A/2, a "0" by a pulse of amplidude –A/2
Receiver must only decide, if the signal level is above 0 or not:
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transmitted signal
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received distorted
signal without noise
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received distorted signal with noise
•
regenerated signal
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Analog versus Digital communication (Cont’d)
• Distorted and noisy digital signals can mostly be recovered without error
• if repeaters are placed along a digital communication path, they can
regenerate the signal before amplifying it.
• digital messages can be reliably transmitted over long distances
• Distorted and noisy analog signals cannot be recovered
• there is no way to avoid accumulation of noise and distortion
• amplification does not help because both signal and noise are amplified in
the same proportion!
• analog messages can only be transmitted over short distances if a high
quality is desired
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Classification of signals
–Deterministic signal: No uncertainty with respect to the
signal value at any time.
–each value of the signal is fixed and can be determined by
a mathematical expression, rule, or table.
– future values of the signal can be calculated from past
values with complete confidence.
–Random signal: Some degree of uncertainty in signal values
before it actually occurs.
• Thermal noise in electronic circuits due to the random movement of
electrons
• Reflection of radio waves from different layers of ionosphere
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(a) Deterministic Signal
(b) Random Signal
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Classification of signals …
• Periodic and non-periodic signals
– Periodic signals repeat with some period T,
while aperiodic, or non-periodic, signals do not
A periodic signal
A non-periodic signal
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Classification of Signals
• Causal vs. Anticausal vs. Noncausal
– Causal signals are signals that are zero for all negative
time, while anticausal are signals that are zero for all
positive time. Noncausal signals are signals that have
nonzero values in both positive and negative time
(b) An anticausal signal
(a) A causal signal
(c) A noncausal signal
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Classification of Signals
• Even vs. Odd
– An even signal is any signal f such that f(t) =f(−t) .
– Even signals can be easily spotted as they are symmetric
around the vertical axis.
– An odd signal, on the other hand, is a signal f such that
f(t) =−(f(−t) )
(a) An even signal
(b) An odd signal
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Classification of Signals
• Right-Handed vs. Left-Handed
– A right-handed signal and left-handed signal are those
signals whose value is zero between a given variable and
positive or negative infinity.
(a) Right-handed signal
(b) Left-handed signal
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Signal Operations
• Time Shifting
– the shifting of a signal in time. This is done by adding or
subtracting the amount of the shift to the time variable in
the function. Subtracting a fixed amount from the time
variable will shift the signal to the right (delay) that
amount, while adding to the time variable will shift the
signal to the left (advance).
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Signal Operations
• Time Scaling
– Time scaling compresses and dilates a signal by multiplying
the time variable by some amount. If that amount is
greater than one, the signal becomes narrower and the
operation is called compression, while if the amount is less
than one, the signal becomes wider and is called dilation
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Signal Operations
• Time Reversal
– What happens when the time variable is multiplied by a
negative number? The answer to this is time reversal. This
operation is the reversal of the time axis, or flipping the
signal over the y-axis.
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Signal Energy and Signal Power
• Size
– The idea of the "size" of a signal is crucial to many
applications. It is nice to know how much electricity can be
used in a defibrillator without ill effects, for instance. It is
also nice to know if the signal driving a set of headphones
is enough to create a sound. For this reason, it is
convenient to quantify this idea of "size". This leads
to the ideas of signal energy and signal power.
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Signal Energy
• signal is a function of varying amplitude through time, so a good
measurement of the strength of a signal would be the area under the
curve.
• However, this area may have a negative part. This negative part does not
have less strength than a positive signal of the same size
• The negative part cancels the positive
Figure 1
•This suggests either squaring the
signal or taking its absolute value, then
finding the area under that curve
Figure 2
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Signal Energy
Fig 1
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Fig 2
A signal is an energy signal if, and only if, it has nonzero but finite energy for all time:
In integral form it can be represented as
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Signal Power
•
We know that the energy of a signal is given by squaring the signal or taking its
absolute value, then finding the area under that curve
•
But what if the signal does not decay? In this case we have infinite energy for any
such signal.
Power is defined as energy over a specific time interval and is given by
A signal is a power signal if, and only if, it has finite but nonzero power for all time:
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And in integral form it can be given as
General rule: Periodic
and random signals
are power signals.
Signals that are both
deterministic and
non-periodic are
energy signals.
SIGNAL TO NOISE RATIO
Two cases of SNR: a high SNR and a low SNR
3.40
SIGNAL TO NOISE RATIO
The power of a signal is 10 mW and the power of the noise is 1 μW; what are the
values of SNR and SNRdB ?
Solution
The values of SNR and SNRdB can be calculated as follows:
The values of SNR and SNRdB for a noiseless channel are
We can never achieve this ratio in real life; it is an ideal.
3.41
DATA RATE LIMITS
A very important consideration in data communications is how fast we can send
data, in bits per second, over a channel. Data rate depends on three factors:
1. The bandwidth available
2. The level of the signals we use
3. The quality of the channel (the level of noise)
We consider two laws
1. Nyquist Law
2. Shannon Law
3.42
Increasing the
levels of a signal
may reduce the
reliability of the
system.
Nyquist Law And Shannon Law
Nyquist Law :
C  2  B  Log2 L
Shannon’s Law :
C  B  Log2 SNR  1
Where
And
C= Data rate of the channel
B= Bandwidth of the signal
L= Number of levels in the signal
The Shannon capacity gives us the upper limit; the
Nyquist formula tells us how many signal levels we need.
•For Noiseless Channel:
•We use Nyquist Bit Rate
•For Noisy Channel:
•We use Shannon Capacity
•We also can use Both Limits
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Nyquist Law Examples
1.Consider a noiseless channel with a bandwidth of 3000 Hz transmitting a signal
with two signal levels. The maximum bit rate can be calculated as
2.Consider the same noiseless channel transmitting a signal with four signal levels
(for each level, we send 2 bits). The maximum bit rate can be calculated as
3.We need to send 265 kbps over a noiseless channel with a bandwidth of 20 kHz.
How many signal levels do we need?
using Nyquist formula as shown:
Since this result is not a power of 2, we need to either increase the number of
levels or reduce the bit rate. If we have 128 levels, the bit rate is 280 kbps. If we
have 64 levels, the bit rate is 240 kbps.
3.44
Shannon’s Law Examples
1.Consider an extremely noisy channel in which the value of the signal-to-noise
ratio is almost zero. In other words, the noise is so strong that the signal is faint.
For this channel the capacity C is calculated as
This means that the capacity of this channel is zero regardless of the bandwidth.
In other words, we cannot receive any data through this channel.
2.We can calculate the theoretical highest bit rate of a regular telephone line. A
telephone line normally has a bandwidth of 3000. The signal-to-noise ratio is
usually 3162. For this channel the capacity is calculated as
This means that the highest bit rate for a telephone line is 34.860 kbps. If we want
to send data faster than this, we can either increase the bandwidth of the line or
improve the signal-to-noise ratio.
3.45
Shannon’s Law Examples
3.The signal-to-noise ratio is often given in decibels. Assume that SNRdB = 36 and
the channel bandwidth is 2 MHz. The theoretical channel capacity can be
calculated as
4.For practical purposes, when the SNR is very high, we can assume that SNR +
1 is almost the same as SNR. In these cases, the theoretical channel capacity can
be simplified to
For example, we can calculate the theoretical capacity of the previous example as
3.46
Example
We have a channel with a 1-MHz bandwidth. The SNR for this channel is 63. What
are the appropriate bit rate and signal level?
Solution
First, we use the Shannon formula to find the upper limit.
The Shannon formula gives us 6 Mbps, the upper limit. For better performance we
choose something lower, 4 Mbps, for example. Then we use the Nyquist formula
to find the number of signal levels.
3.47