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Vestigial Sideband ModulationKEEE343 Communication Theory

Lecture #11, April 7, 2011Prof. Young-Chai Kokoyc@korea.ac.kr

Summary

·•Vestigial sideband modulation

·•Baseband representation of modulated wave

·•Baseband representation of pass-band filter

·•Frequency division multiplexing

·•Introduction to Angle Modulation

Generation of LSB SSB Using Wideband Low-Pass Filter

HL(f)

DSB Spectrum

�fc

�fc

fc

fc

SSB Spectrum

sgn(f + fc)

�sgn(f � fc)

HL(f)

Generation of USB SSB Using High-Pass (or Passband) Filter

DSB Spectrum

�fc

�fc

fc

fc

SSB Spectrum

sgn(f � fc)sgn(f + fc)

HHP (f) = sgn(f + fc) + sgn(f + fc)

HHP (f)

SSB Modulated Wave

• Lower Sideband SSB

• Upper sideband SSB

sLSB(t) =1

2

m(t) cos(2�fct) +1

2

m(t) sin(2�fct)

sUSB(t) =1

2

m(t) cos(2�fct)�1

2

m(t) sin(2�fct)

Applications of SSB and Difficulties in Implementing SSB

• Two difficulties of SSB modulations

• Designing and implementing the sharp Low-pass (or High-pass/pass-band) filter is not easy for circuit designer.

• Hence, the message signal which does not contain the significant energy in the DC area is often modulated by the SSB such as the speech signal.

• However, the SSB cannot be applicable for the message signal which contains the significant energy around zero frequency such as video signal, computer data, and etc.

0 [Hz]

Spectrum of Speech Signal (Example)

Vestigial Sideband (VSB) Modulation

• VSB Modulation

• Modulation to overcome the two difficulties of the SSB modulations.

• Allow a small amount, or vestige, of the unwanted sideband to appear at the output of an SSB modulator

• The design of the sideband filter is simplified since the need for sharp cutoff at the carrier frequency is eliminated.

• In addition, a VSB system has improved low-frequency response and can even have dc response.

Idea of VSB Modulator

• Pass-band (or High-pass) filter for USB-SSB modulation

• The filter below is much easier to design and implement

fc�fc

|HU (f)|

fcfc � f1

✏

1� ✏1

1

fc + f1

• Consider the two-tone message signal given as

• Message signal multiplied by the carrier wave, that is, DSB signal

m(t) = A cos(2�f1t) +B cos(2�f2t)

eDSB(t) = (A cos(2�f1t) +B cos(2�f2t)) · cos(2�fct)

=

1

2

A cos(2�(fc + f1)t) +1

2

A cos(2�(fc � f1)t)

+

1

2

B sin(2�(fc + f1)t) +1

2

B sin(2�(fc � f1)t)

• Spectrum of DSB signal

• Frequency response of the VSB filter

• Output response

1

2B

1

2B1

2A

1

2A

fcfc � f2 fc + f2fc + f1fc � f1

✏

1� ✏1

fcfc � f2

fc + f2

fc + f1fc � f1

1

2A�

1

2[A(1� �)]

1

2B

fc � f1 fc + f1

fc + f2

s(t) =

1

2

A� cos(2⇥(fc � f1)t)

+

1

2

A(1� �) cos(2⇥(fc + f1)t)

+

1

2

B cos(2⇥(fc + f2)t)

• Downconvert (by Multiplying ) and low pass filtering

• Downconvert

Demodulation of VSB Signal (Coherent method)

4 cos(2�fct)

d(t) = s(t) · 4 cos(2⇥fct)

=

1

2

A� cos(2⇥(fc � f1)t) · 4 cos(2⇥fct)

+

1

2

A(1� �) cos(2⇥(fc + f1)t) · 4 cos(2⇥fct)

+

1

2

B cos(2⇥(fc + f2)t) · 4 cos(2⇥fct)

cos(2�(fc + f1)t) · cos(2�fct) =1

2

cos(2�(2fc + f1)t) + cos(2�f1t)

�

Low-Pass Filtering 1

2

cos(2�f1t)

• Signal after Low-pass filtering

⇥(t) = A� cos(2⇤f1t) +A(1� �) cos(2⇤f1t) +B cos(2⇤f2t)

= A cos(2⇤f1t) +B cos(2⇤f2t)

Television Signals

[Ref: Haykin & Moher, Textbook]

Baseband Representation of Modulated Waves

• DSB modulated wave signal

• SSB modulated wave signal

• In general, we can write the “linear modulated wave” as

sDSB(t) = Am(t) cos(2�fct)

sSSB(t) =1

2

Am(t) cos(2�fct)±1

2

Am(t) sin(2�fct)

s(t) = sI(t) cos(2�fct)� sQ(t) sin(2�fct)

Carrier wave with frequencyfc quadrature-phase version of the carrier

c(t) = cos(2�fct) c(t) = sin(2�fct)

Orthogonal each other

• We can rewrite the modulated wave as

s(t) = sI(t)c(t)� sQ(t)c(t)

in-phase component of s(t) quadrature(-phase) component of s(t)

• Introduce the complex envelop of the modulated wave s(t)

• Define the complex carrier wave

s(t) = sI(t) + jsQ(t)

c(t) = cI(t)� jcQ(t)

• Consider the following

• Real term

• Imaginary term

s(t) · exp(j2�fct) =

sI(t) + jsQ(t)

�·cos(2�fct) + j sin(2�fct)

�

⇥s(t) · exp(j2�fct)

�= sI(t) · cos(2�fct)� sQ(t) · sin(2�fct)

�s(t) · exp(j2�fct)

�= sI(t) sin(2�fct) + sQ(t) cos(2�fct)

Xs(t)

exp(j2�fct)

�·�

s(t)

• Now consider

• Then we can represent the modulated wave as

s(t) = sI(t) + jsQ(t) = a(t)ej�(t)

where

a(t) =q

s2I(t) + js2Q(t), �(t) = tan�1 sQ(t)

sI(t)

s(t) = <s(t)ej2⇥fct

�= <

a(t)ej�(t)ej2⇥fct

�

= <a(t)ej[2⇥fct+�(t)]

= a(t) cos[2⇥fct+ �(t)]

• Three different representation of modulated wave using its equivalent baseband signal

s(t) = sI(t) cos(2⇥fct)� sQ(t) sin(2⇥fct)

= <s(t)ej2�fct

�

= a(t) cos[2⇥fct+ �(t)]

Superheterodyne Receiver

[Ref: Haykin & Moher, Textbook]

Digital BasebandIC

ABB

ABB Section

900

÷ 2

PLLLNA

PowerAmplifier

÷ 2

PLL

900

PA Ctrl

LDO’s

26MHz Osc.

Switch-plexer

module

antennaswitch

Transmitter

Communication Chipset ArchitectureReceiver

• To transmit a number of communication signals over the same channel, the signals must be kept apart so that they do not interfere with each other, and thus they can be separated at the receiving end.

• FDM (Frequency division multiplexing)

• TDM (Time division multiplexing)

• SDM (Space division multiplexing)

• CDM (Code division multiplexing)

Frequency-Division Multiplexing

Block Diagram of FDM

• Basic Definition of Angle Modulation

• Phase modulation (PM) if

• Frequency modulation (FM) if

Angle Modulation

s(t) = Ac cos[�i(t)] = Ac cos[2⇥fct+ ⇤c]

�i(t) = 2⇥fct+ kpm(t)

�i(t) = 2⇥fct+ 2⇥kf

Z t

0m(⇤) d⇤