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. 1-3.5 (Analog Comm), pp. 6-14, 16.5-22 (15-16.5 - Hilbert Transform - optional, OWN Chp. 8.1-8.3) Review of Last Lecture Amplitude Modulation Quadrature Modulation Frequency Modulation

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)

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

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

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

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