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Unformatted text preview: ECE220 Practice problems Spring 2007 May, 2007 1. The exam covers Chapters 10, 11, 12 from the textbook as well as material discussed in sections, homeworks and in labs. 2. Practice problems were not proofread so typos are possible. 3. There will be review sessions M,T,W,Th May 1417, at 10:30am. Check the location on Blackboard. 1 Problem 1 Compute the convolution of the following functions: 1. e 2 t u ( t ) and u ( t ) 2. e t u ( t + 3) and u ( t + 4) 3. e 2 t u ( t ) and u ( t ) 4. e t u ( t ) and u ( t ) 5. e 2 t u ( t 2) and u ( t 1) 6. e 2 t u ( t ) and e 2 t u ( t ) Problem 2 Determine the Fourier transform of the following signals: 1. x ( t ) = ( t 5) cos( t ), ( t ) is the Dirac delta function 2. x ( t ) = ( t 5) * cos( t ) 3. x ( t ) = u ( t ) u ( t 5), u ( t ) is the unit step function 4. x ( t ) = e 7 t u ( t ) e 7 t u ( t 3) 5. x ( t ) = e ( a + jb ) t u ( t ) where a, b are real and a > 6. x ( t ) = ( u ( t ) u ( t 5)) cos(50 t ) 7. x ( t ) = ( t ) + 2 ( t T ) ( t 2 T ), T is a constant 8. x ( t ) = 400 ( t . 1)) ( t . 1) 9. x ( t ) = e 2 t u ( t ) e 2 t u ( t 3) 10. x ( t ) = u ( t + 3) u (3 t ) 11. x ( t ) = sin(4 t ) sin(50 t ) 12. x ( t ) = sin(4 t ) t sin(50 t ) 13. x ( t ) = sin(4 t ) t sin(50 t ) Problem 3 Determine the inverse Fourier transform for the following functions: 2 1. X ( j ) = sin 2 (200 ) 2 2. X ( j ) = cos 2 ( ) 3. X ( j ) = j 4+3 j 4. X ( j ) = j ( + 1) * ( ( ) (  2)) + 2 Problem 4 You are given a stable, continuoustime, linear, timeinvariant system defined by the Fourier transform H ( j ) of its impulse response. Determine the value of the output y ( t ) when t ap proaches infinity when 1. the input to the system is x ( t ) = ( t ) and H ( j ) = j...
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 Spring '05
 JOHNSON

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