EXPERIMENT 2
INTRODUCTION TO COMMUNICATION SYSTEMS
USING SCILAB
1.0
OBJECTIVES
1.1
To characterize communication signal using SCILAB software.
1.2
To generates the Amplitude Modulation (AM) wave in time domain and
analyzing its frequency domain.
1.3
To analyze Amplitude Modulation signal with different modulation index
and other
2.0
types of AM signal.
Equipment / Apparatus
SCILAB Software
3.0
THEORY
3.1 Introduction to Communication Signal
In electronic communications one of the most important concepts that students
must learn that of time and frequency representation of communication signals.
Students must be able to analyze the time and frequency representation of a
signal, modify parameters, and immediately see the effect. An effective way of
doing this is using numerical computation and graphics program such as SCILAB.
Time and frequency domain representation of signals are concepts that is essential
in understanding the characteristics of amplitude and frequency modulated
signals. The ability to modify parameters and immediately see their effect on the
time and frequency representation of a signal is invaluable in understanding
communication signals.
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3.2 Amplitude Modulation (AM)
Amplitude modulation is the kind of modulation that is commonly used in AM
radio broadcasting, short-wave radio communications and telephone systems.
It is produced as the product of mixing 2 different frequencies, a lower frequency
called modulating signal ( m ) and a higher frequency called carrier signal ( c ),
through a balanced modulator circuit or mixer. The AM wave produced in this
manner is also called “ Double-Sideband Full Carrier “ or simply AM DSBFC. It
is shown as in Fig 1.1.
Fig 1.1 : Generation of AM wave.
The instantaneous modulating frequency signal equation can be expressed as,
(t)
Vsin(
2

f t)
m
m
m
---- (1.1)
where Vm is the peak amplitude of the modulating signal and f m is the frequency
of the modulating signal.
Also, the instantaneous carrier frequency signal equation can be expressed as,

(t)
V
2

fct)
c
csin(
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---- (1.2)
2
where Vc is the peak amplitude of the carrier signal and f c is the frequency of
the carrier signal.
Then, the instantaneous AM wave equation produced can be shown as,
 am (t )  [Vc  Vm sin( 2f mt )] sin( 2f ct )
If we consider the modulation index,
m
--- (1.3)
Vm
V  mVc ,
Vc , hence m
then substitute Vm into equation 1.3, the instantaneous AM wave equation would
be,





(
t
)

V

mV
sin(
2
f
t
)]
sin(
2
f
t
)
c
m
c
amc

V
[
1

m
sin(
2
f
t
)]
sin(
2
f
t
)
c
m
c
--- (1.4)
Modulation Index (m)
The modulation index (m) also can be determined by AM wave output waveform
shown as in Fig.1.2
Fig.1.2 : AM wave output waveform
The modulation index,
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V 
V
m
 max min
V

V
max
min
----- ( 1.5)
3
E
E
max
c
m and
where V
V
E
E
min
c
m
Normal modulation index operation, 0  m  1. If m  1 , over-modulation
will occur.
3.2 Amplitude Modulation (AM) in SCILAB
AM Definition:
Amplitude modulation is a process of varying the amplitude of a radio frequency
(RF) carrier wave by a modulating voltage or audio signal which usually consists
of a range of audio frequencies, for example speech or music signals.
Why we have to modulate a signal for transmission. There are two reasons for
modulation 1) law of electromagnetic propagation and 2) the simultaneous
transmission of different signal. There are many different types of AM, such as
Double Sideband Suppressed Carrier (DSB-SC) and Single Sideband (SSB).
The modulation of a carrier signal will be performed in this lab which is using
SCILAB. The Spectral calculation will be made using the mtlab_fft () function.
The SCILAB environment can be effective tool for viewing effects of various
form of modulation. In the following exercise, the modulated signal will examine
in both the time and frequency domain.
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4.0
EXAMPLE
Example 1:
1. Equation 1 below is a sinusoidal expression for amplitude modulation signal.
 
V
(
t
)

(
E

E
Sin
(
t
)

E
Sin
(
t
)

E
Sin
(
t
))

Sin
(
t
)
AM
c
m
1
m
1
m
2
m
2
m
3
m
3
c
Compute the expression using Scilab to analyze the signal in Time Domain. Given
the carrier frequency is 500 Hz and the amplitude is 4V. It is modulated by a signal
made up of three sinusoidal or modulating signals with the following frequencies:-
fm1 = 400 Hz , Em1 = 5 V ; fm2 = 250 Hz , Em2 = 2 V ; fm3 = 125 Hz , Em3 = 8 V
Solution
// generate time domain signal
t = 0:0.01:1; // declare interval
// insert all the information given
Ec = 4;
Em1 = 5;
Em2 = 2;
Em3 = 8;
fm1 = 400;
fm2 = 250;
fm3 = 125;
fc = 500;
// Amplitude modulation Equation
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A=
Ec+Em1*sin(((2*%pi)*fm1)*t)+Em2*sin(((2*%pi)*fm2)*t)+Em3*sin(((2*%pi)*fm3
)*t);
Vam = A .*sin(((2*%pi)*fc)*t);
scf(1);
// figure1
plot (1:size(A,2),A);
scf(2);
//figure2
plot(1:size(vam,2),Vam)
Figure 1: Carrier Frequency
Figure 2: Time Domain representation of AM with a modulation signal composed of
three sinusoids plotted by SCILAB
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The frequency domain of the complex AM signal can be obtained by taking the Fast
Fourier transform of the time domain signal. The expression for evaluating FFT using
SCILAB is shown below.
Vf = abs(mtlb_fft(vam,2048))/1024;
scf(3); //figure3
plot(Vf)
NOTE: command scf() also can use subplot()
210 , 211  for graph scale, can use any number
The FFT result, display the three separate frequency component of the modulation
signals. Their frequency and amplitude characteristic are present of the frequency
representation. This information is not evident in the time domain representation.
Figure 3: Frequency Domain representation of AM with a modulation signal composed
of three sinusoids.
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Example 2:
With the following data, use SCILAB to generate and display an Amplitude Modulation
signal.
Carrier frequency fc = 5 kHz
Amplitude Carrier frequency = Ac = 9 V
Sampling time = 100 ms
Modulating frequency =500 Hz
Amplitude Modulating Signal Am = 4.5 V
Hint :   2ft
Solution
// generate carrier signal
fc = 5000;
Ac = 9;
t = linspace(0,10*(10^(-3)),500);
Vc = Ac*sin(((2*%pi)*fc)*t);
subplot(411)
plot(t,Vc)
// generate modulating signal
fm = 500;
Am = 4.5;
Vm = Am*sin(((2*%pi)*fm)*t);
subplot(412)
plot(t,Vm)
// generate modulation signal with index modulation m = 0.5
m = Am/Ac;
Vt = (Ac*(1+m*sin(((2*%pi)*fm)*t))) .*sin(((2*%pi)*fc)*t);
subplot(413)
plot(t,Vt)
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Figure 4) i) Carrier Signal
ii) Modulating Signal
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iii) Amplitude Modulation Signal
9
5.0
EXERCISE
1. Generate Amplitude Modulation signal for index modulation, m<1 , m = 1 and
m > 1.
2. Use SCILAB to produce AM wave with the following specification
Modulating Wave
Sinusodal
Modulation Frequency
1kHz
Carrier frequency
20kHz
Percentage Modulation
75%
3. In Double Side Band – Suppressed Carrier (DSB-SC) modulated wave, the carrier
is suppressed and both sideband are transmitted in full. The signal is produced
simply by multiplying the modulating wave by the carrier wave.
Given, carrier signal, Vc(t) = 10 Sin 10000t , Modulating signal Vm(t) = 5 Sin
1000t and the modulation index m = 1.
a) Generate and display the DSB-SC modulated wave (time
domain)
b) Computed and display the spectrum of the modulated wave.
(frequency domain.)
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