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midterm1

# midterm1 - EE 5501 Prof Jindal Digital Communication...

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Unformatted text preview: EE 5501 Prof. Jindal Digital Communication October 15, 2009 Midterm 1 You have 75 minutes to complete this exam. You must show your work to receive credit. 1. Baseband and Passband Signals (30 pts) In this problem we will study the upconversion and downconversion processes in the frequency domain. For this problem it will be helpful to recall: FT { cos(2 πf c t ) } = 1 2 [ δ ( f- f c ) + δ ( f + f c )] FT { sin(2 πf c t ) } = 1 2 j [ δ ( f- f c )- δ ( f + f c )] and that 1 /j =- j . (a) The real passband signal s p ( t ) is written in terms of the real baseband signals s c ( t ) and s s ( t ) as: s p ( t ) = s c ( t ) √ 2cos(2 πf c t )- s s ( t ) √ 2sin(2 πf c t ) . Let S p ( f ), S c ( f ), and S s ( f ) denote the Fourier transforms of s p ( t ), s c ( t ), and s s ( t ), respectively. Show: S p ( f ) = 1 √ 2 [ S c ( f- f c ) + jS s ( f- f c ) + S c ( f + f c )- jS s ( f + f c )] ....
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midterm1 - EE 5501 Prof Jindal Digital Communication...

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