EE3054
Signals and Systems
Amplitude Modulation
Yao Wang
Polytechnic University
Some slides included are extracted from lecture presentations prepared by
McClellan and Schafer
License Info for SPFirst Slides
This work released under a Creative Commons License
with the following terms:
Attribution
The licensor permits others to copy, distribute, display, and perform
the work. In return, licensees must give the original authors credit.
Non-Commercial
The licensor permits others to copy, distribute, display, and perform
the work. In return, licensees may not use the work for commercial
purposes—unless they get the licensor's permission.
Share Alike
The licensor permits others to distribute derivative works only under
a license identical to the one that governs the licensor's work.
Full Text of the License
This (hidden) page should be kept with the presentation
4/9/2008
© 2003, JH McClellan & RW Schafer
2
LECTURE OBJECTIVES
Review of FT properties
Convolution <--> multiplication
Frequency shifting
Sinewave Amplitude Modulation
AM radio
Frequency-division multiplexing
FDM
Reading: Chapter 12, Section 12-2
4/9/2008
© 2003, JH McClellan & RW Schafer
3
Table of Easy FT Properties
Linearity Property
ax1 (t) + bx2 (t) ⇔ aX1 ( jω ) + bX2 ( jω )
Delay Property
x(t − td ) ⇔ e
− jω t d
X( jω )
Frequency Shifting
x(t)e
Scaling
4/9/2008
jω 0 t
x(at) ⇔
⇔ X( j(ω − ω 0 ))
1
|a|
ω
X( j( a ))
© 2003, JH McClellan & RW Schafer
4
Table of FT Properties
x(t) ∗ h(t) ⇔ H( jω )X( jω )
x(t)p(t) ⇔
1
X( jω )∗ P( jω )
2π
jω 0 t
x(t)e
⇔ X( j(ω − ω 0 ))
Differentiation Property
dx(t)
⇔ ( jω )X( jω )
dt
4/9/2008
© 2003, JH McClellan & RW Schafer
5
Convolution Property
x(t)
y(t) = h(t) ∗ x(t)
X( jω )
Y( jω ) = H( jω )X( jω )
Convolution in the time-domain
∞
y(t) = h(t) ∗ x(t) = ∫ h(τ )x(t − τ )dτ
−∞
corresponds to MULTIPLICATION in the
frequency-domain
Y( jω ) = H( jω )X( jω )
4/9/2008
© 2003, JH McClellan & RW Schafer
6
Cosine Input to LTI System
Y (j ω ) = H( jω )X(j ω )
= H( jω )[πδ (ω − ω 0 ) + πδ (ω + ω 0 )]
= H( jω 0 )πδ (ω − ω 0 ) + H(− jω 0 )πδ (ω + ω 0 )
y(t)
=
=
=
4/9/2008
1
2
jω 0 t
1
2
jω 0 t
H (j ω 0 ) e
1
2
− jω 0t
1
2
− jω 0 t
+ H(− j ω 0 ) e
*
H( jω 0 ) e + H ( jω 0 ) e
H( jω 0 ) cos(ω 0t + ∠H( jω 0 ))
© 2003, JH McClellan & RW Schafer
7
Ideal Lowpass Filter
Hlp ( jω )
−ω co
ω co
y(t) = x(t)
y(t) = 0
4/9/2008
if ω 0 < ω co
if ω 0 > ω co
© 2003, JH McClellan & RW Schafer
8
Ideal LPF: Fourier Series
1
H( jω ) = 
0
ω < ω co
ω > ω co
f co "cutoff freq."
y(t) =
4/9/2008
4
π
sin(50πt ) +
4
sin (150πt )
3π
© 2003, JH McClellan & RW Schafer
9
Frequency Shifting
Property
x(t)e
jω 0 t
⇔ X( j(ω − ω 0 ))
x(t ) cos(ωc t ) ⇔
Y ( jω ) =
1
2
X ( j (ω − ωc )) + 12 X ( j (ω + ωc ))
The way communication
systems work
How do we share
bandwidth ?
4/9/2008
© 2003, JH McClellan & RW Schafer
11
Amplitude Modulator
y(t) = x(t)cos(ω c t)
x(t)
X( jω )
Y( jω ) =
cos(ω ct)
1
X( j(ω − ω c ))
2
1
+ X( j(ω + ω c ))
2
x(t) modulates the amplitude of the cosine
wave. The result in the frequency-domain
is two shifted copies of X(jω).
4/9/2008
© 2003, JH McClellan & RW Schafer
12
y (t ) = x (t ) cos(ωct ) ⇔
Y ( jω ) = 12 X ( j (ω − ωc )) + 12 X ( j (ω + ωc ))
1
x (t ) = 
0
t <T
⇔
t >T
sin(ω T )
X ( jω ) = 2
(ω )
y (t ) = x (t ) cos(ω c t ) ⇔
sin((ω − ω c )T ) sin((ω + ω c )T )
Y ( jω ) =
+
(ω − ω c )
(ω + ω c )
4/9/2008
© 2003, JH McClellan & RW Schafer
13
y (t ) = x (t ) cos(ωc t ) ⇔
Y ( jω ) = 12 X ( j (ω − ωc )) + 12 X ( j (ω + ωc ))
x(t)
1
2
X ( j (ω + ωc ))
X ( j (ω − ωc ))
ωc
−ω c
4/9/2008
1
2
© 2003, JH McClellan & RW Schafer
14
DSBAM Modulator
y(t) = x(t)cos(ω c t)
x(t)
X( jω )
Y( jω ) =
cos(ω ct)
1
X( j(ω − ω c ))
2
1
+ X( j(ω + ω c ))
2
If X(jω)=0 for |ω|>ωb and ωc >ωb,the result
in the frequency-domain is two shifted and
scaled exact copies of X(jω).
4/9/2008
© 2003, JH McClellan & RW Schafer
15
DSBAM Waveform
In the time-domain, the “envelope” of sinewave peaks follows |x(t)|
4/9/2008
© 2003, JH McClellan & RW Schafer
16
Double Sideband AM (DSBAM)
“Typical”
bandlimited
input signal
Frequency-shifted
copies
4/9/2008
Lower sideband
© 2003, JH McClellan & RW Schafer
Upper sideband
17
DSBAM DEmodulator
x(t)
y(t) = x(t)cos(ω ct)
cos(ω ct)
w(t)
v(t)
cos(ω ct)
1
1
w(t) = x(t)[cos(ω c t)] = x(t) + x(t)cos(2ω c t)
2
2
1
1
1
W( jω ) = X( jω ) + X( j(ω − 2ω c )) + X( j(ω + 2ω c ))
2
4
4
2
V ( jω ) = H( jω )W( jω )
4/9/2008
© 2003, JH McClellan & RW Schafer
18
DSBAM Demodulation
2 | ω |< ω co
H( jω ) = 
0 | ω |> ω co
V4/9/2008
( jω ) = H( jω )W( jω ) = X( jω ) if ω b < ω co < 2ω c −19ω b
© 2003, JH McClellan & RW Schafer
Frequency-Division
Multiplexing (FDM)
Shifting spectrum of signal to higher
frequency:
Permits transmission of low-frequency signals
with high-frequency EM waves
By allocating a frequency band to each signal
multiple bandlimited signals can share the same
channel
AM radio: 530-1620 kHz (10 kHz bands)
FM radio: 88.1-107.9 MHz (200 kHz bands)
4/9/2008
© 2003, JH McClellan & RW Schafer
20
FDM Block Diagram (Xmitter)
cos(ω c1t)
Spectrum of inputs
must be bandlimited
Need ω c 2 − ω c1 > 2ω b
4/9/2008
cos(ω c 2t)
© 2003, JH McClellan & RW Schafer
ω c1 ω c2
21
Frequency-Division De-Mux
ω c1 ω c2
cos(ω c1t)
cos(ω c 2t)
4/9/2008
© 2003, JH McClellan & RW Schafer
22
Bandpass Filters for De-Mux
4/9/2008
© 2003, JH McClellan & RW Schafer
23
QAM
Modulate two signals using the same
carrier freq but orthogonal in phase
Go through in class: modulator and
demodulator
Application in color TV transmission
Quadrature Amplitude
Modulation (QAM)
A method to modulate two signals onto the
same carrier frequency, but with 90o phase shift
cos( 2π f1t )
cos( 2π f1t )
s1 ( t )
s1 ( t )
m (t )
LPF
m (t )
LPF
s2 (t )
sin( 2π f1t )
QAM modulator
s2 (t )
sin( 2π f1t )
QAM demodulator
QAM in more detail
Proof (in time and freq. domain) the demodulator can separate the
signal on board!
Multiplexing of Luminance
and Chrominance
Y(t)
I(t)
LPF
0-4.2MHz
LPF
0-1.5MHz
-π/2
Q(t)
Σ
BPF
2-4.2MHz
LPF
0-0.5MHz
Gate
∼
Acos(2πfct)
Color burst
signal
Σ
Composite
video
DeMultiplexing of Luminance
and Chrominance
Composite
video
Y(t)
Comb Filter
0-4.2MHz
+
LPF
0-1.5MHz
_ Σ
I(t)
Horizontal
sync signal
-π/2
Gate
2Acos(2πfct)
Phase
comparator
∼
Voltage
controlled
oscillator
LPF
0-0.5MHz
Q(t)
Multiplexing of luminance,
chrominance and audio
6.0 MHz
Luminance
I
I and Q
Audio
4.5 MHz
1.25
MHz
4.2 MHz
3.58 MHz
fp
fc
Picture
carrier
fa
Color
Audio
subcarrier subcarrier
(b)
f
Luminance/Chrominance
Separation
In low-end TV receivers, a low pass filter with cut-off frequency at
3MHz is typically used to separate the luminance and chrominance
signal.
The high frequency part of the I component (2 to 3 Mhz) is still retained
in the luminance signal.
The extracted chrominance components can contain significant
luminance signal in a scene with very high frequency (luminance
energy is not negligible near fc)
These can lead to color bleeding artifacts
For better quality, a comb filter can be used, which will filter out
harmonic peaks correspond to chrominance signals.
Show example of comb filter on board
What will a Monochrome
TV see?
The monochrome TV receiver uses a LPT with cut-off at
4.2 MHz, and thus will get the composite video
(baseband luminance plus the I and Q signal modulated
to fc =3.58 MHz)
Because the modulated chrominance signal is at very high
frequency (227.5 cycles per line), the eye smoothes it out
mostly, but there can be artifacts
The LPF in Practical TV receivers have wide transition bands,
and the response is already quite low at fc.
Composite Video Viewed as a
Monochrome Image w/o filtering
Original Y
Composite Signal as Y
On the right is what a B/W receiver will see if no filtering is applied to the baseband video signal
Recovered Y with Filtering
Original Y
Recovered Y
On the right is what a B/W receiver will see if a lowpass filter with cutoff frequency at about
0.75 MHz is applied to the baseband video signal. This is also the recovered Y component
by a color receiver if the same filter is used to separate Y and QAM signal.
Color TV Broadcasting and
Receiving
RGB
--->
YC1C2
Luminance,
Chrom inanc e,
Audio
Multiplexing
Modulation
YC1C2
--->
RGB
DeMultiplexing
DeModulation
Transmitter in More
Details
Audio
FM modulator
4.5MHz
G(t)
B(t)
RGB to YIQ conversion
R(t)
Y(t)
LPF
0-4.2MHz
I(t)
LPF
0-1.5MHz
-π/2
Q(t)
Σ
BPF
2-4.2MHz
∼
Acos(2πfct)
VSB
To
transmit
antenna
LPF
0-0.5MHz
Gate
Σ
Color
burst
signal
Receiver in More Details
Audio
FM demodulator
From antenna
LPF
0-1.5MHz
_Σ
I(t)
-π/2
2Acos(2πfct)
∼
Voltage
Phase
controlled
comparator
oscillator
Horizontal
sync signal
LPF
0-0.5MHz
Q(t)
R(t)
G(t)
B(t)
To CRT
+
Gate
VSB
Demodulator
Y(t)
Comb Filter
0-4.2MHz
YIQ to RGB conversion
BPF, 0-4.2 MHz
BPF, 4.4-4.6MHz
Composite
video
To
speaker
Readings
Sec. 12.2
B. P. Lathi, Modern digital and analog
communication systems, 3rd ed. Oxford
Press, 1998. Chap. 4.
Y. Wang, J. Ostermann, Y. Q. Zhang,
Video Processing and Communications,
Prentice Hall, 2002. chapter 1.