TE311 Lecture09 SSB SC VSB Modulation

8/10/2019 TE311 Lecture09 SSB SC VSB Modulation

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TE311: Introduction toAnalogue Telecommunications

PART II

Lecture #9Linear CW Modulation III

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Introduction

Points to be discussed in this lecture

Single Side-Band Suppressed Carrier (SSB-SC)Modulation

Generation of SSB-SC Signals

Demodulation of SSB-SC Signals

Vestigial Sideband (VSB) Modulation

Generation of VSB SignalsDemodulation of VSB Signals

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Single-Sideband Suppressed Carrier(SSB-SC) Modulation

AM and DSB-SC signals transmission bandwidth is

twice that of the message signal ( ).m tOne sideband can be transmitted for bandwidth

conservation as either the upper sideband or thelower sideband contains complete information aboutthe message signal.

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Single sideband (SSB) modulation results when onlyone sideband is used for transmission of themodulated signal.


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B B

( )M f

f

( )0M

cf

cf

( )SSBS f

f

cf B cf B+

Upper

sideband

cf

cf

( )SSBS f

f

cf B + cf B

Lower

sideband

cf cf

( )DSBS f

f

cf B + cf B cf B cf B+

Uppersideband

Lowersideband( )0.5 0M


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Advantage of SSB modulation is reducedtransmission bandwidth requirements.

Disadvantage of SSB is implementation cost and

complexity.

We define the Hilbert transform of a message signal

( ), denoted bym t ( ) asm t

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( ) ( )

( )1 1

m

m t d m t t t

= =


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Fourier transform on both sides using convolutionproperty gives

( ) ( ) ( )

( ) ( )

( ) ( )

2

2

sgn

exp , 0 0, 0

exp , 0

M f j f M f

j M f ff

j M f f

=

>= =


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We define the pre-envelope of

( )m t as

( ) ( ) ( )m t m t jm t + = +

Taking the Fourier transform on both sides gives

( ) ( ) ( ) ( ) ( )

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( )

( )

( )

sgn

2 , 0

0 , 0

0, 0

f M f jM f M f j j f M f

M f f

M f

f

+ = + = +

>

= =


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We define the conjugate of pre-envelope of

( )m t as

( ) ( ) ( )m t m t jm t =

Taking the Fourier transform on both sides gives

( ) ( ) ( ) ( ) ( ) ( )

( )( )

sgn

0, 0

0 , 0

2 , 0

f M f jM f M f j j f M f

f

M f

M f f

= =

>

= =


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Time-domain description of USB signal is given as

( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

exp 2 exp 2

cos 2 sin 2

c c

c c

s t m t j f t m t j f t

m t f t m t f t

+ = +

=

Time-domain description of LSB signal is given as

( ) ( ) ( ) ( ) ( )( ) ( ) ( ) ( )

exp 2 exp 2

cos 2 sin 2

c c

c c

s t m t j f t m t j f t

m t f t m t f t

+ = += +

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Generation of SSB-SC SignalsFrequency Discrimination Method

To avoid sharp filter cutoff characteristics, thismethod is suitable when the message signal has verylittle frequency content near dc.

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( )m t ( )s t

( )cos 2 cf t

BPF( )x t

DSB-SC Signal SSB-SC Signal


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Generation of SSB-SC SignalsPhase-Shift Method

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2

2

( )m t

+ ( )s t

( )m t

( )sin 2 cf t

( )cos 2 cf t

( ) ( )cos 2 cf t m t

( ) ( )sin 2 cf t m t

+


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Demodulation of SSB-SC SignalsSynchronous Demodulator

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( )s t

( )cos 2 cf t

Lowpass

filter

( )s t ( )x t


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Demodulation of DSB-SC SignalsLowpass filter input signal ( )s t

( ) ( ) ( )

( ) ( ) ( ) ( ) ( )

( ) ( ) { }( ) ( ) { }( )

2

cos 2

cos 2 sin 2 cos 2

1 1 cos 2 2 sin 2 22 2

c

c c c

c c

s t s t f t

m t f t m t f t f t

m t m t f t m t f t

=

=

= +

Lowpass filter output signal

( ) ( )1

2x t m t=

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Baseband signal Bandpass signal


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Vestigial Sideband (VSB) ModulationSSB-SC modulation is suitable for transmission of

signals ( )m t with energy gap in the spectrumbetween zero and a few hundred hertz e.g. voicesignals.

For signals containing significant componentsnear dc, it is difficult to isolate one sideband andvestigial sideband (VSB) modulation is preferred.

( )m t

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In VSB modulation, one sideband is passed almostcompletely whereas just a vestige of the othersideband is retained.


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Vestigial Sideband (VSB) Modulation

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B B

( )M f

f

( )0M

cf

cf

( )SSBS f

f

cf B cf B+

Uppersideband

cf

cf

( )SSBS f

f

cf B + cf B

Lowersideband

cf cf

( )DSBS f

f

cf B + cf B cf B cf B+

Upper

sidebandLower

sideband( )0.5 0M


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Generation of VSB Signals

The spectrum of VSB signal ( )s t

( ) ( ) ( )( ) ( ) ( )

1

2 c c

S f X f H f

f f M f f H f

=

= + +

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( )m t

( )s t

( )cos 2 cf t

VSB

H f

( )x t

DSB-SC Signal VSB Signal


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Demodulation of VSB SignalsSynchronous Demodulator

Lowpass filter input signal

( ) ( ) ( )cos 2 cs t s t f t =

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( )s t

( )cos 2 cf t

Lowpassfilter

( )s t ( )x t

f B


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Demodulation of VSB SignalsTaking the Fourier transform it follows that

( ) ( ) ( ) ( )

( ) ( ) ( ) ( )

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1 + 2 2

4

c c

c c c c

S f M f H f f H f f

f f H f f M f f H f f

= + +

+ + +

Spectrum of the lowpass filter output signal

( ) ( ) ( ) ( )1

4 c cx f M f H f f H f f = + +

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Demodulation of VSB SignalsDistortionless reproduction of the baseband signalrequires that

( ) ( ) constantc cH f f H f f

B f B

+ + =

f

cf

cf c vf f c vf f+ c vf f cf B+ c vf f +

( )H f

f 2

cf

( ) ( )c cH f f H f f + +

2c

f B vf

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Reading Assignments

1. B.P. Lathi, Modern Digital and Analog

Communication Systems , Chap. 4, Part 1.

2. Extra reading:

W. Tomasi, Electronic CommunicationsSystems, Chaps. 4 & 5.

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TE311 Lecture09 SSB SC VSB Modulation

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