6 003 Signals and Systems Lecture 23 December 3 2009 6 003 Signals and Systems Communications Systems Modulation 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 December 3 2009 Works well basis of local land based telephones Wireless Communication Check Yourself In cellular communication systems signals are transmitted via electromagnetic E M waves speaker 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 mic amp E M wave amp speaker 0 4 m 3 4 km 1 40 m 4 40 km 2 400 m 5 400 km 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 Wireless Communication Speech is not well matched to the wireless medium 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 Many applications require the use of signals that are not well matched to the required media 2 20 MHz 5 20 GHz 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 1 6 003 Signals and Systems Lecture 23 Check Yourself December 3 2009 Amplitude Modulation Multiplying a signal by a sinusoidal carrier signal is called amplitude modulation AM AM shifts the frequency components of X by c Construct a signal Y that codes the audio frequency information in X using frequency components near 2 GHz X j x t c y t cos c t Y j X j Determine an expression for Y in terms of X c c Y j 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 c c Amplitude Modulation Amplitude Modulation Multiplying a signal by a sinusoidal carrier signal is called amplitude modulation The signal modulates the amplitude of the carrier x t How could you recover x t from y t y t x t cos c t y t cos c t x t t cos c t t x t cos c t t Frequency Division Multiplexing Frequency Division Multiplexing Multiple transmitters can co exist as long as the frequencies that they transmit do not overlap Multiple transmitters simply sum to first order z1 t x1 t z1 t x1 t cos w1t cos w1t z2 t x2 t z t LPF z3 t x3 t z3 t cos w3t cos w3t 2 z t LPF cos wct cos w2t y t cos wct cos w2t x3 t z2 t x2 t y t 6 003 Signals and Systems Lecture 23 December 3 2009 Frequency Division Multiplexing Broadcast Radio The receiver can select the transmitter of interest by choosing the corresponding demodulation frequency Broadcast radio was championed by David Sarnoff who previously worked at Marconi Wireless Telegraphy Company point to point envisioned radio music boxes Z jw analogous to newspaper but at speed of light w receiver must be cheap as with newsprint transmitter can be expensive as with printing press w w X3 jw w w1 w2 w3 Sarnoff left and Marconi right Check Yourself AM with Carrier One way to synchronize the sender and receiver is to send the carrier along with the message The problem with making an inexpensive radio receiver is that you must know the carrier signal exactly x t L PF z t cos wc t x t z t C y t cos c t cos wc t f z t x t cos c t C cos c t x t C cos c t What happens if there is a phase shift between the signal used to modulate and that used to demodulate x t C t z t Adding 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 Receiver Inexpensive Radio Receiver If the carrier frequency is much greater than the highest frequency in the message AM with carrier can be demodulated with a peak detector AM with carrier requires more power to transmit the carrier than to transmit the message x t xp xp 35xrms y t xrms z t R C t y t t z t Speech sounds have high crest factors peak value divided by rms value The DC offset C must be larger than xp for simple envelope detection to work In AM radio the highest frequency in the message is 5 kHz and the carrier frequency is between 500 kHz and 1500 kHz This circuit is simple and inexpensive The power needed to transmit the carrier can be 352 1000 that needed to transmit the message But there is a problem Okay for broadcast radio WBZ 50 kwatts Not for point to point cell phone batteries wouldn t last long 3 6 003 Signals and Systems Lecture 23 December 3 2009 Superheterodyne Receiver Amplitude Phase and Frequency Modulation Edwin Howard Armstrong invented the superheterodyne receiver which made broadcast AM practical There are many ways to recode a signal to a different frequency band Here are three Amplitude Modulation AM y1 t x t cos c t Phase Modulation PM y2 t cos c t kx t Rt y3 t cos c t k x d Frequency Modulation FM Edwin Howard Armstrong also invented and patented the regenerative positive feedback circuit for amplifying radio signals while he was a junior at Columbia University He also invented wide band FM Frequency Modulation Frequency Modulation In FM the instantaneous frequency of the carrier is modulated by the signal Z t x d FM y3 t cos c t k z Compare AM to FM for x t cos m t AM y1 t cos m t 1 1 cos c t t t d i t c t c kx t dt FM y3 t cos c t m sin m t t Advantages of FM constant power no need to transmit carrier unless DC important bandwidth Frequency Modulation Frequency Modulation Early investigators thought that narrowband FM could have arbitrarily narrow bandwidth allowing more channels than AM Wrong Z t x d y3 t cos c t k Z t Z t cos c t cos k x d sin c t sin k x d Wideband FM is useful because it is robust to noise AM y1 t cos m t 1 1 cos c t t If k 0 then Z t cos k x …
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