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Unformatted text preview: ECE 5520, Spring 2010 Mid Term 1 Jan 28, 2010 Time: 75 minutes 1. Find the Fourier transform of (a) (7 points) x ( t ) = 3 ( t- 2 6 ) . (b) (6 points) y ( t ) = 2 sin(2 t ) + 3 cos(2 ( t + 1). (2 points) Simplify your answer. 2. (10 points) In the system shown below, find the Fourier transform of the output y ( t ). h ( t ) = te- t u ( t ) x ( t ) = e j 10 t y ( t ) 3. (a) (5 points) Consider a system with the input x ( t ), impulse response h ( t ) = 1 t , and output x ( t ). Find an expression for X ( f ) in terms of X ( f ). (b) (5 points) Define y ( t ) = x ( t ) + j x ( t ) and find an expression for Y ( f ) in terms of X ( f ). (c) (5 points) Present a plot of Y ( f ), assuming that X ( f ) = ( f/ 10). (d) (5 points) Present a plot of the power spectral density vv ( f ) of v ( t ) = y ( t )cos(100 t ). 4. (10 points) Binary data symbols are transmitted through a channel with a bandwidth of 10 MHz....
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