Analogue and Digital Communication Lab

(EL-3003)

LABORATORY MANUAL

Engr. Fakhar Abbas

DSB-SC, SSB-SC and Conventional Amplitude Modulation
using Matlab
(LAB # 05)
Student Name: Muhammad Sarmad Fowad

Roll No: 22I-2222 Section: A

Date performed: 9 September, 2024

NATIONAL UNIVERSITY OF COMPUTER AND EMERGING SCIENCES, ISLAMABAD

Prepared by: Engr. Fakhar Abbas Version: 2.01

Verified by: Dr. Shazad Saleem Updated: Fall 2024

 Analogue and Digital National University Roll No: L
Communication Lab
(EL3003)
of Computer and Emerging Sciences
Islamabad Fall 2024
a
b 05
#

Lab # 05: DSB-SC, SSB-SC and Conventional Amlitude Modulation using

Matlab
Learning Objectives:
1. Implementation of DSB-SC, SSB-SC and Conventional AM Schemes in both time and frequency
domain using MATLAB
2. Effect of Modulation Index on the Modulated Signal in case of CAM.
Equipment Required:
1. PC
2. Matlab

In this lab we will study the performance of various analog amplitude modulation-demodulation schemes,
both in the presence and in the absence of additive noise. Systems studied in this chapter include
amplitude-modulation (AM) schemes, such as DSB-AM, SSB-AM, and conventional AM. Each member of
the class of analog modulation systems is characterized by five basic properties:
1. Time-domain representation of the modulated signal
2. Frequency-domain representation of the modulated signal
3. Bandwidth of the modulated signal
4. Power content of the modulated signal
5. Signal-to-noise ratio (SNR) after demodulation

A)Amplitude Modulation (AM)

Amplitude modulation (AM), which is frequently referred to as linear modulation, is
the family of modulation schemes in which the amplitude of a sinusoidal carrier ischanged as a function of
the modulating signal. This class of modulation schemesconsists of DSB-AM (double-sideband amplitude
modulation), conventional amplitude modulation, SSB-AM (single-sideband amplitude modulation), and
VSB-AM (vestigial-sideband amplitude modulation). The dependence between the modulatingsignal and
the amplitude of the modulated carrier can be very simple, as, for example,in the DSB-AM case, or much
more complex, as in SSB-AM or VSB-AM. Amplitude-modulation systems are usually characterized by a
relatively low bandwidth requirement and power inefficiency in comparison to the angle-modulation
schemes. Thebandwidth requirement for AM systems varies between W and 2W, where W denotesthe
bandwidth of the message signal. For SSB-AM the bandwidth is W, for DSB-AM and conventional AM the
bandwidth is 2W, and for VSB-AM the bandwidthis between W and 2W. These systems are widely used in
broadcasting (AM radioand TV video broadcasting), point-to-point communication (SSB), and
multiplexingapplications (for example, transmission of many telephone channels over microwavelinks).

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 Analogue and Digital National University Roll No: L
Communication Lab
(EL3003)
of Computer and Emerging Sciences
Islamabad Fall 2024
a
b 05
#

1) DSB-SC:
In DSB-AM, the amplitude of the modulated signal is proportional to the message signal. This means that
the time-domain representation of the modulated signal is given by
𝑢(𝑡) = 𝐴 𝑚(𝑡) 𝑐𝑜𝑠(2π𝑓 𝑡)
𝐶 𝐶

Where
𝑐(𝑡) = 𝐴 𝑐𝑜𝑠(2π𝑓 𝑡)
𝐶 𝐶

is the carrier and m(t) is the message signal. The frequency-domain representation of the DSB-AM signal
is obtained by taking the Fourier transform of u(t) and results in
𝐴𝐶 𝐴𝐶
𝑈(𝑓) = 𝑀(𝑓 − 𝑓𝑐) + 𝑀(𝑓 + 𝑓𝑐)
2 2

where M(f) is the Fourier transform of m(t). Obviously, this type of modulation results in a shift of ±fc and
a scaling of Ac/2 in the spectrum of the message signal. The transmission bandwidth, denoted by Bt, is
twice the bandwidth of the message signal:
𝐵𝑇 = 2𝑊

A typical message spectrum and the spectrum of the corresponding DSB-AM modulated signal are shown
in below given Figure

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 Analogue and Digital National University Roll No: L
Communication Lab
(EL3003)
of Computer and Emerging Sciences
Islamabad Fall 2024
a
b 05
#

The power content of the modulated signal is given by

2
𝐴𝐶
𝑃 = 𝑃
𝑢 2 𝑚
𝑇
where 𝑃 = 1 2 2
𝑚 𝑇
∫ 𝑚 (𝑡) 𝑑𝑡
𝑇
−2

Pm is called the power content of message signal.

Block diagram of DSB-SC is given below.

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 Analogue and Digital National University Roll No: L
Communication Lab
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of Computer and Emerging Sciences
Islamabad Fall 2024
a
b 05
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2. SSB-SC Modulation:
SSB-AM is derived from DSB-AM by eliminating one of the sidebands. Therefore,it occupies half the
bandwidth of DSB-AM. Depending on the sideband that remains,either the upper or the lower sideband,
there exist two types of SSB-AM: Upper Single Sideband AM (USSB-AM) and Lower Single-Sideband
AM (LSSB-AM). The timerepresentation for these signals is given by
𝐴𝐶 𝐴𝐶 ^
𝑢(𝑡) = 𝑚(𝑡)𝑐𝑜𝑠(2π𝑓 𝑡) ∓ 𝑚(𝑡)𝑠𝑖𝑛(2π𝑓 𝑡)
2 𝑐 2 𝑐

where the minus sign corresponds to USSB-AM and the plus sign corresponds toLSSB-AM. The signal
^ ^
denoted by 𝑚(𝑡) is the Hilbert transform of m(t), defined by 𝑚(𝑡) = 𝑚(𝑡) * 1/(π𝑡) or,in the frequency
^
domain,by 𝑀(𝑓) =− 𝑗𝑠𝑔𝑛(𝑓)𝑀(𝑓).
In other words, the Hilbert transform of a signal represents a π/2 phase shift in all frequency components.
In the frequency domain, we have

Typical plots of the spectra of a message signal and the corresponding USSB-AM
modulated signal are shown in below given Figure:

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 Analogue and Digital National University Roll No: L
Communication Lab
(EL3003)
of Computer and Emerging Sciences
Islamabad Fall 2024
a
b 05
#

The bandwidth of the SSB signal is half the bandwidth of DSB and conventionalAM and so is equal to the
bandwidth of the message signal; that is, 𝐵 = 𝑊
𝑇
2
𝐴
The power in the SSB signal is given by 𝑃 = 𝐶
𝑃
𝑢 4 𝑚

Note that the power is half of the power in the corresponding DSB-AM signal becauseone of the sidebands
has been removed.

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 Analogue and Digital National University Roll No: L
Communication Lab
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of Computer and Emerging Sciences
Islamabad Fall 2024
a
b 05
#

3) Conventional AM:
In many respects conventional AM is quite similar to DSB-AM; the only difference is that in conventional
AM, m(t) is substituted with [1 + 𝑎𝑚 (𝑡)], where 𝑚 (𝑡) is the normalized message signal (i.e.,
𝑛 𝑛
|𝑚 (𝑡)| < 1 and 𝑎 is the index of modulation, which is a positive constant between 0 and 1. Thus we
𝑛
have
𝑢(𝑡) = 𝐴 [1 + 𝑎𝑚 (𝑡)] 𝑐𝑜𝑠(2π𝑓 𝑡)
𝐶 𝑛 𝑐

And
𝑈(𝑓) = 𝐴 [δ(𝑓 − 𝑓𝑐) + 𝑎𝑀 (𝑓 − 𝑓𝑐) + δ(𝑓 + 𝑓𝑐) + 𝑎𝑀 (𝑓 + 𝑓𝑐)]
𝐶 𝑛 𝑛

The net effect of scaling the message signal and adding a constant to it is that the term[1 + 𝑎𝑚 (𝑡)] is
𝑛
always positive. This makes the demodulation of these signals much easier by employing envelope
detectors. Note the existence of the sinusoidal component at the frequency fc in U(f). This means that a
(usually substantial) fraction of the transmitted power is in the signal carrier that does not really serve the
transmission of information. This fact shows that compared to DSB-AM, conventional AM is a less
economical modulation scheme in terms of power utilization. The bandwidth, of course, is equal to the
bandwidth of DSB-AM and is given by
𝐵 = 2𝑊
𝑇

Typical frequency-domain plots of the message and the corresponding conventional

AM signal are shown in below given Figure:

The power content of the modulated signal, assuming that the message signal is azero-mean signal, is
2
𝐴𝐶 2
given by 𝑃 = (1 + 𝑎 𝑃 )
𝑢 2 𝑚
𝑛

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 Analogue and Digital National University Roll No: L
Communication Lab
(EL3003)
of Computer and Emerging Sciences
Islamabad Fall 2024
a
b 05
#
2 2
𝐴𝐶 𝐴𝐶 2
which comprises two parts, , which denotes the power in the carrier, and 𝑎𝑃 which is the power
2 2 𝑚
𝑛

in the message-bearing part of the modulated signal. This is the power that is really used to transmit the
message. The ratio of thepower that is used to transmit the message to the total power in the modulated
signal iscalled the modulation efficiency and is defined by
2
𝑎 𝑃
𝑚
η= 2
𝑛

1+𝑎 𝑃
𝑚
𝑛

Because |𝑚 (𝑡)|< 1 and a < 1, we always have η< 0.5. In practice, however, thevalue of η is around 0.1.
𝑛

Problem 01: DSB-SC, SSB-SC & CAM Analysis

□ Set 𝐹𝑠 = 1000 samples/sec.

□ Set 𝑓 = 5 𝐻𝑧
𝑚

□ Set 𝑓 = 100 𝐻𝑧
𝑐
𝐴
□ Take 𝐴 & 𝐴 accordingly and define modulation index 𝑎 = 𝑚

𝑚 𝑐 𝐴𝑐

□ Set the time vector of 1sec duration for plotting the message signal .
□ Define message signal that is 𝑚(𝑡) = 𝐴 𝑐𝑜𝑠(2π𝑡5𝑡) .
𝑚

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Analogue and Digital National University Roll No: L
Communication Lab
(EL3003)
of Computer and Emerging Sciences
Islamabad Fall 2024
a
b 05
#

□ Define the carrier signal as 𝑐(𝑡) = 𝐴 𝑐𝑜𝑠(2π100𝑡) .

𝑐

□ Define DSB-SC modulated signal by mulitplying 𝑚(𝑡) & 𝑐(𝑡)

□ Define SSB-SC modulated signal by first taking hilbert of message signal and then multiply it with
𝑗2π𝑓𝑐𝑡
complex exponential 𝑒 . Now take the real part of this SSB-SC Modulated Signal. Note here 𝑓
𝑐
is +ve, so we are cancelling lower sideband and taking only upper sideband. If we mulitply with
−𝑗2π𝑓 𝑡
𝑐
𝑒 , we will retain the lower sideband.
□ Define CAM as [1 + 𝑎𝑚(𝑡)]𝑐(𝑡).
□ Plot all time domain signals 𝑚(𝑡), 𝐷𝑆𝐵 & 𝐶𝐴𝑀 in Figure 1 using subplots.
𝑆𝐶
𝐹𝑠 𝐹𝑠
□ Define the frequency axis from − 𝑡𝑜 containing samaples equals to the number of samples
2 2
in time domain signal that is N.
□ Take fft of all modulated siganls, normalize them that is divide by N and then apply fftshift on the
result.
□ Plot the magnitude specturm in the frequency domain for all modulated siganals in Figure 2 using
subplots.
□ Now change the amplitude of either message or carrier and see the effect in the time & frequency
domain plots.

Fs = 1000;
fm = 5;
fc = 100;
Am = 1;
Ac = 1;
a = Am * Ac;
t = 0:1/Fs:1-1/Fs;
% Define Signals
mt = Am * cos(2 * pi * fm * t); % Message signal
ct = Ac * cos(2 * pi * fc * t); % Carrier signal
% DSB-SC Modulated Signal
dsb_sc = mt .* ct;
% SSB-SC Modulated Signal
mt_analytic = hilbert(mt); % Analytic signal of mt
ssb_sc = real(mt_analytic .* exp(1j * 2 * pi * fc * t)); % SSB-SC Modulated
Signal
% CAM Signal
cam = (1 + a * mt) .* ct;
% Plot Time-Domain Signals
figure;
subplot(3, 1, 1);

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Analogue and Digital National University Roll No: L
Communication Lab
(EL3003)
of Computer and Emerging Sciences
Islamabad Fall 2024
a
b 05
#

plot(t, mt);
title('Message Signal (mt)');
xlabel('Time (s)');
ylabel('Amplitude');
grid on;
subplot(3, 1, 2);
plot(t, dsb_sc);
title('DSB-SC Modulated Signal');
xlabel('Time (s)');
ylabel('Amplitude');
grid on;
subplot(3, 1, 3);
plot(t, cam);
title('Carrier Amplitude Modulation (CAM)');
xlabel('Time (s)');
ylabel('Amplitude');
grid on;
% Compute and Plot Frequency-Domain Signals
N = length(t);
f = (-N/2:N/2-1)*(Fs/N);
% FFT and normalization
fft_dsb_sc = fftshift(fft(dsb_sc) / N);
fft_ssb_sc = fftshift(fft(ssb_sc) / N);
fft_cam = fftshift(fft(cam) / N);
% Plot Frequency-Domain Signals
figure;
subplot(3, 1, 1);
plot(f, abs(fft_dsb_sc));
title('Frequency Domain - DSB-SC');
xlabel('Frequency (Hz)');
ylabel('Magnitude');
grid on;
subplot(3, 1, 2);
plot(f, abs(fft_ssb_sc));
title('Frequency Domain - SSB-SC');
xlabel('Frequency (Hz)');
ylabel('Magnitude');
grid on;
subplot(3, 1, 3);
plot(f, abs(fft_cam));
title('Frequency Domain - CAM');
xlabel('Frequency (Hz)');
ylabel('Magnitude');
grid on;

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Analogue and Digital National University Roll No: L
Communication Lab
(EL3003)
of Computer and Emerging Sciences
Islamabad Fall 2024
a
b 05
#

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