ECC1015 Communication System I

Communication System I

Electronics and Communication EngineeringHanyang University

Haewoon Nam

Lecture 7

(ECC1015)

1

ECC1015 Communication System I

Summary of the Previous Lecture

• Theory– DSB-SC (product modulation) consists of the product of the message

signal and the carrier wave,

– Fourier transform of s(t)

– Its only advantage is saving transmitted power, which is important enough when the available transmitted power is at a premium

2

)8.3()()2cos( )()()(

tmtfAtmtcts

cc π==

)9.3()]()([21)( ccc ffMffMAfS ++−=

ECC1015 Communication System I

Summary of the Previous Lecture

• DSB-SC

3[Ref] Introduction to Analog and Digital Communications,

by Haykin and Moher, Wiley

ECC1015 Communication System I

Summary of the Previous Lecture

• Coherent detection (synchronous demodulation)

– Using the trigonometric identity

– Through the low pass filter

4[Ref] Introduction to Analog and Digital Communications,

by Haykin and Moher, Wiley

)cos()cos()()cos()()( φππφπυ +′=+′= tfAtfAtmtfAtst cccccc 222)}cos(){cos()()( φφπυ ++′= tfAAtmt ccc 421

)cos()()( φυ 21ccO AAtmt ′=

)cos(21)cos(

21)cos()cos( 212121 θθθθθθ −++=

ECC1015 Communication System I

Double Side Band Suppressed Carrier

• Coherent detection (synchronous demodulation)– The recovery of the message signal m(t) can be accomplished by first

multiplying s(t) with a locally generated sinusoidal wave and then low-pass filtering the product.

• The quadrature null effect– The zero demodulated signal, when occurs for Φ=±π/2– The phase error Φ in the local oscillator causes the detector output to be

attenuated by a factor equal to cos Φ

5

)2cos(21

21)(cos2 θθ +=

ECC1015 Communication System I

Double Side Band Suppressed Carrier

• Same examplein Slide 9

6[Ref] Introduction to Analog and Digital Communications,

by Haykin and Moher, Wiley

ECC1015 Communication System I

Double Side Band Suppressed Carrier

7[Ref] Introduction to Analog and Digital Communications,

by Haykin and Moher, Wiley

ECC1015 Communication System I

Double Side Band Suppressed Carrier

• Costas receiver– Consists of two coherent detectors supplied with the same input signal

• Two local oscillator signals that are in phase quadrature with respect to each other

• I-channel : in-phase coherent detector• Q-channel :

quadrature-phase coherent detector

– Phase control in the Costas receiver ceases with modulation,

• Which means that phase-lock would have to be re-established with the reappearance of modulation

8[Ref] Introduction to Analog and Digital Communications,

by Haykin and Moher, Wiley

ECC1015 Communication System I

Single Side Band Modulation

• Single sideband (SSB)– Suppress one of the two sidebands

in the DSB-SC modulated wave

• Comparison of DSB-SCand Single sideband (SSB)

9

)( fM

f0 WW−

fCfCf−

W2W2

0

fCfCf−

W

0

W

fCfCf−

W

0

W

DSB-SC

SSBUpper sideband

Lower sideband

ECC1015 Communication System I

Single Side Band Modulation

• Review of DSB-SC– A DSB-SC modulator using the sinusoidal modulating wave

– The resulting DSB-SC modulated wave is

• In upper SSB

10

)2cos()( tfAtm mm π=

)13.3(])(2cos[21])(2cos[

21

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

tffAAtffAA

tftfAAtmtctS

mcmcmcmc

mcmc

DSB

−++=

==

ππ

ππ

)14.3(])(2cos[21)( tffAAtS mcmcUSSB += π

)15.3()2sin()2sin(21)2cos()2cos(

21)( tftfAAtftfAAtS cmmccmmcUSSB ππππ −=

Upper sideband Lower sideband

)2sin()(ˆ21)2cos()(

21)( tfAtmtfAtmtS ccccUSSB ππ −=

Hilbert transform of m(t)

ECC1015 Communication System I

Hilbert Transform

• A Hilbert transformer is a wide-band phase-shifter whose frequency response is characterized in two parts as follows

– Signum function

– The Hilbert transform of the message signal

11

)22.3()sgn()( fjfH −=

HilbertTransformer

),( fH )(th

)( fX

<>−

=−=0 ),(0 ),(

)()sgn()(ˆffjXffjX

fXfjfX

<−>

=0 ,1

0 ,1)sgn(

ff

f f0

1+

1−

<>−

=0 ),(0 ),(

)(ˆffjMffjM

fM)(

1)(ˆ tmt

tmπ

=

)()(ˆ txt

tx ∗= 1π

tth

1)(

π=

)(tx

)(ˆ fM

f

j+

j−

Phaserotation

ECC1015 Communication System I

Single Side Band Modulation

• Cosine and Sine function in frequency domain

• In upper SSB

12

)2sin()(ˆ21)2cos()(

21)( tftmAtftmAtS ccccUSSB ππ −= Hilbert

transformof m(t)

)2cos( tfA cc π

fCfCf− 0

2cA

)2sin( tfA cc π

fCfCf− 0

Phaserotation

90+

90−

)(ˆ fM

f

j+

j−

fCfCf−

W2W2

0

2cA

fCfCf−

W2W2

0

2cA

fCfCf− 0

)( fSUSSB

cA

ECC1015 Communication System I

Single Side Band Modulation

• In lower SSB

13

)2sin()(ˆ21)2cos()(

21)( tftmAtftmAtS ccccLSSB ππ += Hilbert

transformof m(t)

)(ˆ fM

f

j+

j−

fCfCf−

W2W2

0

2cA

fCfCf−

W2W2

0

2cA

fCfCf− 0

)( fSLSSB

cA

ECC1015 Communication System I

Announcement and Assignment

• Reading assignment– Amplitude Modulation

14