Outline

•Revisit Analog Modulation Schemes

•Amplitude Modulation (AM)

•Frequency Modulation (FM)

•Analog-to-Digital Conversion - Sampling

•Digital Modulation Schemes

Modulation Process

•Information-bearing signals (e.g., voice, video) are called baseband signals. Other terms for information-bearing signals are message signal and modulating wave.

•Modulation is defined as the process by which some characteristics of a carrier signal (typically a cosine wave) is varied in accordance with a message signal.

•Modulation process is required to shift the frequency content of our message signals to a range that is acceptable by the transmission medium. (e.g., above 30 KHz for wireless transmission).

Modulation Types

Analog Modulation: Digital Modulation:

Message signal is analog (a.k.a continuous-time).

Message signal is digital (a.k.a discrete-time).

•Amplitude Modulation (AM)

•Frequency Modulation (FM)

•Phase Modulation (PM)

•Amplitude Shift Keying (ASK)

•Frequency Shift Keying (FSK)

•Phase Shift Keying (PSK)

Digital Modulation Schemes

Digital Modulation Schemes

Figure 4-8

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Amplitude Change

Figure 4-9

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Frequency Change

Figure 4-10

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Phase Change

Figure 5-24

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Amplitude Shift Keying

Also known as Symbol Rate

Frequency Shift KeyingFigure 5-27

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Phase Shift KeyingFigure 5-29

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PSKConstellation

Figure 5-30

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Quadrature PSK - QPSK4-PSK

Figure 5-31

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QPSKConstellation

Figure 5-32

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8-PSKConstellation

Figure 5-33

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4-QAM and 8-QAMConstellations

Figure 5-35

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8-QAM SignalFigure 5-36

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16-QAMConstellation

Figure 5-37

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Figure 5.17 Bit and baud

Table 5.1 Bit and baud rate comparison

ModulationModulation UnitsUnits Bits/BaudBits/Baud Baud rateBaud rate Bit Rate

ASK, FSK, 2-PSKASK, FSK, 2-PSK Bit 1 N N

4-PSK, 4-QAM4-PSK, 4-QAM Dibit 2 N 2N

8-PSK, 8-QAM8-PSK, 8-QAM Tribit 3 N 3N

16-QAM16-QAM Quadbit 4 N 4N

32-QAM32-QAM Pentabit 5 N 5N

64-QAM64-QAM Hexabit 6 N 6N

128-QAM128-QAM Septabit 7 N 7N

256-QAM256-QAM Octabit 8 N 8N

Sampling – Pulse Amplitude Modulation (PAM)

Sampling – Pulse Amplitude Modulation (PAM)

Quantized PAM Signal

Figure 3.11Illustration of the quantization process. (Adapted from

Bennett, 1948, with permission of AT&T.)

Figure 5-20-continued

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From Analog to PCM

Figure 5-20-continued

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From Analog to PCM

Figure 5-20-continued

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From Analog to PCM

Figure 5-19

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Pulse Coded Modulation

Nyquist’s Sampling Theorem

A band-limited signal of finite energy, which has no frequency components higher than W Hertz, may be completely described by specifying the values of the signal at instants of time separated by (1/2W) seconds or can be recovered from a knowledge of its samples taken at a rate of 2W samples per second.

fs = 2 × W

Sampling frequency

Bandwidth of signal

Impact of Sampling on the Frequency Domain

Sampling frequency = message bandwidth

Message signal cannot be recovered from the sampled signal !!

Impact of Sampling on the Frequency Domain

Message signal Frequency Content

Frequency Content of the sampled message signal

Sampling frequencyMessage bandwidth

fs = 2 × W

•Revisit Analog Modulation Schemes

•Amplitude Modulation (AM)

•Frequency Modulation (FM)

•How to produce AM Signal?

Amplitude Modulation

Amplitude Modulation

ttvvtV cSCAM cos)(

Carrier Signal: tvtc cc cos

Message Signal or modulating signal: tvtv SSS cos

Modulated Signal:

Modulation Index

vS(t)

vC cos C t

Modulating signal

Carrier Amplitude Carrier Frequency

ttv

vvtV cS

C

SCAM coscos1

ttMvtV cSCAM coscos1

VAM(t)

C

S

v

vM

Amplitude Modulation

• Modulation Index M is determined by the peak amplitudes of the carrier and the modulating signal.

• In practice, carrier signal amplitude vC is usually fixed and the M ratio is changed by varying the amplitude of the modulating signal vS.

• Hence, higher vS produce higher M but M < 1.

• M is kept as high as possible to ensure good SNR of the received AM signal for recovery.

• When M > 1, over-modulated carrier signal distorts the information – Clipping or saturation.

C

S

v

vM

Amplitude Modulation

Illustrating the amplitude modulation process. (a) Baseband signal vs(t). (b) AM wave for M < 1 for all t. (c) AM wave for M > 1 for some t.

Envelope of the modulated signal has the same shape with the message signal. Envelope is

distorted

C

S

v

vM

AM : Double-sided band (DSB)

where modulating signal: tvtv SSS cos

ttvvtV cSCAM cos)(AM Signal:

ttvtvtV CSSCCAM cos.coscos Thus,

Carrier

Component

Lower side band(LSB)

Double-side band components (DSB)

ttv

SCSCS coscos2

Upper side band(USB)

Wasted energy in carrier component because it contains

no information

Action: To suppress the carrier

Amplitude Modulation

AM is the earliest type of modulation in history.

Its main advantage is its simplicity. – linear modulation

technique

AM is wasteful in power consumption. Although the carrier

signal does not carry any information, it is still transmitted.

AM is wasteful in bandwidth usage. The upper sideband is

reflection of the lower sideband. One sideband is sufficient to

express the frequency content of the message signal. Yet, AM

still transmits one unnecessary sideband.

Spectrum of AM wave

fc

ffc+fS

fc-fS

|v|

fS

fc

ffc+fS

fc-fS

|v|

(a) Spectrum of AM Signal: both carrier and double-sided bands

(b) Spectrum of Double-Sided Band - Carrier Suppression (DSB-SC)

Double Sideband-Suppressed Carrier Modulation (DSB-SC)

cos C t

Modulating signal

Carrier Frequency

DSB-SC signal

• Balance Modulator

-90o

-90o

vS(t)

vC(t)

DSB-SC

tv SS cos

tv SS sin

tv cc cos

tv cc sin

Carrier

Oscillator

vS(t)

Double Sideband-Suppressed Carrier Modulation (DSB-SC)

modulating signal:

DSB-SC signal:

Single Sideband-Suppressed Carrier Modulation (SSB-SC)

cos C t

Modulating signal

Carrier Frequency

DSB-SC signalvS(t)

Sideband filter

(crystal filter)

SSB-SC signal

Bandpass filter applied at the DSB-SC signal to generate SSB-SC signal.

Problem: It is very difficult and costly to design a bandpass filter that is sharp enough to select only one sideband !

Demodulation of AM signal

cos C t

Modulating signal

Carrier Frequency

DSB-SC signal

• Balance Modulator

-90o

-90o

vS(t)

vC(t)

DSB-SC

tvtv SSS cos

tv SS cos

tv SS sin

tv cc cos

tv cc sin

ttvv

SCSCSC coscos

2

ttvv

SCSCSC coscos

2

Carrier

Oscillator

Demodulation of AM signal• Most basic: Envelope detector (for AM signal only)

diode D+ –

R C

AM signal

vAM(t)

• As VAM(t) increases in amplitude, the diode conducts (forward bias) and capacitor C start to charge-up very quickly to 1st peak vp1 with a time constant = Cr, where r is the diode’s forward resistance (usually very small when diode is conducting).

• As VAM(t) decreases in amplitudes, the diode switch-off (reverse bias) and capacitor C start to discharge slowly with a time constant = CR, where R must be greater than r.

• When VAM(t) increases again, D conducts and C charges up rapidly to 2nd peak vp2 and when VAM(t) decreases again D is off and C discharges slowly and this is repeated according to the amplitude of VAM(t) signal.

• If CR is too small, C discharge too rapidly; results in ripple amplitude in demodulated output.

• If CR is too large, C discharge too slowly; vs(t) fails to follow the envelope results in distortion (or diagonal clippling) in demodulated output.

• Hence, time constant must be optimum.

Charging/Discharging voltage

vs(t)Cc

To remove DC component & smoothen vs(t)

Optimum AM Demodulation

Ripple amplitude in AM Demodulation – RC too small

Diagonal Clipping/distortion in AM Demodulation – RC too large

Demodulation of (DSB-SC) signal (1)

cos C t

DSB-SC signal

local oscillator

Recovered modulating signal

• Synchronous detection

Low Pass Filter

• Local oscillator produce the exactly coherent oscillation output that is synchronized with the original carrier in both frequency and phase.

• The output is then filter by low-pass filter that only allowed the desired signal to pass through.

tvV cDSBSCx cos

DSBSCvxV

tttv CCS coscos.

ttv CS cos.

ttv CS2cos.

ttvtv

cSS 2cos2

)(

2

)(

ttvC

S 2cos1.2

fc

ffc+fS

fc-fS

|v|

fS

Desired signal

Unwanted signal

Demodulation of (DSB-SC) signal (2)• Costal Loop / Phase Lock Loop (PLL)

-90o

-90o

DSB-SC

ttv CS cos)(

ttv CS sin)(

tv cc cos

VCO Loop

filter

LPF

LPF

tv cc sin

cos2

)(tvS

sin2

)(tvS

Output:

• The frequency fc is know a priori to the demodulator and generated by the voltage control oscillator, VCO.

• PLL circuit (VCO + Loop filter) try to lock the phase so that local oscillation is synchronized with original fc.of the DSBSC signal.

• Once synchronization is achieved, the difference in phase will be eliminated, thereby, recover the modulating signal.

CS tv

2coscos2

)(

CS tv

2sinsin2

)(

Frequency Modulation (FM)

In FM, the information is conveyed by varying the frequency of the carrier signal fC in step with the instantaneous amplitude of the modulating signal vs.

vs

fC

fi

• FM signal is produced by a frequency modulator which converts the voltage variation in the modulating signal vs to a frequency variation of the carrier signal

• The “instantaneous” frequency fi is the sum of carrier frequency fC and the “frequency deviation” as the result of the ‘amplitude-frequency’ conversion.

Frequency Modulation (FM)

Frequency Modulator

vs(t) fi

f

( : / ). ;where is conversion gain unit Hz volti c f s ff f f f k v k

• When no modulating signal is applied, the output frequency is the same as the carrier frequency since ; no deviation is observed.

• When a modulating signal is applied, the instantaneous output frequency fi will start to vary/deviate from fc with the amount of .

• The conversion can be seen from the graph

0f

f

fc

fi

vs0

kf = Hz

volt

Conversion gain

Frequency Modulation (FM)

Fact in FM :

Instantaneous frequency fi of the cosine wave is:

dt

tdtf i

i

2

1

1

2

FM Modulated Signal:

icvts cos

Carrier Signal:

tfvtc cc 2cos

(Distance = speed × time)

tfii 2

Angular displacement :

Constant speed

varying speed

Instantaneous angular

displacement

Frequency Modulation (FM)• General FM signal

can be expressed as: iCFM vtV cos.)(

• Recall that instantaneous frequency i of FM:

tvkffff ssfCCi cos.

dtfdt iii 2where i is the instantaneous angular displacement:

dttvkf ssfCi cos2• hence i can be re-written as:

sf vkf

dttvkdtf ssfC cos212

s

ssfC f

tvkt

2

sin2

tf

vkt s

s

sfC sin

tt sC sin

ss

sf

f

f

f

vk

FM modulation index:

Frequency Modulation (FM)

• Therefore, FM signal can be expressed as:

ttvtV sCCFM sincos.)(

s

sf

s f

vk

f

f

FM modulation index: Carrier frequency is varied or deviated

by the amount of ts sin

controls the amount of frequency change in FM signal.

• In FM, can be greater than 1: ( > 1), since can be set independent of fs and both values are not bounded by fC.

• However, fs must be kept smaller than fC in order for FM to work successfully.

f

FM is a non-linear modulation. FM signal envelope is constant.

Frequency ModulationCarson’s Rule:

The transmission bandwidth required by a frequency modulated signal is given below.

1

12 maxfBT

Maximum frequency deviation

s

sf

s f

vk

f

f

FM modulation index:

Example

KHzfBT 1805

11752

112

KHzfBT 180

5

11752

112

KHzf 75

KHzWorf s 15

A message signal with a bandwidth of 15 KHz is to be used to frequency modulate a carrier signal at 400 KHz. Given that maximum frequency deviation is 75 KHz. According to Carson’s Rule, what is the transmission bandwidth required for the frequency modulated signal?

515

75

sf

f

1) message bandwidth ?

2) maximum frequency deviation ?

3) modulation index ?

4) Using Carson’s rule, the required transmission bandwidth:

Tutorial

1- What is Amplitude Modulation ?

Amplitude modulation is the process by which the amplitude of a carrier signal is varied according to a message signal.

2- What frequency range will be covered by a 412 KHz carrier signal after it has been amplitude modulated by an audio signal that is bandlimited to 24 KHz ?

Due to amplitude modulation, the frequency spectrum of the audio signal will shift to the carrier signal frequency.The frequency range from (412-24) KHz to (412+24) KHzwill be covered by the amplitude modulated signal.

Tutorial3- Consider the video signal that has a frequency content between 0 Hz and 6 MHz. What is the required transmission bandwidth if Frequency Modulation is used with a maximum frequency deviation of 30 MHz according to Carson’s Rule ?

MHzfBT 725

11302

112

MHzfBT 72

5

11302

112

MHzf 30

56

MHz

f

maximum frequency deviation ?

modulation index ?

With aid of diagram, explain the process of amplitude modulation? Your answer should include the carrier signal, modulating signal and the AM signal itself.

Tutorial

Tutorial4- What is Amplitude Shift Keying (ASK)?

ASK is a digital modulation technique where the amplitude of a carrier signal is varied to transmit ones and zeros.

5- What is Phase Shift Keying (PSK)?

PSK is a digital modulation technique where the phase of a carrier signal is varied to transmit ones and zeros.

6- What is Frequency Shift Keying (FSK)?

FSK is a digital modulation technique where the frequency of a carrier signal is varied to transmit ones and zeros.

Tutorial7- Sketch the ASK modulated signal for a bit pattern of 01100101. Use a cosine wave as the carrier signal!

Tutorial8- Sketch the PSK modulated signal for a bit pattern of 01100101. Use a cosine wave as the carrier signal!

Tutorial

Briefly explain the Pulse Amplitude Modulation (PAM) and Quantisation process.

PAM converts the analog signal to a series of pulse-trains with different amplitude corresponding to the amplitude of the analog signal at different interval in time.

Quantisation is a process to convert these pulse-trains amplitude from analog value to discrete value by binary level representation. The number levels (L) that can be represented is corresponding to the number of bit (N) used. L = 2N

TutorialWith the aid of block diagram, describe how a analog signal is sent using a digital system with PAM.