1. Lecture 9 Outline: AM and FM Modulation
Announcements:
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 (Analog Comm), pp. 6-14, ( Hilbert Transform - optional, OWN Chp )
Review of Last Lecture
Amplitude Modulation
Quadrature Modulation
Frequency Modulation

2. Modulator (Transmitter)
Review of Last Lecture
Digital Downsampling
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
Communication System Block Diagram 1 2 3 4 1 2 3 …
xd[n]=x(nTs)
xc[n]
Downsample
By M (M)
p/M
-p/M W’
Xd(ejW’) p -p
Xc(ejW)
-2p 2p …
p/M
-p/M W’
Xd(ejW’) p -p
Xc(ejW)
-2p 2p …
W=MW’
W=MW’
Modulator (Transmitter)
Analog
Channel
Demodulator
(Receiver)

3. Amplitude Modulation DSBSC, SSB, Broadcast AM
(DSBSC) Modulated signal is s(t)=m(t)cos(wct)
Signal bandwidth (bandwidth occupied in positive frequencies) is 2W
Redundant information: can either transmit upper sidebands (USB) only or lower sidebands (LSB) only and recover m(t)
Single sideband modulation (SSB); uses 50% less bandwidth (less $$$)
Demodulator for DSBSC/SSB: multiply by cos(wct) and LPF
Broadcast AM has s(t)=[1+kam(t)]cos(wct) with [1+kam(t)]>0
Can recover m(t) with envelope detector (see lecture 12 of 102a notes) 1 ka W 2W
USB
LSB w -W W
-wc w wc

4. Quadrature Modulation
Sends two info. signals on the cosine and sine carriers
DSBSC Demod
m1(t)
LPF
m1(t)cos(wct)+
m2(t)sin(wct)
cos(wct)
-90o
sin(wct)
m2(t)
DSBSC
Demod
LPF

5. Depends on max deviation from wc and how fast wi changes
FM Modulation
Message signal m(t) encoded in carrier frequency
FM modulated signal:
Instantaneous frequency: wi=wc+kfm(t)
Signal robust to amplitude variations and reflections
Frequency analysis nonlinear (hard, will skip)
Frequency Deviation: Df=kf max|m(t)|
Maximum deviation of wi from wc: wi=wc+kfm(t)
Carson’s Rule for bandwidth of s(t):
FM Demod: Differentiator + Envelope Detector
s(t)=Acos(q(t))=Acos(wct+kfm(t)dt)
Bs2Df+2Bm
Depends on max deviation from wc and how fast wi changes

6. Main Points
Modulation is the process of encoding an analog message signal (or bits) into a carrier signal
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!)
SSB is a spectrally efficient AM technique with half the BW requirements of standard AM and DSBSC.
Quadrature modulation sends two different signals in the same bandwidth using sin and cosine carriers (which are orthogonal)
FM modulation encodes information in signal frequency. More robust to amplitude errors and signal reflections than AM
Bandwidth depends on info. signal bandwidth and freq. deviation