6.003: Signals and SystemsModulationDecember 3, 2009Communications SystemsToday we will look at applications of signals and systems in com-munication systems.Example: Transmit voice via telephone wires (copper)mic amp telephone wire amp speakerWorks well: basis of local land-based telephones.Wireless CommunicationIn cellular communication systems, signals are transmitted via elec-tromagnetic (E/M) waves.mic amp E/M wave amp speakerFor efficient transmission and reception, antenna length should be≈ one-quarter of the wavelength.Telephone-quality speech contains frequencies from 200 to 3000 Hz.How long should the antenna be?Check YourselfFor efficient transmission and reception, the antenna lengthshould be comparable to one-quarter of the wavelength.Telephone-quality speech contains frequencies between 200 Hzand 3000 Hz.How long should the antenna be?0. 4 m 1. 40 m 2. 400 m3. 4 km 4. 40 km 5. 400 kmCheck YourselfThe wavelength is λ =cfso the lowest frequencies (200 Hz) producethe longest wavelengthsλ =cf=3 × 108m/s200 Hz= 1.5 × 106m = 1500 km .Therefore the antenna length should be on the order ofλ4=1500 km4≈ 400 km ≈ 250 miles .Check YourselfFor efficient transmission and reception, the antenna lengthshould be comparable to one-quarter of the wavelength.Telephone-quality speech contains frequencies between 200 Hzand 3000 Hz.How long should the antenna be? 50. 4 m 1. 40 m 2. 400 m3. 4 km 4. 40 km 5. 400 kmCheck YourselfWhat frequency E/M wave is well matched to an antennawith a length of 4 cm (about 1.5 inches)?0. 200 kHz 1. 2 MHz 2. 20 MHz3. 200 MHz 4. 2 GHz 5. 20 GHzCheck YourselfA quarter-wavelength should be 4 cm,λ4∼ 4 cmso the frequency isf =cλ∼3 × 108m/s16 cm≈ 2 GHz .Modern cell phones use frequencies near 2 GHz.Check YourselfWhat frequency E/M wave is well matched to an antennawith a length of 4 cm (about 1.5 inches)? 4.0. 200 kHz 1. 2 MHz 2. 20 MHz3. 200 MHz 4. 2 GHz 5. 20 GHzWireless CommunicationSpeech is not well matched to the wireless medium.Many applications require the use of signals that are not wellmatched to the required media.signal applicationsaudio telephone, radio, phonograph, CD, cell phone, MP3video television, cinema, HDTV, DVDinternet coax, twisted pair, cable TV, DSL, optical fiber, E/MWe can often modify the signals to obtain a better match.Today we will introduce simple matching strategies based onmodulation.Check YourselfConstruct a signal Y that codes the audio frequency informationin X using frequency components near 2 GHz.ω|X(jω)|ωωc|Y (jω)|Determine an expression for Y in terms of X.1. y(t) = x(t) ejωct2. y(t) = x(t) ∗ ejωct3. y(t) = x(t) cos(ωct) 4. y(t) = x(t) ∗ cos(ωct)5. none of the aboveCheck YourselfConstruct a signal Y that codes the audio frequency informationin X using frequency components near 2 GHz.ω|X(jω)|ωωc|Y (jω)|Determine an expression for Y in terms of X. 11. y(t) = x(t) ejωct2. y(t) = x(t) ∗ ejωct3. y(t) = x(t) cos(ωct) 4. y(t) = x(t) ∗ cos(ωct)5. none of the aboveAmplitude ModulationMultiplying a signal by a sinusoidal carrier signal is called amplitudemodulation (AM). AM shifts the frequency components of X by ±ωc.×x(t) y(t)cos ωctω|X(jω)|ωωc−ωcωωc−ωc|Y (jω)|Amplitude ModulationMultiplying a signal by a sinusoidal carrier signal is called amplitudemodulation. The signal “modulates” the amplitude of the carrier.×x(t) y(t)cos ωcttx(t) cos ωcttx(t)tcos ωctAmplitude ModulationHow could you recover x(t) from y(t)?×x(t) y(t)cos ωctSynchronous DemodulationX can be recovered by multiplying by the carrier and then low-passfiltering. This process is calledsynchronous demodulation.y(t) = x(t) cos ωctz(t) = y(t) cos ωct = x(t) × cos ωct × cos ωct = x(t)12+12cos(2ωct)Synchronous DemodulationSynchronous demodulation: convolution in frequency.ωωc−ωc|Y (jω)|ωωc−ωcω2ωc−2ωc|Z(jω)|Synchronous DemodulationWe can recover X by low-pass filtering.ωωc−ωc|Y (jω)|ωωc−ωcω2ωc−2ωc|Z(jω)|Frequency-Division MultiplexingMultiple transmitters can co-exist, as long as the frequencies thatthey transmit do not overlap.x1(t)x2(t)x3(t)z1(t)z2(t) z(t)y(t)z3(t)cosw1tcosw2tcoswctcosw3tLPFFrequency-Division MultiplexingMultiple transmitters simply sum (to first order).x1(t)x2(t)x3(t)z1(t)z2(t) z(t)y(t)z3(t)cosw1tcosw2tcoswctcosw3tLPFFrequency-Division MultiplexingThe receiver can select the transmitter of interest by choosing thecorresponding demodulation frequency.Z(jw)X1(jw)wwwww1w2w3Frequency-Division MultiplexingThe receiver can select the transmitter of interest by choosing thecorresponding demodulation frequency.Z(jw)X2(jw)wwwww1w2w3Frequency-Division MultiplexingThe receiver can select the transmitter of interest by choosing thecorresponding demodulation frequency.Z(jw)X3(jw)wwwww1w2w3Broadcast Radio“Broadcast” radio was championed by David Sarnoff, who previouslyworked at Marconi Wireless Telegraphy Company (point-to-point).• envisioned “radio music boxes”• analogous to newspaper, but at speed of light• receiver must be cheap (as with newsprint)• transmitter can be expensive (as with printing press)Sarnoff (left) and Marconi (right)Inexpensive Radio ReceiverThe problem with making an inexpensive radio receiver is that youmust know the carrier signal exactly!z(t)x(t) y(t)cos(wct) cos(wct+f)L P FCheck YourselfThe problem with making an inexpensive radio receiver is thatyou must know the carrier signal exactly!z(t)x(t) y(t)cos(wct) cos(wct+f)L P FWhat happens if there is a phase shift φ between the signalused to modulate and that used to demodulate?Check Yourselfy(t) = x(t) × cos(ωct) × cos(ωct + φ)= x(t) ×12cos φ +12cos(2ωct + φ)Passing y(t) through a low pass filter yields12x(t) cos φ.If φ = π/2, the output is zero!If φ changes with time, then the signal “fades.”AM with CarrierOne way to synchronize the sender and receiver is to send the carrieralong with the message.× +Cx(t) z(t)cos ωctz(t) = x(t) cos ωct + C cos ωct = (x(t) + C) cos ωcttz(t)x(t) + CAdding carrier is equivalent to shifting the DC value of x(t).If we shift the DC value sufficiently, the message is easy to decode:it is just the envelope (minus the DC shift).Inexpensive Radio ReceiverIf the carrier frequency is much greater than the highest frequencyin the message, AM with carrier can be demodulated with a peakdetector.z(t)z(t)y(t)RCty(t)In AM radio, the highest frequency in the message is 5 kHz and thecarrier frequency is between 500
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