Dar es Sala Salaam am instit institute ute of Techn Technolog ology y (DIT) (DIT)
ET 8117 Introduction to Communication Systems Ally, J
[email protected]
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Course Outline
Principle of Communication System
AM Modulation
Angle Modulation
Digital coding
Digital Modulation
Errors
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Principle of Communication System
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Information Representation
Communication systems convert information into a format appropriate for the transmission medium. Channels convey electromagnetic waves (signals). Analog communication systems convert (modulate) analog signals into modulated (analog) signals Digital communication communication systems convert information in the form of bits into binary/digital signals Types of Information:
Analog Signals: Voice, Music, Temperature readings
Analog signals or bits: Video, Images
Bits: Text, Computer Data
Analog signals can be converted into bits by quantizing/digitizing
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Basic Mode of Communication There are two basic modes of communication:
Broadcasting: Broadcasting: which involves the use of a single powerful transmitter and numerous receivers that are relatively inexpensive to build. Here information-bearing signals flow only in one direction. Point-to-point communication: communication: in which the communication process process takes place place over a link between between a single transmi transmitter tter and a receiver. In this case, there is usually a bidirectional flow of information-bearing signals, which requires the use of a transmitter and receiver at each end of the link.
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Primary Communication Resources In a communication system, two primary resources are employed: Transmitted Power and Power and Channel Bandwidth. Bandwidth.
The Transmitted Power: is the average power of the transmitted signal The channel bandwidth is defined as the band of frequencies allocated for the transmission of the message signal
NB: A general system design objective is to use these two resources as efficiently as possible.
In most communication channels, one resource may be considered more important than the other. Therefore we may classify communication channels as Power limited or Band-limited. Example, the telephone circuit is a typical Band-limited channel, channel, whereas a space communication link or satellite channel is typically Power limited. limited.
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Source of Informatio Information n The telecommunications environment is dominated by four important sources of information: speech, music, pictures, and computer data
Speech Speech is the primary primary method method of human commu communicati nication on Music Music is the one originates originates from from instrument instruments s such as the piano, piano, violin, and flute Pictures Pictures is the one relies relies on the human human visual system system for for its perception. The picture can be dynamic, as in television, or static, as in fascim fascimile ile (fax) (fax) machin machine e Computer data is the information transmitted or exchanged through computer or other electronic devices
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Communication System Block Diagram
m(t )
x(t )
ˆ(t ) x
ˆ m
( t )
Source Source encoder converts converts message message into message message signal or bits. bits. Transmitter converts message message signal signal or bits into format appropriate appropriate for channel transmission (analog/digital signal).
Channel Channel introduces introduces distorti distortion, on, noise, and interferen interference. ce.
Receiver Receiver decodes decodes received received signal back back to message message signal.
Source Source decoder decodes decodes message signal signal back into original original message. message.
NB: NB: The good communication communication system system is to produce at the destination destination (receiver) an acceptable replica of the source message.
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Modulation and Demodulation
Modulation Is the process of changing ore or more properties such as amplitude, frequency, and phase of the analog carrier in proportion with the information signal
Performed in a transmitter by a circuit called a modulator
Demodulation
Is the reverse process of modulation and converts the modulated carrier back to the original information Performed in a receiver by a circuit called a demodulator
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Two Basic of Electronic Communication Communication System
An analog communication system Is a system in which energy is transmitted and received in analog form (a continuously varying signal such as sine wave)
Both the information and the carriers are analog signal
The digital communication system Covers a broad range of communication techniques, including digital digital transmi transmission ssion and digital digital radio
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Two Basic of Electronic Communication System(2)
Digital transmission - Is a true digital system system where digital digital pulses pulses are transferred transferred between between two or more point a communication system - There is no analog analog carrier, and the original source may be in digital or analog form - Require physical transmission medium medium such as metallic cable or optical fiber Digital Radio - Is the transmitted transmitted of digitally modulated modulated carrier between two or more points in a communication system - The modulating modulating signal and the demodulated signal signal are digital pulses - Digita Digitall pulse pulse modula modulate te an an analo analog g carrie carrier r - Transmissio Transmission n medium medium may be be a physica physicall facilit facility y or free space space (i.e. The Earth’s atmosphere)
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Advantage of using Digital transmission compared to Analog transmission
Increased immunity to channel noise and external interference Flexible operation of the system A common format for the transmission of different kinds of message signals (e.g. voice signals, video signals, computer data) Improved security of communication through the use of encryption
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Summary of various modulation technique
Analog Modulation Types
Amplitude Modulation Modulation (AM): is the one if the information information signal is analog analog and the amplitude (V) of the carrier is varied proportional to the information signal Frequency Modulation (FM): is the one if the frequency frequency (f) of the carrier is varied varied proportional to the information signal Phase modulation modulation (PM): (PM): is the one if the phase (θ) of the carrier is varied proportional to the information signal Digital Modulation Types
Amplitude Shift Shift Keying (ASK): (ASK): is the one if the information information signal is digital and the amplitude (V) of the carrier is varied proportional to the information signal Frequency Shift Keying (FSK): (FSK): is the one if the frequency frequency (f) of the carrier carrier is varied varied proportional to the information signal Phase Shift Keying (PSK): is the one if the phase (θ) of the the carrie carrierr is varied varied proportional to the information signal Quadrat Quadrature ure Amplitude Amplitude Modulat Modulation ion (QAM): (QAM): is the one if both the the amplitude amplitude (V) and and the phase (θ) of the carrier are varied proportional to the information information signal
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Why Modulation is necessary
It is extremely difficult to radiate low frequency signals from an antenna in the form of electromagnetic energy It is possible to combine a number of baseband (information) signal and send them through the medium, provided different carrier frequencies are used used for diffe differen rentt baseban baseband d signal signals s Transmitting signals over large distance, because low frequency signals have poor radiation characteristics
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Analog vs. Digital Systems
Analog signals
The amplitude changes continuously with respect to time with no discontinuities
Digital signals
The one which are discrete and their amplitudes maintains a constant level for prescribed period of time and then it changes to another level
Digital systems more robust
x(t)
t x(t)
Binary signals
Has at most 2 values Used to represent bit values Bit time T needed to send 1 bit Data rate R=1/T bits per second
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t x(t)
1 0
T
1 0 0
1 0
t
j
=
−
1
Line Spectra and Fourier Series Phasor Phasors s and line line spec spectra tra -we express sinusoids in terms of the cosine function and write
where A is the peak value or amplitude or amplitude θ
is the radian frequency
-The reciprocal of the period equals the cyclical frequency
-The phasor representation of a sinusoidal signal comes from Euler's theorem -we can write any sinusoid as the real part of a complex exponential, namely
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Periodic Signals and Average Power
Given any time function v(t), its average value over all time is defined as:
In the case of a periodic signal, the equation above reduces to the average over any interval of duration To, thus
Our definition of the average average power associated associated with an arbitrary arbitrary periodic signal then becomes
In any case, case, the value of P will be real and nonnegative nonnegative and the the signal v(t) is said said to have well defined average power, and will be called a periodic power signal
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Fourier Series
Let be a power signal with period Fourier series expansion is
The series coefficients are related to
. Its exponential
by
so , equals the average of the product since the coefficients are complex quantities in general, they can be xpressed in the polar form
where arg c, stands stands for for the angle of c
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Three important spectral properties of periodic power signals
All frequencies are integer multiples or harmonics or harmonics of the fundamental frequency fo = l/To. Thus Thus the spectral spectral lines have have uniform uniform spacing fo. fo.
The dc component equals the average value of the signal, by setting n = 0
If v(t) is a real (noncomplex) function of time, then
Replace the above equation by n=-n. Hence
which means that the amplitude spectrum has even symmetry and the phase spectrum has odd symmetry
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Example:
Consider the periodic train of rectangular pulses amplitude, A and width or duration
To calculate the Fourier
coefficients, we'll take the range of integration over the central period
,where
Thus,
For simplification simplification we use the sinc function, which which is Multiplying and dividing by
finally gives
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Fourier Transform Properties
Useful Properties
Linearity, time shift,Parseval
Key Properties
Time scaling
Duality
Operations in time lead to dual operations in frequency Fourier transform pairs are duals of each other
Frequency shifting
Contracting in time yields expansion in frequency
Multiplying in time by an exponential leads to a frequency shift.
Convolution and Multiplication
Multiplication in time leads to convolution in frequency Convolution in time leads to multiplication in frequency
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Fourier Transforms
If v(t) is the voltage across a resistance, resistance, the total total delivered energy would be found by integrating the instantaneous power . We therefore define normalized normalized signal energy as
NB: When the integral in the above equation exists and yields the signal u(t) is said to have well-defined well-defined energy and is called called a nonperiodic energy signal. signal.
To introduce the Fourier Fourier transform, transform, we'll start with the Fourier series representation representation of a periodic power signal
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Fourier Transforms(2)
Let the frequency spacing infinity such that the product
approach zero, and the index n approach approaches a continuous frequency variable f. Then
The bracketed term is the Fourier transform of v(t) symbolized by
or
and defined as:
The time function v(t) is recovered from V(f) by the inverse Fourier transform
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Pars Pa rsev eval al’s ’s Po Powe werr Theor Theorem em
Parseval's theorem relates the average power P of a periodic signal to its Fourier coefficients, which is
Homework Derive Derive Parseval's Parseval's theorem theorem by using the following following expression expression
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Rayle Ra yleigh igh's 's En Energ ergy y Th Theor eorem em
Rayleigh's Rayleigh's energy energy theorem theorem is is analogous analogous to to Parseval Parseval's 's power theorem. theorem. It states that the energy E of a signal v(t) is related to the spectrum V(f) by
it implies that gives the distribution of energy in the frequency domain, and therefore may be termed the energy spectral density
Rayleigh's theorem is actually a special case of the more more general integral relationship
Homework: Prove Rayleigh's Rayleigh's theorem by follows the same lines for the derivation of Parsev Parseval’ al’s s theore theorem m
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Duality Theorem
The theorem states that if v(t) and V(f) constitute a known transform pair, and if there exists a time function z(t) related to the function V(f) by then where v(-f) equals v(t) with t = -f
Therefore, we may replace f in fourier fourier transform equation with the dummy variable and write
Furthermore, since t is a dummy variable, z(t) = V(t) in the theorem,
Comparing these integrals then confirms that
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Time delay and Scale change
Specifically, replacing t by
, produces the time-delayed signal
If , is a negative quantity, the signal is advanced in time and the added phase has positive slope. The amplitude spectrum remains unchanged in either case, since
Scale change in the time domain becomes reciprocal scale change in the frequency domain, since
Hence, compressing a signal expands its spectrum, and vice versa. If then so both the signal and spectrum are reversed.
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Frequency Translation and Modulation
Besides generating new transform pairs, duality can be used to generate transform theorems. In particular, a dual of the time-delay theorem is
Since is not a real time function and cannot occur as a communication signal. However, signals of the form are common-in fact, they are the basis of carrier modulation-and by direct extension of the equation above we have the following modulation theorem: theorem:
The theorem is easily proved with the aid of Euler’s theorem
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Differentiation and Integration Differentiation in the time domain
Let
and assume that the first derivative of v(t) is Fourier transformable. transformable.
then
and by iteration we get
which is the differentiation theorem. Integration in the time domain
Let
then, provided V(0), the integration theorem says that then
The zero net area condition in the above equation ensures that the integrated signal goes to zero as
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Convolution Theorems
This property is listed below along with the associative and distributive properties
we now list the two convolution theorems:
The prove of above theorem is by using time delay theorem
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Special Functions
Dira Dirac c delt delta a func functi tion on
Exponentials Ae j2
f ct
π
(t)
(f-f c)
⇔
f c
Sinusoids Acos(2πf ct)
(f+f c)
⇔
(f-f c) -f c
f c
Delta Function Train Ts
-3Ts
-2Ts
-Ts
n
0
(t-nTs)
Ts
2Ts
3Ts
n
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-1/Ts
0
(t-n/Ts)
1/Ts
Sampling
Sampling (Time):
x(t)
0
(t-nTs)
n
=
xs(t)
0
0
Sampling (Frequency) X(f) 1
-B
*
(1/Ts)
n
(t-n/Ts)
Xs(f)
=
1/Ts
1/Ts
0
B
-1/Ts
0
1/Ts
-1/Ts
0
1/Ts
Nyquist: Must sample at T s<1/(2B) DITto recreate signal from samples
