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Unformatted text preview: ECSE 2410 SIGNALS AND SYSTEMS FALL 2002 Rensselaer Polytechnic Institute FINAL EXAM (3 hour) (corrected) December 11, 2002 Check One: C Sect. 1 10 am (Wozny) C Sect. 2 12:30 pm (Yuksel) NAME: __________________________________________ C Sect. 3 2 pm (Yuksel) Do all work on these pages. Tables will be handed out separately. Five pages of crib notes allowed. Calculators allowed. Label and Scale axes on all sketches and indicate all key values Show all work for full credit PART I Total Grades for Exam #1: 1 Problem Points Grade 1 6 2 6 3 6 4 8 5 6 TOTAL 32 Grades for Points Score Part I 32 Part II 36 Part III 32 TOTAL 100 1(6). Perform the following convolution, ) ( ) ( 2 1 ) ( 2 1 t u t u e t y t = . You must solve this problem via convolution in the time domain. A maximum of half credit if transforms are used! 2 1 2 3321 x [ n ] 1 2 3321 w [ n ] 2(6). For a discretetime LTI system, the output is a unit step u [ n ] when the input is x [ n ], as shown below. (a)(2) Find the output of the system, y [ n ], when the input is w [ n ] as sketched below. (b)(4) Find the impulse response h [ n ] of the system. 3 LTI 11 n y [ n ] =u [ n ] x [ n ] 11 n y [ n ] = h [ n ] = 3(6). Find the transfer function ) ( ) ( s X s W . Make sure that Y ( s ) does not appear in your answer. X ( s ) ) ( s G ) ( s H Y ( s ) ) ( s F 4 W ( s ) + + 4(8). For the system shown (note that the forward loop is unstable), X ( s ) ) 1 )( 2 2 ( ) 3 )( 2 ( 2 + + + + s s s s s Y ( s ) K (a)(4)Sketch the root locus diagram as K varies from zero to infinity. No need to calculate any critical points, just approximate.points, just approximate....
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 Spring '07
 WOZNY

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