1/21 chapter 5 – signal encoding and modulation techniques

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1/21 Chapter 5 – Signal Encoding and Chapter 5 – Signal Encoding and Modulation Techniques Modulation Techniques

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Page 1: 1/21 Chapter 5 – Signal Encoding and Modulation Techniques

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Chapter 5 – Signal Encoding and Chapter 5 – Signal Encoding and Modulation Techniques Modulation Techniques

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Analog Data, Digital SignalAnalog Data, Digital Signal

Digitization is conversion of analog data into digital data which can then:

be transmitted using NRZ-L (digital signal) be transmitted using code other than NRZ-L be converted to analog signal by using modulation

techniques (ASK, PSK, FSK)

signal

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Codec (Coder-decoder)Codec (Coder-decoder)

Analog to digital conversion done using a codec (coder-decoder). Two techniques:

1. Pulse Code Modulation (PCM)

2. Delta Modulation (DM)

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Pulse Code Modulation (PCM)Pulse Code Modulation (PCM)

Sampling Theorem:“If a signal is sampled at regular intervals at a rate

higher than twice the highest signal frequency, the samples contain all information in original signal”

Samples can be used to reconstruct the original signal

e.g., 100-4000Hz voice data, requires 2*4000=8000 sample per sec

These are analog samples, called Pulse Amplitude Modulation (PAM) samples

To convert to digital, each of these analog samples must be assigned a binary code

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Pulse Code Modulation (PCM) ExamplePulse Code Modulation (PCM) Example

The signal is assumed to be band-limited with bandwidth B The PAM samples are taken at a rate of 2B, or once every

Ts=1/(2B) seconds Each PAM sample

is quantized into one of 16 levels

Each sample is then represented by 4 bits.

8 bits→256 level →better quality

4000Hz voice→(8000sample/s)*8bits/sample=64Kbps

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Pulse Code Modulation (PCM)Pulse Code Modulation (PCM)Block DiagramBlock Diagram

By quantizing the PAM samples, the resulting signal is an approximation of the original one

This effect is known as quantization error or quantization noise

The Signal-to-Noise-Ratio (SNR) for quantizing noise:

bitsofnumberndBnSNRdB :,76.102.6

Page 7: 1/21 Chapter 5 – Signal Encoding and Modulation Techniques

Linear Versus Non-Linear EncodingLinear Versus Non-Linear Encoding

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Linear Encoding (uniform quantization): Equally spaced quantization steps Lower amplitude values are relatively more distorted

Non-Linear Encoding (non-uniform quantization): Non-equally spaced quantization steps Large number of quantization steps for signals with low amplitude, and smaller number of

quantizing steps for signals with large amplitude

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Companding (Compressing-Companding (Compressing-Expanding)Expanding)

Instead of non-linear encoding, use companding+linear encoding

Companding gives more gain to weak signals than to strong signals on the input. At output, the reverse operation is performed

10000104010000log*1010000

100010301000log*101000

1001020100log*10100

10101010log*1010

)10()log*10()(

10/4010

10/3010

10/2010

10/1010

10/10

XYX

XYX

XYX

XYX

XExpandedXYcompressedXvalueNormal Y

Compressing ExpandingXY

X

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Delta Modulation (DM)

An analog input is approximated by a staircase function that moves up or down by one quantization level () at each sampling interval (Ts).

A 1 is generated if the staircase function is to go up during the next interval; a 0 is generated otherwise.

The staircasefunction tracks the original waveform

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Delta Modulation Operation For transmission: the analog input is compared

to the most recent value of the approximating staircase function.

If the value of the analog input exceeds that of the staircase function, a 1 is generated; otherwise, a 0 is generated.

Thus, the staircase is always changed in the direction of the input signal.

For reception: The output of the

DM process is therefore a binary sequence that can be used at the receiver to reconstruct the staircase function.

Staircase

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Pulse Code Modulation (PCM) Versus Delta Modulation (DM)

DM has simplicity compared to PCMDM has worse SNR compared to PCMPCM requires more bandwidth

eg., for good voice reproduction with PCM want 128 levels (7 bit) & voice bandwidth 4khz need 8000 sample/s x 7bits/sample = 56kbps

PCM is more preferred than DM for analog signals

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Analog Data, Analog Signal

Modulate carrier signal with analog data (voice)Why modulate analog signals?

higher frequency can give more efficient transmissionpermits frequency division multiplexing (chapter 8)

Types of modulationAmplitude Modulation (AM)Frequency Modulation (FM)Phase Modulation (PM)

Demodulator)(tm)(tsModulator

analog data

)(tm

carrier signal)2cos( tfA cc

modulated signal)(ts

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Amplitude Modulation (AM)

AM is the simplest form of analog modulationUsed in AM radio with carrier Used also in analog TV broadcastingAnalog data modulates a carrier signalMathematically, the AM wave can be expresses as

frequencycarrierf

indexModulationn

signaldatainputtmtxn

where

tftxnts

c

a

a

ca

:

:10

:)()(

)2cos()](1[)(

MHzfMHz c 605.1535.0

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Time Domain description of AM Signal Derive an expression for the AM wave if the input signal:

Envelope of AM signal:

cmma fftfntm ),2cos()(

)2cos()]2cos(1[

)2cos()](1[)(

tftfn

tftmts

cma

c

Modulationn

AA

AAn

n

n

A

A

tfwhen

tfwhen

tfn

a

a

a

a

m

m

ma

%:%100*

1

1

1)2cos(.min

1)2cos(.max

)]2cos(1[

minmax

minmax

min

max

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Frequency Domain description of AM Signal

The Double SideBand Transmitted Carrier (DSBTC):

)])(2cos())(2[cos(2

)2cos()(

)]cos()[cos(2

1)cos()cos(:

)2cos()2cos()2cos(

)2cos()]2cos(1[)(

tfftffn

tfts

identityrictrigonomettheemploying

tftfntf

tftfnts

mcmca

c

cmac

cma

cfmc ff mc ff 0f

)( fS

Upper Side Band(USB)

Lower Side Band(LSB)

Carrier

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Frequency Domain description of AM Signal Consider a voice signal m(t) with a

bandwidth that extend from 300Hz to 3000Hz being modulated on a 60 KHz Carrier

KHzatCarrier

KHzKHzSideBandLower

KHzKHzSideBandUpper

containssignalresultingThe

KHzfcarrier

KHzBBandwidth

c

60

7.5957:

633.60:

:

60

3

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Variations of AM signal

Double Side Band Transmitted carrier (DSBTC)wast of power as the carrier is transmitted with the side

bandswast of bandwidth as both upper and lower side bands are

transmitted (each side band contains the complete spectrum of the message signal m(t) ): Transmitted bandwidth=BT=2B

Double Side Band Suppressed Carrier (DSBSC)Less power is required as no carrier is transmittedwast of bandwidth as both upper and lower side bands are

transmitted: Transmitted bandwidth=BT=2BSingle Side Band (SSB)

Less power is required as no carrier is transmittedLess bandwidth as one side band is transmitted: BT=B

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Angle Modulation

Frequency Modulation (FM) and Phase Modulation (PM) are special cases of angle modulation

Used in FM radio with carrier The angle modulated signal is expressed as:

Phase Modulation (PM): - Example: find s(t) if

MHzfMHz c 10888

))(2cos()( ttfAts cc

)(.max

.

:)(

:

)()(

tmoftheisAwhere

AndeviationphaseMax

signalmessageinputtm

indexModulationphasen

where

tmnt

m

mp

p

p

pmp

mpcc

mp

nAndeviationphaseMax

tfntfAts

tfnt

.

)]2cos(2cos[)(

)2cos()(

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Frequency Modulation (FM)

The angle modulated signal is expressed as:

FM when: - Example: find s(t) if

))(2cos()( ttfAts cc

)(.max

2/..

2/)()(

)](2[)(2

:

:

)()(

tmoftheisAwhere

AnFdeviationfreqMax

tmnftf

ttfdt

dtf

timeanyatfrequencyThe

indexModulationfrequencyn

tmndt

td

m

mf

fci

ci

f

f

])2cos(2

2cos[)(

)2cos(2

)2sin()(

)2sin()(

tff

ntfts

tff

n

dttfnt

tfndt

td

mm

fc

mm

f

mf

mf

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Transmitted Bandwidth for AM, PM and FM

Transmitted bandwidth for AM:

Transmitted bandwidth for PM and FM:

Thus, both PM and FM require greater bandwidth than AM

bandwidthsignalmessagetheisBwhere

BBT 2

FMforB

AnPMforAn

where

BB

mf

mp

T

2

)1(2

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AM, PM, FM