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Unformatted text preview: .003: Signals and Systems odulation ay 6, 2010 ommunications Systems Signals are not always well matched to the media through which we wish to transmit them. 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 mplitude Modulation Amplitude modulation can be used to match audio frequencies to radio frequencies. It allows parallel transmission of multiple channels. x 1 (t) z 1 (t) cos 1 t z 2 (t) z(t) z 3 (t) cos 2 t cos c t cos 3 t LPF x 2 (t) y(t) x 3 (t) Superheterodyne Receiver Edwin Howard Armstrong invented the superheterodyne receiver, which made broadcast AM practical. 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 in vented wideband FM. mplitude, Phase, and Frequency Modulation There are many ways to embed a message in a carrier. Here are three. Amplitude Modulation (AM): y 1 ( t ) = x ( t ) cos( c t ) Phase Modulation (PM): y 2 ( t ) = cos( c t + kx ( t )) t Frequency Modulation (FM): y 3 ( t ) = cos c t + k x ( ) d Frequency Modulation In FM, the signal modulates the instantaneous carrier frequency. t y 3 ( t ) = cos c t + k x ( ) d ( t ) i ( t ) = c + d ( t ) = c + kx ( t ) dt Frequency Modulation Compare AM to FM for x ( t ) = cos( m t ) . AM: y 1 ( t ) = (cos( m t ) + 1 . 1) cos( c t ) t FM: y 3 ( 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 Early investigators thought that narrowband FM could have arbitrar ily narrow bandwidth, allowing more channels than AM. Wrong! t y 3 ( t ) = cos c t + k x ( ) d t t = cos( c t ) cos k x ( ) d sin( c t ) sin k x ( ) d If k then t cos k x ( ) d 1 t t sin k x ( ) d k x ( ) d t y 3 ( t ) cos( c t ) sin( c t ) k x ( ) d Bandwidth of narrowband FM is the same as that of AM! (integration does not change bandwidth) hase/Frequency Modulation Find the Fourier transform of a PM signal....
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 Fall '11
 Freeman

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