1. Lecture 1.7. AM FM PM OOK BPSK FSK

2. AM, FM, and Digital Modulated Systems
Amplitude Modulation (AM)
Double Sideband Suppressed carrier (DSSC)
Assymetric Sideband Signals
Single sideband signals (SSB)

3. Bandpass Signaling Review
The modulated bandpass signal can be described by
Where
Modulation Mapping function: Convert m(t) →g(t) Ref : Table 4-1
The voltage spectrum of the bandpass signal is
The PSD of the bandpass signal is
Where

4. Amplitude Modulation
The Complex Envelope of an AM signal is given by
Ac indicates the power level of AM and m(t) is the Modulating Signal
Representation of an AM signal is given by
Ac[1+m(t)] In-phase component x(t)
If m(t) has a peak positive values of +1 and a peak negative value of -1
AM signal  100% modulated
Envelope detection can be used if % modulation is less than 100%.

5. Amplitude Modulation An Example of a message signal m(t)
Waveform for Amplitude modulation of the message signal m(t)

6. Carrier component together with the message
Amplitude Modulation B
An Example of message energy spectral density.
Carrier component together with the message 2B
Energy spectrum of the AM modulated message signal.

7. AM – Percentage Modulation
Definition: The percentage of positive modulation on an AM signal is
The percentage of negative modulation on an AM signal is
The percentage of overall modulation is
If m(t) has a peak positive values of +1 and a peak negative value of -1
AM signal  100% modulated

8. AM Signal Waveform % Positive modulation= 50%
% Negative modulation =50%
Overall Modulation = 50%
Amax = 1.5Ac
Amin = 0.5 Ac

9. AM – Percentage Modulation
Under modulated (<100%)
100% modulated
Envelope Detector
Can be used
Gives Distorted signal
Over Modulated (>100%)

10. Discrete Carrier Power
AM – Normalized Average Power
The normalized average power of the AM signal is
If the modulation contains no dc level, then
The normalized power of the AM signal is
Discrete Carrier Power
Sideband power

11. AM – Modulation Efficiency
Definition : The Modulation Efficiency is the percentage of the total power of the modulated signal that conveys information.
Only “Sideband Components” – Convey information
Modulation Efficiency:
Highest efficiency for a 100% AM signal : 50% - square wave modulation
Normalized Peak Envelope Power (PEP) of the AM signal:
Voltage Spectrum of the AM signal:
Unmodulated Carrier Spectral Component
Translated Message Signal

12. Double Side Band Suppressed Carrier (DSBSC)
Carrier Power
Sideband power
Power in a AM signal is given by
DSBSC is obtained by eliminating carrier component
If m(t) is assumed to have a zero DC level, then
Spectrum 
Power 
Modulation Efficiency 
Disadvantages of DSBSC:
Less information about the carrier will be delivered to the receiver.
Needs a coherent carrier detector at receiver

13. No Extra Carrier component
DSBSC Modulation B
An Example of message energy spectral density.
No Extra Carrier component 2B
Energy spectrum of the DSBSC modulated message signal.

14. Single Sideband (SSB) Modulation
An upper single sideband (USSB) signal has a zero-valued spectrum for
A lower single sideband (LSSB) signal has a zero-valued spectrum for
SSB-AM – popular method ~ BW is same as that of the modulating signal.
Note: Normally SSB refers to SSB-AM type of signal
USSB
LSSB

15. Single Sideband Signal
Theorem : A SSB signal has Complex Envelope and bandpass form as:
Upper sign (-)  USSB
Lower sign (+)  LSSB
– Hilbert transform of m(t) 
Where
and
Hilbert Transform corresponds to a -900 phase shift
H(f) f -j j

16. Single Sideband Signal
Proof: Fourier transform of the complex envelope
Upper sign  USSB
Lower sign  LSSB
Using
Recall from Chapter 4
Upper sign  USSB
If lower signs were used  LSSB signal would have been obtained

17. Single Sideband Signal

18. SSB - Power The normalized average power of the SSB signal
Hilbert transform does not change power.
SSB signal power is:
Power of the modulating signal
Power gain factor
The normalized peak envelope (PEP) power is:

19. Generation of SSB Advantages of SSB SSB signals have both AM and PM.
The complex envelope of SSB:
For the AM component,
For the PM component,
Advantages of SSB
Superior detected signal-to-noise ratio compared to that of AM
SSB has one-half the bandwidth of AM or DSB-SC signals

20. Generation of SSB SSB Can be generated using two techniques
Phasing method
Filter Method
This method is a special modulation type of IQ canonical form
of Generalized transmitters discussed in Chapter 4 ( Fig 4.28)

21. Generation of SSB Filter Method
The filtering method is a special case in which RF processing (with a
sideband filter) is used to form the equivalent g(t), instead of using
baseband processing to generate g(m) directly. The filter method is the
most popular method because excellent sideband suppression can be
obtained when a crystal oscillator is used for the sideband filter.
Crystal filters are relatively inexpensive when produced in quantity at
standard IF frequencies.

22. Weaver’s Method for Generating SSB.

23. Generation of VSB

24. AM, FM, and Digital Modulated Systems
Phase Modulation (PM)
Frequency Modulation (FM)
Generation of PM and FM
Spectrum of PM and FM
Carson’s Rule
Narrowband FM

25. AM and FM Modulation (a) Carrier wave.
(b) Sinusoidal modulating signal.
(c) Amplitude-modulated signal.
(d) Frequency modulated signal.

26. Angle Modulation Advantages: Disadvantages:
Constant amplitude means Efficient Non-linear Power Amplifiers can be used.
Superior signal-to-noise ratio can be achieved (compared to AM) if bandwidth is sufficiently high.
Disadvantages:
Usually require more bandwidth than AM
More complicated hardware

27. Modulation Index The Peak Phase Deviation is given by:
∆θ is related to the peak modulating voltage by:
Where
The Phase Modulation Index is given by:
Where ∆θ is the peak phase deviation
The Frequency Modulation Index is given by:
∆F Peak Frequency Deviation
B Bandwidth of the modulating signal

28. Spectra of Angle modulated signals
Where
Spectrum of Angle modulated signal
Spectra for AM, DSB-SC, and SSB can be obtained with simple formulas relating S(f) to M(f).
But for angle modulation signaling, because g(t) is a nonlinear function of m(t). Thus, a general formula relating G(f) to M(f) cannot be obtained.
To evaluate the spectrum for angle-modulated signal, G(f) must be evaluated on a case-by-case basis for particular modulating waveshape of interest.

29. Spectrum of PM or FM Signal with Sinusoidal Modulating Signal
Assume that the modulation on the PM signal is
Then
Where is the phase Modulation Index.
Same θ(t) could also be obtained if FM were used
where
and
The peak frequency deviation would be
The Complex Envelope is:
which is periodic with period

30. Spectrum of PM or FM Signal with Sinusoidal Modulating Signal
Using discrete Fourier series that is valid over all time, g(t) can be written as
Where
Which reduces to
Jn(β) – Bessel function of the first kind of the nth order
Is a special property of Bessel Functions
Taking the fourier transform of the complex envelope g(t), we get or

31. Bessel Functions of the First Kind
J0(β)=0 at β=2.4, 5.52 & so on

32. Bessel Functions of the First Kind

33. Frequency spectrum of FM
The FM modulated signal in time domain
Observations:
From this equation it can be seen that the frequency spectrum of an FM waveform with a sinusoidal modulating signal is a discrete frequency spectrum made up of components spaced at frequencies of c± nm.
By analogy with AM modulation, these frequency components are called sidebands.
We can see that the expression for s(t) is an infinite series. Therefore the frequency spectrum of an FM signal has an infinite number of sidebands.
The amplitudes of the carrier and sidebands of an FM signal are given by the corresponding Bessel functions, which are themselves functions of the modulation index

34. Spectra of an FM Signal with Sinusoidal Modulation
The following spectra show the effect of modulation index, , on the bandwidth of an FM signal, and the relative amplitudes of the carrier and sidebands
1.0 f BT

35. Spectra of an FM Signal with Sinusoidal Modulation
J0(1.0)
1.0
J1(1.0)
J2(1.0) f BT

36. Spectra of an FM Signal with Sinusoidal Modulation
1.0 f BT

37. Carson’s rule
Although the sidebands of an FM signal extend to infinity, it has been found experimentally that signal distortion is negligible for a bandlimited FM signal if 98% of the signal power is transmitted.
Based on the Bessel Functions, 98% of the power will be transmitted when the number of sidebands transmitted is 1+ on each side.
(1+b)fm

38. Carson’s rule Note: When β =0 i.e. baseband signals
Therefore the Bandwidth required is given by
β – phase modulation index/ frequency modulation index
B – bandwidth of the modulating signal
For sinusoidal modulation
Carson’s rule : Bandwidth of an FM signal is given by
Note: When β =0 i.e. baseband signals

39. AM, FM, and Digital Modulated Systems
Binary Bandpass Signalling Techniques
OOK
BPSK
FSK

40. Binary Bandpass Signaling techniques
On–Off keying (OOK) [amplitude shift keying (ASK)] - Consists of keying (switching) a carrier sinusoid on and off with a unipolar binary signal.
- Morse code radio transmission is an example of this technique.
- OOK was one of the first modulation techniques to be used and precedes analog communication systems.
Binary Phase-Shift Keying (BPSK) - Consists of shifting the phase of a sinusoidal carrier 0o or 180o with a unipolar binary signal.
- BPSK is equivalent to PM signaling with a digital waveform.
Frequency-Shift Keying (FSK) - Consists of shifting the frequency of a sinusoidal carrier from a mark frequency (binary 1) to a space frequency (binary 0), according to the baseband digital signal.
- FSK is identical to modulating an FM carrier with a binary digital signal.

41. Binary Bandpass Signaling techniques

42. On-Off Keying (OOK) Also known as Amplitude Shift Keying (ASK) Carrier
Cos(2fct)
Message
m(t)
OOK output
Acm(t)Cos(2fct)
The complex envelope is
The OOK signal is represented by
The PSD of this complex envelope is given by
where m(t) has a peak value of
So that s(t) has an average normalized power of

43. Tb – bit period ; R – bit rate
On-Off Keying (OOK)
Message
Unipolar
Modulation
Bipolar
OOK signal
m(t)
s(t)
Tb – bit period ; R – bit rate

44. On-Off Keying (OOK) PSD of the bandpass waveform is given by
Null-to-Null bandwidth is and absolute bandwidth is
The Transmission bandwidth is
Where B is the baseband bandwidth

45. Detection of OOK Non-Coherent Detection Binary output OOK in Envelope
Detector
Coherent Detection with Low-pass filter
OOK in
LPF
Binary output

46. Binary Phase Shift Keying (BPSK)
Generation:
Carrier:Cos(2fct)
Message: m(t)
BPSK output
AcCos(2fct+Dpm(t))
-90
Phase shift
Message
Unipolar
Modulation
Bipolar
BPSK output
m(t)
s(t)

47. Binary Phase Shift Keying (BPSK)
The BPSK signal is represented by
let
pilot carrier term
data term
The level of the pilot carrier term is set by the value of the peak deviation
The digital modulation index ‘h’ is given by
2∆θ – maximum peak-to-peak deviation during time Ts
If Dp is small, then there is little power in data term & more in pilot term
To maximize performance (minimum probability of error)
Optimum case :
BPSK signal :

48. Binary Phase Shift Keying (BPSK)
The complex envelope for this BPSK is given by
The PSD for this complex envelope is given by
PSD of the bandpass waveform is given by
Average normalized power of s(t) :
Null-to-Null BW
PSD of optimum BPSK

49. Binary Phase Shift Keying (BPSK)
Power Spectral Density (PSD) of BPSK: fc
2R = 2/Tb
If Dp  /2
Pilot exists

50. Frequency Shift Keying (FSK)
Discontinuous FSK :
Cos(2f1t)
Message: m(t)
FSK output
AcCos(2f1t+1) or
AcCos(2f2t+2)
Osc. f2
Osc. f1
Cos(2f2t)
The discontinuous-phase FSK signal is represented by
for t during a binary ‘1’ signal
for t during a binary ‘0’ signal

51. Frequency Shift Keying (FSK)
Continuous FSK :
Frequency
Modulator fc
FSK output
Message: m(t)
The Continuous-phase FSK signal is represented by or
where
for FSK

52. Frequency Shift Keying (FSK)
Message
Unipolar
Modulation
Bipolar
FSK output
(Discontinuous)
(Continuous)
Mark(binary 1) frequency: f1
Space(binary 0) frequency: f2
m(t)
s(t)

53. Frequency Shift Keying (FSK)
Computer
FSK modem
(Originate)
Center
(Answer)
Digital
data
PSTN
Dial up
phone line
f1 = 1270Hz
f2 = 1070Hz
f1 = 2225Hz
f2 = 2025Hz
FSK modem with 300bps

54. END