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Unformatted text preview: Signal Transmission Lecture 6b (advanced concepts/issues) • how to relate the basic concepts to Fourier Transform • more picture analysis in the frequency domain • what can go wrong with coherent (synchronous) modulation • concepts on I/Q modulation (quadrature multiplexing) Some content taken with permission from material developed for the course EECS6.02 by C. Sodini, M. Perrot and H. Balakrishnan The Concept of Modulation Why Modulation? • Easier to transmit electromagnetic waves at higher frequencies • Transmitting multiple signals through the same medium using different carriers  multiplexing • Fitting signals to “channels” with limited passbands • Others... • Many methods (amplitude, frequency, phase) • Focus here for the most part on A mplitude M odulation ( AM ) How? Transmitted Signal x(t) Carrier Signal Modulation Consider a message signal x(t) has frequency spectrum X(f) In modulation, the message is multiplied (mixed) by a carrier cos (2 π f c t) [ ] ) ( ) ( 2 1 ) 2 cos( ) ( c c c f f X f f X t f t x − + + ↔ π Baseband signal Frequency translated (modulated) signal Modulation Modulation W 2W ) ( ) ( f X t x ↔ (Fourier transform pair) Recovery of Baseband Signal Recovery of Baseband Signal To recover the baseband signal, we can simply multiply the translated signal with cos (2 π f c t) . [ ] ) 4 cos( 2 ) ( 2 ) ( ) 2 ( cos ) ( ) 2 cos( ) 2 cos( ) ( 2 t f t x t x t f t x t f t f t x c c c c π π π π + = = We obtain the baseband signal x(t) and a signal whose spectral range extends from ( 2f cW ) to ( 2f c +W ). As f c >> W , the extra signal is removed by a lowpass filter ....
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 Fall '08
 RossMurchandAmineBermak
 Frequency

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