final08sol

final08sol - MAE 143A Signals and Systems Prof. M. Krstic...

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Unformatted text preview: MAE 143A Signals and Systems Prof. M. Krstic FINAL August 1, 2008 NAME: SOLUTIONS Closed book. One sheet (both sides) of handwritten notes allowed. Present your reasoning and calculations clearly. Random or inconsistent etchings will not be graded. Write only on the paper provided. If you run out of space for a given problem, continue on the pages at the end of the set and indicate Continued on page X. The problems are not ordered by difficulty. Total points: 45. Time: 2 hours and 30 minutes. Problem 1. (6 points) Compute the impulse response of the following systems: (a) (3 points) H ( s ) = e- 5 s 1 ( s + 4) 2 + 2 (b) (3 points) H ( s ) = 1 (2 s + 3) 5 Solution: (a) Impulse response is given by L- 1 { H ( s ) } . Since H ( s ) = 1 2 e- 5 s 2 ( s + 4) 2 + 2 2 and L- 1 braceleftBigg 2 ( s + 4) 2 + 2 2 bracerightBigg = e- 4 t sin parenleftBig 2 t parenrightBig , we get L- 1 { H ( s ) } = 1 2 e- 4( t- 5) sin parenleftBig 2( t- 5) parenrightBig 1( t- 5) . (b) L- 1 braceleftbigg 1 (2 s + 3) 5 bracerightbigg = L- 1 braceleftbigg 1 32( s + 3 / 2) 5 bracerightbigg = 1 32 t 4 4!...
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final08sol - MAE 143A Signals and Systems Prof. M. Krstic...

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