1-4 - EE160 — Fall 2009 San Jos´ e State University...

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Unformatted text preview: EE160 — Fall 2009 San Jos´ e State University Solution of Homework # 5 1. The modulated signal is u ( t ) = m ( t ) · c ( t ) = 100 [2 cos(2 π 2000 t ) + 5 cos(2 π 3000 t )] cos(2 πf c t ) . Therefore, U ( f ) = 50 [ δ ( f + 52000) + δ ( f + 48000) + 2 . 5 δ ( f + 53000) + 2 . 5 δ ( f + 47000) δ ( f- 52000) + δ ( f- 48000) + 2 . 5 δ ( f- 53000) + 2 . 5 δ ( f- 47000)] , which is sketched in the figure below: f (kHz) U(f) 47 48 52 53-53-52-48 -47 50 50 50 50 125 125 125 125 2. A DSB-SC modulated signal is a bandpass signal. As discussed in class, it can be written as u ( t ) = m ( t ) cos(2 πf c t + φ ) = Re m ( t ) e j (2 πft + φ ) = m ( t ) cos(2 πf c t ) cos( φ )- m ( t ) sin(2 πf c t ) sin( φ ) = u c ( t ) cos(2 πf c t )- u s ( t ) sin(2 πf c t ) , where u c ( t ) = m ( t ) cos( φ ) , u s ( t ) = m ( t ) sin( φ ) . The envelope of u ( t ) is, therefore, V u ( t ) = u 2 c ( t ) + u 2 s ( t ) = m ( t ) 2 cos( φ ) 2 + m ( t ) 2 sin 2 ( φ ) = m 2 ( t ) = | m (...
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This note was uploaded on 04/08/2012 for the course ELECTRONIC 101 taught by Professor . during the Spring '10 term at Kadir Has Üniversitesi.

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1-4 - EE160 — Fall 2009 San Jos´ e State University...

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