Exam#3 - ECSE-2410 SIGNALS AND SYSTEMS FALL 2003 Rensselaer...

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ECSE-2410 SIGNALS AND SYSTEMS FALL 2003 Rensselaer Polytechnic Institute EXAM #3 (2 hours) November 24, 2003 Check One: C Sect. 1 10am (Radke) C Sect. 2 12:30pm (Wozny) NAME: __________________________________________ C Sect. 3 2:30pm (Vastola) Do all work on these sheets. Tables will be handed out separately. One page of crib notes allowed. Calculators allowed. Label and Scale axes on all sketches and indicate all key values Show all work for full credit Total Grades for Exam #3: PART I 1 Grades for Points Score Part I 32 Part II 35 Part III 33 TOTAL 100 Problem Points Grade 1 6 2 9 3 8 4 9 TOTAL 32

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1(6). Given find the transfer function, ) ( s H . 2 ) ( ) ( t u e t x t - = LTI ) ( ) ( t tu t y =
2(9). Find the Laplace transform of using the properties and transforms tables. Show all steps clearly. Simplify as much as possible. 3 ) ( t x t 1 0 1

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3(8). Find the inverse Laplace transform of ) 1 ( ) ( + - = - s s e s s X s , using the properties and transforms tables. Show all your work clearly. 4
4(9). Given ) ( 2 ) ( 2 ) ( 2 ) ( 2 2 t u t y dt t dy dt t y d = + + , with initial conditions, 0 ) 0 ( , 2 ) 0 ( = = - - dt dy y , find the Laplace transform of ) ( t y . Assume 0 ) ( = t y for - < 0 t . Use properties and transforms tables. Show all your work clearly. 5

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ECSE-2410 SIGNALS AND SYSTEMS FALL 2003 Rensselaer Polytechnic Institute EXAM #3 (2 hours) November 24, 2003 Check One: C Sect. 1 10am (Radke) C Sect. 2
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