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ECC1015 Communication System I Communication System I Electronics and Communication Engineering Hanyang University Haewoon Nam Lecture 4 (ECC1015) 1
Transcript of Communication System I - KOCWcontents.kocw.net/KOCW/document/2014/hanyang/namhaeun/4.pdf · 2016....
ECC1015 Communication System I
Communication System I
Electronics and Communication EngineeringHanyang University
Haewoon Nam
Lecture 4
(ECC1015)
1
ECC1015 Communication System I
Summary of the Previous Lecture
• A periodic signal can be represented as a sum of complex exponentials
• Fourier transforms can be defined for complex exponentials• Consider a periodic signal gT0(t)
2
)80.2()2exp()( 00 ∞
−∞=
=n
n tnfjctgT π
)81.2()2exp()(10
2/
2/ 00
0
0
dttnfjtgTT
cT
Tn π−= −Complex Fourier coefficient
f0 : fundamental frequency
)82.2(10
0 Tf =
ECC1015 Communication System I
Summary of the Previous Lecture
3
ECC1015 Communication System I
Summary of the Previous Lecture
• Energy signal– Signals of finite signal energy– Zero average power (or vanishing mean signal power)
• Power signal– Signals of infinite signal energy– Finite mean signal power
4
t
xx(t)
t
xx(t)
ECC1015 Communication System I
Summary of the Previous Lecture
• Autocorrelation Function– Autocorrelation function of the energy signal x(t) for a large τ as
– The energy of the signal x(t)– The value of the autocorrelation function Rx(τ) for τ=0
5
∞
∞−−= )124.2()()()( * τττ dtxtxRx
dttxRx ∞
∞−= 2)()0(
[Ref] Introduction to Analog and Digital Communications,by Haykin and Moher, Wiley
ECC1015 Communication System I
Summary of the Previous Lecture
• Cross-Correlation of Energy Signals– The cross-correlation function of the pair
– The energy signals x(t) and y(t) are said to be orthogonal over the entire time domain
– If Rxy(0) is zero
– The second cross-correlation function
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)142.2()()( * ττ −= yxxy RR
)141.2()()()( * dttxtyRyx ∞
∞−−= ττ
)140.2(0)()( * =∞
∞−dttytx
)139.2()()()( * dttytxRxy ∞
∞−−= ττ
ECC1015 Communication System I
Correlation and Spectral Density
• Energy Spectral Density– The energy spectral density is a nonnegative real-valued quantity for all f, even
though the signal x(t) may itself be complex valued.
• Wiener-Khitchine Relations for Energy Signals– The autocorrelation function and energy spectral density form a Fourier-
transform pair
7
)125.2()()( 2fXfx =Ψ
)126.2()2exp()()( ∞
∞−−=Ψ ττπτ dfjRf xx
)127.2()2exp()()( ∞
∞−Ψ= dffjfR xx τπτ
ECC1015 Communication System I
Correlation and Spectral Density
• By setting f=0– The total area under the curve of the complex-valued autocorrelation function of
a complex-valued energy signal is equal to the real-valued energy spectral at zero frequency
• By setting τ=0– The total area under the curve of the real-valued energy spectral density of an
erergy signal is equal to the total energy of the signal.
8
)0()( xx dR Ψ=∞
∞−ττ
)0()( xx Rfdf =Ψ∞
∞−
ECC1015 Communication System I
Correlation and Spectral Density
• Power Spectral Density– Examples include periodic signals and noise– The average power of a signal is
– The total area under the curve of the power spectral density of a power signal is equal to the average power of that signal.
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−∞→=
T
TTdttx
TP )147.2()(
21lim 2
∞<P
∞
∞− ∞→
= )151.2()(
21lim 2 dffXT
P TT
Power spectral density or Power spectrum
)152.2()(21lim)( 2fXT
fS TTx ∞→=
∞
∞−= )153.2()( dffSP x
∞
∞−
∞
∞−= dffXdttx TT
22 )()(
ECC1015 Communication System I
Modulation
• Modulation – The process by which some characteristic of a carrier wave is
varied in accordance with an information-bearing signal.– Continuous-wave modulation
• Amplitude modulation• Frequency modulation
• AM modulation family– Amplitude modulation (AM)– Double sideband-suppressed carrier (DSB-SC)– Single sideband (SSB)– Vestigial sideband (VSB)
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ECC1015 Communication System I
Amplitude Modulation
• A sinusoidal carrier signal
• An amplitude-modulated signal
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)cos()( tfAtc cc 2π=
)cos()]([)( tftmkAts cac 21 π+=
cA : carrier amplitude
cf : carrier frequency
ak : amplitude sensitivity
)(tm : message signal
)(tm )(ts
)cos( tfA cc 2π
Xak
+
(DC)1
(carrier)
ECC1015 Communication System I
Amplitude Modulation
• Without DC addition
• To avoid signal distortion when envelope detector is used, the following condition needs to be met.
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)(tm )(ts
)cos( tfA cc 2π
Xak
(carrier)
Phase reversals
)cos()()( tftmkAts cac 2π=
1<|)(| tmka Therefore DC is added.
ECC1015 Communication System I
Amplitude Modulation
• Amplitude modulated signal
• Fourier transform of the signal
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)cos()]([)( tftmkAts cac 21 π+= )cos()()cos( tftmkAtfA caccc 22 ππ +=
)]()([)]()([)( ccac
ccc ffMffMkAffffAfS 2 2 −+++−++= δδ
[Ref] Introduction to Analog and Digital Communications,by Haykin and Moher, Wiley
ECC1015 Communication System I
Amplitude Modulation
• A simple sinusoidal message signal
• Amplitude modulated signal
• To avoid signal distortion, the modulation factor must be kept below unity.
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)cos()]cos([)( tftfAkAts cmmac 221 ππ+=
)cos()( tfAtm mm 2π=
)cos()]cos([ tftfA cmc 221 ππμ+=
ma Ak=μwhere is the modulation factor or percentage modulation.
ECC1015 Communication System I
Amplitude Modulation
• A simple sinusoidal message signal
15[Ref] Introduction to Analog and Digital Communications,
by Haykin and Moher, Wiley
ECC1015 Communication System I
Amplitude Modulation
• An example
• The modulation factor
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1=cA
50.=μ : under-modulation
Carrier frequency
Carrier amplitude
Modulation frequency
Hzfc 40.=Hzfm 050.=
: 100% modulation
: over-modulation
01.=μ 02.=μ
ECC1015 Communication System I
Amplitude Modulation
17[Ref] Introduction to Analog and Digital Communications,
by Haykin and Moher, Wiley
ECC1015 Communication System I
Amplitude Modulation
18[Ref] Introduction to Analog and Digital Communications,
by Haykin and Moher, Wiley
ECC1015 Communication System I
Amplitude Modulation
19[Ref] Introduction to Analog and Digital Communications,
by Haykin and Moher, Wiley
ECC1015 Communication System I
Announcement and Assignment
• Reading assignment– Amplitude Modulation
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