practice_final - University of Notre Dame Department of Electrical Engineering EE 30344 Signals and Systems I Dr M Haenggi December 5 2005 mh Practice

practice_final - University of Notre Dame Department of...

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University of Notre Dame December 5, 2005 mh Department of Electrical Engineering EE 30344 – Signals and Systems I Dr. M. Haenggi Practice Final Exam 1. A CT LTI system is described by the frequency response 10 H ( ) = e - 3 + ω 2 . Find the output of this system when the input is cos(4 t ). 2. Given x ( t ), 10 t x(t) 4 4 find X ( j 0). 3. Give the simplest form possible for X ( e ) for the signal 10 -1 1 4 n 1 1 2 x[n] -2 -3 -4 0 2 3 4. A DT system is characterized by the difference equation 15 y [ n ] - 0 . 5 y [ n - 1] = x [ n ] + 0 . 5 x [ n - 1] . Find the frequency response H ( e ) and the output if the input is cos( πn ).
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5. An LTI system has the transfer function 10 H ( s ) = s + 1 s 2 + 7 s + 12 with ROC Re { s } > - 3. Find the impulse response h ( t ). 6. Given are two DT signals
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