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Chapter 2 ContinuousWave
Modulation
“
Analog Modulation
” is the subject concerned
in this chapter.
©
PoNing [email protected]
Chapter 22
2.1 Introduction
±
Analog communication system
²
The most common carrier is the sinusoidal wave.
Carrier wave
(Analog)
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Chapter 23
2.1 Introduction
±
Modulation
²
A process by which
some characteristic of a carrier
is varied in accordance with a
modulating wave
(baseband signal).
±
Sinusoidal ContinuousWave (CW) modulation
²
Amplitude modulation
²
Angle modulation
©
PoNing [email protected]
Chapter 24
2.1 Introduction
Amplitude Modulation
Frequency Modulation
Baseband signal
Sinusoidal carrier
©
PoNing [email protected]
Chapter 25
2.2 DoubleSideband with Carrier or simply
Amplitude Modulation
±
Two required conditions on amplitude sensitivity
²
1 +
k
a
m
(
t
)
≥
0, which is ensured by 
k
a
m
(
t
)
1.
±
The case of 
k
a
m
(
t
) > 1 is called
overmodulation
.
±
The value of 
k
a
m
(
t
) is sometimes represented by “percentage”
(because it is limited by 1), and is named (
k
a
m
(
t
)
×
100)%
modulation.
²
f
c
>>
W
, where
W
is the message bandwidth.
±
Violation of this condition will cause
nonvisualized envelope
.
index
modulation
or
y
sensitivit
amplitude
is
where
),
2
cos(
)]
(
1
[
)
(
Signal
Modulated
)
(
Baseband
)
2
cos(
)
(
Carrier
a
c
a
c
c
c
k
t
f
t
m
k
A
t
s
t
m
f
A
t
c
π
+
=
=
©
PoNing [email protected]
Chapter 26
2.2 Overmodulation
overmodulaion
1

)
(

≤
t
m
k
a
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Chapter 27
2.2 Example of
NonVisualized Envelope
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PoNing [email protected]
Chapter 28
2.2 Example of
Visualized Envelope
©
PoNing [email protected]
Chapter 29
2.2 Transmission Bandwidth
[]
)
(
)
(
2
)
(
)
(
2
)
(
)
2
cos(
)]
(
1
[
)
(
c
c
c
a
c
c
c
c
a
c
f
f
M
f
f
M
A
k
f
f
f
f
A
f
S
t
f
t
m
k
A
t
s
+
+
−
+
+
+
−
=
⇒
+
=
δ
π
2
W
Transmission bandwidth
B
T
= 2
W
.
©
PoNing [email protected]
Chapter 210
2.2 Transmission Bandwidth
±
Transmission bandwidth of an AM wave
²
For positive frequencies, the highest frequency
component of the AM wave equals
f
c
+
W
, and the
lowest frequency component equals
f
c
–
W
.
²
The difference between these two frequencies
defines the transmission bandwidth
B
T
for an AM
wave.
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Chapter 211
2.2 Transmission Bandwidth
±
The condition of
f
c
>
W
ensures that the sidebands
do not overlap.
©
PoNing [email protected]
Chapter 212
2.2 Negative Frequency
²
Operational meaning of “negative frequency”
in spectrum
±
If timedomain signal is
realvalued
, the
negative
frequency spectrum
is simply a mirror of the
positive frequency spectrum
.
±
We may then define a onesided spectrum as
±
Hence, if only realvalued signal is considered, it is
unnecessary to introduce “negative frequency”.
.
0
for
)
(
2
)
(
sided

one
≥
=
f
f
S
f
S
©
PoNing [email protected]
Chapter 213
2.2 Negative Frequency
±
So the introduction of
negative frequency part
is
due to the need of
imaginary signal part
.
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This note was uploaded on 02/15/2011 for the course SYSC 3501 taught by Professor Fewrf during the Spring '11 term at Carleton.
 Spring '11
 fewrf

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