Lecture 9 Outline:
AM and FM Modulation
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Announcements:
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Revised slides on upsampling posted
My OHs today: 11:30-12:30, 2-3 (next week extend WF to 11:30-1)
HW 3 posted
Reading today: “3: Communication Systems” pp. 1-3.5 (Analog Comm),
pp. 6-14, 16.5-22 (15-16.5 - Hilbert Transform - optional, OWN Chp. 8.1-8.3)
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Review of Last Lecture
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Amplitude Modulation
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Quadrature Modulation
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Frequency Modulation
Review of Last Lecture
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Digital Downsampling
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Removes samples of x(nTs) for n≠MTs
Repeats Xd(ejW ) every 2p/M and scales W axis by M
Can prefilter Xd(ejW ) by LPF with bandwith p/M prior to
downsampling to avoid downsample aliasing
xd[n]=x(nTs)
0 123…
jW’)
Xdd(ejW’
-p/M
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0
p/M
xc[n]
Downsample
By M (M)
0
Modulator
analog signal : m(t ) (Transmitter)
-2p
s(t )
3
4
……
-p
0
p
Communication System Block Diagram
bits : b1b2 ...
2
Xc(ejW )
…
…
W’
1
Analog
Channel
sˆ(t )
2p
Demodulator
(Receiver)
W=MW’
bˆ1bˆ2 ...
mˆ ( t )
Amplitude Modulation
DSBSC, SSB, Broadcast AM
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(DSBSC) Modulated signal is s(t)=m(t)cos(wct)
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Signal bandwidth (bandwidth occupied in positive frequencies) is 2W
s(t ) = m(t ) cos(wct )  .5[ M ( j (w  wc ))  M ( j (w  wc ))]
1W
2W
ka M ( jw )
S ( jw )
USB
USB
-W
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W
w
LSB
w c
wc
w
Redundant information: can either transmit upper sidebands
(USB) only or lower sidebands (LSB) only and recover m(t)
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Single sideband modulation (SSB); uses 50% less bandwidth (less $$$)
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Demodulator for DSBSC/SSB: multiply by cos(wct) and LPF
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Broadcast AM has s(t)=[1+kam(t)]cos(wct) with [1+kam(t)]>0
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Can recover m(t) with envelope detector (see lecture 12 of 102a notes)
Quadrature Modulation
Sends two info. signals on the cosine and sine carriers
DSBSC
Demod
LPF
m1(t)
m1(t)cos(w ct)+
m2(t)sin(w ct)
cos(w ct)
-90o
sin(w ct)
DSBSC
Demod
LPF
m2(t)
FM Modulation
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Message signal m(t) encoded in carrier frequency
FM modulated signal:
s(t)=Acos(q(t))=Acos(wct+kfm(t)dt)
Instantaneous frequency: wi=wc+kfm(t)
Signal robust to amplitude variations and reflections
 Frequency analysis nonlinear (hard, will skip)
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Frequency Deviation: Df=kf max|m(t)|
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Maximum deviation of wi from wc: wi=wc+kfm(t)
Carson’s Rule for bandwidth of s(t):
Bs2Df+2Bm
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Depends on max deviation from
w c and how fast w i changes
FM Demod: Differentiator + Envelope Detector
Main Points
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Modulation is the process of encoding an analog message
signal (or bits) into a carrier signal
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DSBSC multiplies the message signal and the carrier together.
Synchronous demodulation multiplies by the carrier and then uses a
LPF. Requires learning carrier phase at receiver (hard!)
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SSB is a spectrally efficient AM technique with half the BW
requirements of standard AM and DSBSC.
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Quadrature modulation sends two different signals in the same
bandwidth using sin and cosine carriers (which are orthogonal)
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FM modulation encodes information in signal frequency. More
robust to amplitude errors and signal reflections than AM
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Bandwidth depends on info. signal bandwidth and freq. deviation