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