6 003 Signals and Systems Modulation December 3 2009 Communications Systems Today we will look at applications of signals and systems in communication systems Example Transmit voice via telephone wires copper mic amp telephone wire amp Works well basis of local land based telephones speaker Wireless Communication In cellular communication systems signals are transmitted via electromagnetic E M waves mic amp E M wave amp speaker For 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 Yourself For efficient transmission and reception the antenna length should be comparable to one quarter of the wavelength Telephone quality speech contains frequencies between 200 Hz and 3000 Hz How long should the antenna be 0 4 m 3 4 km 1 40 m 4 40 km 2 400 m 5 400 km Check Yourself c so the lowest frequencies 200 Hz produce f the longest wavelengths The wavelength is c 3 108 m s 1 5 106 m 1500 km f 200 Hz Therefore the antenna length should be on the order of 1500 km 400 km 250 miles 4 4 Check Yourself For efficient transmission and reception the antenna length should be comparable to one quarter of the wavelength Telephone quality speech contains frequencies between 200 Hz and 3000 Hz How long should the antenna be 0 4 m 3 4 km 1 40 m 4 40 km 5 2 400 m 5 400 km Check Yourself What frequency E M wave is well matched to an antenna with a length of 4 cm about 1 5 inches 0 200 kHz 3 200 MHz 1 2 MHz 4 2 GHz 2 20 MHz 5 20 GHz Check Yourself A quarter wavelength should be 4 cm 4 cm 4 so the frequency is f c 3 108 m s 2 GHz 16 cm Modern cell phones use frequencies near 2 GHz Check Yourself What frequency E M wave is well matched to an antenna with a length of 4 cm about 1 5 inches 4 0 200 kHz 3 200 MHz 1 2 MHz 4 2 GHz 2 20 MHz 5 20 GHz Wireless Communication Speech is not well matched to the wireless medium Many applications require the use of signals that are not well matched to the required media signal applications audio telephone radio phonograph CD cell phone MP3 video television cinema HDTV DVD internet coax twisted pair cable TV DSL optical fiber E M We can often modify the signals to obtain a better match Today we will introduce simple matching strategies based on modulation Check Yourself Construct a signal Y that codes the audio frequency information in X using frequency components near 2 GHz X j Y j c Determine an expression for Y in terms of X 1 y t x t e j c t 2 y t x t e j c t 3 y t x t cos c t 4 y t x t cos c t 5 none of the above Check Yourself Construct a signal Y that codes the audio frequency information in X using frequency components near 2 GHz X j Y j c Determine an expression for Y in terms of X 1 1 y t x t e j c t 2 y t x t e j c t 3 y t x t cos c t 4 y t x t cos c t 5 none of the above Amplitude Modulation Multiplying a signal by a sinusoidal carrier signal is called amplitude modulation AM AM shifts the frequency components of X by c x t y t cos c t X j c c Y j c c Amplitude Modulation Multiplying a signal by a sinusoidal carrier signal is called amplitude modulation The signal modulates the amplitude of the carrier x t y t cos c t x t t cos c t t x t cos c t t Amplitude Modulation How could you recover x t from y t x t cos c t y t Synchronous Demodulation X can be recovered by multiplying by the carrier and then low pass filtering This process is called synchronous demodulation y t x t cos c t z t y t cos c t x t cos c t cos c t x t 1 1 cos 2 c t 2 2 Synchronous Demodulation Synchronous demodulation convolution in frequency Y j c c c c Z j 2 c 2 c Synchronous Demodulation We can recover X by low pass filtering Y j c c c c Z j 2 c 2 c Frequency Division Multiplexing Multiple transmitters can co exist as long as the frequencies that they transmit do not overlap z1 t x1 t cos w1t z2 t x2 t cos wct cos w2t z3 t x3 t cos w3t z t LPF y t Frequency Division Multiplexing Multiple transmitters simply sum to first order z1 t x1 t cos w1t z2 t x2 t z3 t cos w3t LPF cos wct cos w2t x3 t z t y t Frequency Division Multiplexing The receiver can select the transmitter of interest by choosing the corresponding demodulation frequency Z jw w w X1 jw w1 w2 w3 w w Frequency Division Multiplexing The receiver can select the transmitter of interest by choosing the corresponding demodulation frequency Z jw w w X2 jw w1 w2 w3 w w Frequency Division Multiplexing The receiver can select the transmitter of interest by choosing the corresponding demodulation frequency Z jw w w X3 jw w1 w2 w3 w w Broadcast Radio Broadcast radio was championed by David Sarnoff who previously worked 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 Receiver The problem with making an inexpensive radio receiver is that you must know the carrier signal exactly x t LPF z t cos wc t cos wc t f y t Check Yourself The problem with making an inexpensive radio receiver is that you must know the carrier signal exactly x t LPF z t cos wc t y t cos wc t f What happens if there is a phase shift between the signal used to modulate and that used to demodulate Check Yourself y t x t cos c t cos c t 1 1 cos cos 2 c t x t 2 2 Passing y t through a low pass filter yields 21 x t cos If 2 the output is zero If changes with time then the signal fades AM with Carrier One way to synchronize the sender and receiver is to send the carrier along with the message x t z t C cos c t z t x t cos c t C cos c t x t C cos c t x t C t z t Adding carrier is equivalent to shifting the DC value of x t …
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