COMMUNICATION SYSTEMS- CONTINUOUS
Group B
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Ali Qasim
Haris Suhail
Imaan Tariq
Mohsin Zafar
Arsalan Hameed
Abdul Rahman
Rida Zainab
Ehsanullah Zafar
Hassan Iqbal
Amna Aziz
Manal Fatima
Qambar Rizvi
Classification of Modulation
LINEAR MODULATION
Amplitude Modulation
𝑦 𝑡 = 𝑥 𝑡 𝑐(𝑡)
Where 𝑥 𝑡 is the information bearing signal
𝑐 𝑡 is the carrier signal (frequency range: 500 kHz to 2 MHz)
𝑦 𝑡 is the modulated signal
There are two ways for amplitude modulation:
1) Complex Exponential Amplitude Modulation
2) Sinusoidal Amplitude Modulation
Complex Exponential Amplitude Modulation
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Carrier signal 𝑐 𝑡 = 𝑒 𝑗(𝜔𝑐 𝑡+𝜃𝑐 )
Assuming that phase angle 𝜃𝑐 = 0 (for simplicity)
𝑦 𝑡 = 𝑥(𝑡)𝑒 𝑗𝜔𝑐 𝑡
Transformation into the frequency Domain
Implementation of Complex Modulation
We get two signals after
modulation one is real
and the other is complex.
Sinusoidal Amplitude Modulation
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Carrier wave : 𝑐 𝑡 = cos(𝜔𝑐 𝑡 + 𝜃𝑐 )
Assuming that phase angle 𝜃𝑐 = 0
𝑦 𝑡 = 𝑐 𝑡 𝑐𝑜𝑠𝜔𝑐 𝑡
Transformation into frequency domain
Complex Modulation vs Sinusoidal Modulation
• In complex Modulation 2 waves are generated (real and imaginary)
which requires 2 multipliers and costs more power for
transmission.
• Sinusoidal Modulation is better in this regard , it requires 1
multiplier only and hence less power is consumed .
• Sinusoidal modulation is preferably done through cosine waves.
• In sinusoidal modulation 𝜔𝑐 > 𝜔𝑀 to avoid overlapping of the two
replications of𝑋(𝑗𝜔).This condition is the disadvantage of
sinusoidal modulation.
Demodulation
• Demodulation is the recovery of the information bearing signal
𝑥 𝑡 at the receiver end.
• 𝑦 𝑡 = 𝑥 𝑡 𝑐(𝑡)
• There are two ways for demodulation
1) Synchronous Demodulation
2) Asynchronous Demodulation
Synchronous Demodulation
• In synchronous modulation the frequencies of the modulated
wave and demodulating wave are same.
• 𝑦 𝑡 = 𝑥 𝑡 𝑐(𝑡)
• 𝑦 𝑡 = 𝑥(𝑡)𝑐𝑜𝑠𝜔𝑐 𝑡
• 𝑤 𝑡 = 𝑦(𝑡)𝑐𝑜𝑠𝜔𝑐 𝑡
• 𝑤 𝑡 = 𝑥(𝑡)𝑐𝑜𝑠 2 𝜔𝑐 𝑡
• A low pass filter is used to extract the information bearing
signal , it has a voltage gain of 2 , it recovers the actual signal.
Asynchronous Demodulation
• In Asynchronous modulation the frequencies of the modulated wave
and demodulating wave are different.
• Assumption: 𝑥(𝑡) must not have a negative part . In order to remove
negative part of the signal we give it a positive offset.
𝐾
𝐴
• Modulation Index= where K= maximum Amplitude of 𝑥(𝑡) and
A=Offset
• For best Modulation , Modulation Index shall be equal to 1. M.I of
the second signal is 1 .
• Half wave rectifier circuit acts as an envelope detector (detects
peaks of the signal)
Synchronous Demodulation vs Asynchronous
Demodulation
• Asynchronous Demodulation consumes more power if we do
not increase Modulation Index , but increasing Modulation
Index lessens the efficiency of the Envelope detector.
• Synchronous Demodulation is used where we already know
the frequency of the wave .
Applications
• Asynchronous Demodulation: Used in public broadcasting
where we can afford power losses e.g radio transmission
where we have many receivers.
• Synchronous Demodulation: Used in satellites where we have
to transmit information to only 1 recipient many times
therefore we want to minimize the power used for this
purpose, this is done by using complicated devices which
insures that the frequency of the modulated signal and the
frequency of demodulation signal are the same.
Modulation of Carrier Wave using Pulse
Train
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Technique of amplitude modulation with a pulse train.
Sinusoidal waves are used in sinusoidal amplitude modulation.
Pulse train used is used in this modulation.
Pulse Train: a constant high frequency square wave whose
peak time is negligible or approaches to 0.
In Time Domain
• Carrier wave(pulse train) is represented as c(t).
• Signal to be transmitted by x(t).
• Modulated signal by y(t).
Y(t)=x(t)c(t)
Signal to be transmitted
x(t)
Carrier wave
c(t)
Modulated signal
y(t)
Frequency Domain
Fourier transform is taken for representation in frequency
domain.
Benefits:
Better representation of signals
Calculations are easy because differentiation is converted to
multiplication and integration is converted to division.
Signal to be transmitted
X(jw)
C(jw)= Carrier wave in
frequency domain
Modulated signal Y(jw)
Y(jw) is obtained after taking the Fourier transform of y(t) and
ak is the Fourier series coefficient.
Advantages
Time Division Multiplexing: Multiple signals can be transmitted
through a single channel.
Disadvantages
Data loss because of nature of pulse train. A solution to this
problem is to have a high frequency of pulse train relative to
the signal to be transmitted.
Time Division Multiplexing
Background of Pulse-Amplitude Modulation
• Previously, we described a system of modulation, in which a continuous time signal is modulated by
a periodic pulse train and it corresponds to its transmitting time slices of duration (delta T) seconds.
However, we know from our investigation that recovering this information not only depends on the
time but also on the frequency.
• In modern communication systems, we send sample values of information bearing signals rather
than the time slices. This results in a phenomena that is known as ‘Pulse Amplitude Modulation’.
Definition of Pulse-Amplitude Modulation
• Pulse amplitude modulation (PAM) is a form of signal modulation where the
• Message information is encoded in the amplitude of a series of a signal pulse.
The amplitude of train of carrier pulses are varied according to the sample value
of the message signals
Intersymbol Interference in PAM Systems
To explain this phenomena let us first consider time
multiplexed signals that consist of pulse modulated
versions of three signals x1, x2 and x3. Now if we sample
these signals at appropriate time then we can easily
separate the samples of the three signals.
However, this method is based on the assumption that the
transmitted signal remains unaffected by additive noise
because additive noise will introduce amplitude errors at
the sampling times and this can also cause a smearing of
the individual pulses that can cause the received pulses to
overlap in time. This interference is referred to as
intersymbol interference.
Digital Pulse-Amplitude and Pulse-Code Modulation
As described in previous slides, a PAM system generate samples of information that are
somewhat similar to discrete time signal and we know that in many applications discrete
time signals are either generated or stored.
In general, each sample of information is represented as a binary number that is a string of O's
and 1 's. Hence one value of amplitude correspond to a 0 and other value
corresponds to a 1. This phenomena can be utilized to protect against
transmission errors or provide secure communication
For example, a very simple error detection mechanism is to transmit one additional
modulated pulse for each sample of information and this will represent a parity check.
Therefore, this extra bit would be set to 1 if the binary representation
of information has an odd number of 1 's and 0 if there is an even number of 1 's. The receiver can
then check the received parity bit against the other received bits in order to detect
errors. For these reasons, a PAM system modulated by an encoded sequence of
O's and 1 's is referred to as a pulse-code modulation (PCM) system.
NON LINEAR MODULATION
Angle Modulation
Consider a sinusoidal carrier wave of the form
xc = Ac cos (ωc t + θc) , where
ωc = frequency of carrier wave
θc = phase of carrier wave
Ac = amplitude of carrier wave
TYPES OF ANGLE MODULATION
 Phase modulation
The phase is varied using the modulating signal.
 Frequency modulation
The derivative of angle is varied proportionally with the modulating signal
Relating both,
𝑑𝜃(𝑡)
𝑑𝑡
= wc +
𝑑𝑥(𝑡)
kp
𝑑𝑡
• Phase modulation with
• a ramp as modulating signal
• Frequency modulation with a
ramp as a modulating signal
Frequency modulation with a step as the modulating signal
(derivative of the ramp)
FREQUENCY MODULATION SYSTEM
Frequency Modulation is the encoding of information in a
carrier wave by varying the instantaneous frequency of the
wave
ADVANTANGES OF FM
 Improved signal to noise ratio
 Smaller geographical interference between neighboring
stations
 Less radiated power
DISADVANTAGES OF FM
 Requires greater bandwidth than amplitude modulation
 Complicated analysis of reception and transmission
• The modulator combines
the carrier with the
baseband data signal to
get the transmitted
signal:
• y(t) = Ac cos(2p∫ f(t) dt)
After a few complicated substitutions and assumptions, the previous equation becomes:
y(t) = cos [ wc t + (Dw/wm )sinwm t ]
The factor Dw/wm is the modulation index (m)
and its magnitude determines the properties of FM system
Small values of m define Narrowband FM whereas large values of m end up as Wideband
FM.
NARROWBAND FREQUENCY MODULATION
𝜋
Assuming m to be <<
2
The spectrum of modulated signal depends only on the bandwidth of the modulating
signal and not on the amplitude of the modulating signal, as proven by this
simplified equation.
WIDEBAND FREQUENCY MODULATION
If values of m are large, the assumption of m << p/2 cannot be
applied.
Thus, the spectrum of modulated signal depends both on the amplitude
and the bandwidth of the modulating signal.
• We note that the terms of cos and sin in ωm are periodic signals.
• Hence the Fourier transform is an impulse train with impulses at
integer multiples of ωm and amplitudes proportional to Fourier
series coefficients.
The impulses are centered at ± ωc.
DIFFERENTIATING FM AND AM
 AM signal is amplitude modulated. FM signal is amplitude as well as
frequency modulated
 The bandwidth of FM is larger than the bandwidth of AM
 AM instantaneous phase contains bandwidth signal. FM instantaneous
phase contains bandwidth as well as higher order odd harmonics