1. COMMUNICATION SYSTEMS- CONTINUOUS

2. Group B Ali Qasim Haris Suhail Imaan Tariq Mohsin Zafar Arsalan Hameed
Abdul Rahman
Rida Zainab
Ehsanullah Zafar
Hassan Iqbal
Amna Aziz
Manal Fatima
Qambar Rizvi

3. Classification of Modulation

4. LINEAR MODULATION

5. 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:
Complex Exponential Amplitude Modulation
Sinusoidal Amplitude Modulation

6. Complex Exponential Amplitude Modulation
Carrier signal 𝑐 𝑡 = 𝑒 𝑗( 𝜔 𝑐 𝑡+ 𝜃 𝑐 )
Assuming that phase angle 𝜃 𝑐 =0 (for simplicity)
𝑦 𝑡 =𝑥(𝑡) 𝑒 𝑗 𝜔 𝑐 𝑡
Transformation into the frequency Domain

8. Implementation of Complex Modulation
We get two signals after modulation one is real and the other is complex.

9. Sinusoidal Amplitude Modulation
Carrier wave : 𝑐 𝑡 =cos⁡( 𝜔 𝑐 𝑡+ 𝜃 𝑐 )
Assuming that phase angle 𝜃 𝑐 =0
𝑦 𝑡 =𝑐 𝑡 𝑐𝑜𝑠 𝜔 𝑐 𝑡
Transformation into frequency domain

11. 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 𝜔 𝑐 > 𝜔 𝑀 to avoid overlapping of the two replications of𝑋(𝑗𝜔).This condition is the disadvantage of sinusoidal modulation.

12. 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

13. 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)𝑐𝑜𝑠 𝜔 𝑐 𝑡
𝑤 𝑡 =𝑦(𝑡)𝑐𝑜𝑠 𝜔 𝑐 𝑡
𝑤 𝑡 =𝑥(𝑡) 𝑐𝑜𝑠 2 𝜔 𝑐 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.

15. 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.
Modulation Index= 𝐾 𝐴 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)

17. 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 .

18. 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.

19. Modulation of Carrier Wave using Pulse Train
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.

20. 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)

21. Signal to be transmitted
x(t)
Carrier wave
c(t)
Modulated signal
y(t)

22. 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.

23. Signal to be transmitted X(jw)
Modulated signal Y(jw)
C(jw)= Carrier wave in frequency domain

24. Y(jw) is obtained after taking the Fourier transform of y(t) and ak is the Fourier series coefficient.

25. Advantages Disadvantages
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.

26. Time Division Multiplexing

27. 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’.

28. 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

29. 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.

30. 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.

31. NON LINEAR MODULATION

32. 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

33. 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 + kp 𝑑𝑥(𝑡) 𝑑𝑡

34. Frequency modulation with a ramp as a modulating signal
Phase modulation with
a ramp as modulating signal
Frequency modulation with a ramp as a modulating signal

35. Frequency modulation with a step as the modulating signal (derivative of the ramp)

37. FREQUENCY MODULATION SYSTEM
Frequency Modulation is the encoding of information in a carrier wave by varying the instantaneous frequency of the wave

38. ADVANTANGES OF FM Improved signal to noise ratio
Smaller geographical interference between neighboring stations
Less radiated power

39. DISADVANTAGES OF FM
Requires greater bandwidth than amplitude modulation
Complicated analysis of reception and transmission

40. The modulator combines the carrier with the baseband data signal to get the transmitted signal:
y(t) = Ac cos(2p∫ f(t) dt)

41. y(t) = cos [ wc t + (Dw/wm )sinwm t ]
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.

42. NARROWBAND FREQUENCY MODULATION
Assuming m to be << 𝜋 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.

43. 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.

44. 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.

45. 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