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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