SignalsExam3S03

# SignalsExam3S03 - ECSE-2410 SIGNALS AND SYSTEMS SPRING 2003...

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ECSE-2410 SIGNALS AND SYSTEMS SPRING 2003 Rensselaer Polytechnic Institute EXAM #3 (1 hour and 50 minutes) March 26, 2003 Check One: C Sect. 1 10am (Wozny) C Sect. 2 12:30pm (Desrochers) NAME: __________________________________________ C Sect. 3 2:30pm (Yuksel) 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: PART I Grades for Points Score Part I 34 Part II 31 Part III 35 TOTAL 100 Problem Points Grade 1 8 2 4 3 8 4(a) 10 4(b) 4 TOTAL 34

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1. (8 pts) A second-order system is described by ( 29 ) ( ) ( 6 ) ( 8 ) ( 2 2 2 t x t y K dt t dy dt t y d = + + + , where K is a constant. (a) (4 pts) If K = 4, find the damping ratio, ζ . = (b) (4 pts) Find the value of K that will make the system critically damped. K =
2. (4 pts) The input-output behavior of an LTI system is described by the differential equation, ) ( 2 ) ( 2 ) ( t x t y dt t dy = + . Find the frequency response H ( ϖ ) for this system. H ( ) = 3

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3. (8 pts) A communication system utilizing asynchronous amplitude modulation is shown below. Suppose x ( t ) has the following spectrum, else 0 2 | | = ) X( π ϖ cos . (No need to find x ( t )!) (a) (5 pts) Sketch S ( ) if c =3 . Label and scale your axes. S ( ) if c =3 . You can express S ( ) in terms of X ( ). 4 2 1 x(t) c ( t ) = 10cos c t + + S( [ ] t t x t s c cos ) ( 1 10 ) ( 2 1 + =
4. (14 pts) The system below is used for frequency-division multiplexing where three signals, x 1 ( t ), x 2 ( t ), and x 3 ( t ) are simultaneously transmitted via w ( t ).

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SignalsExam3S03 - ECSE-2410 SIGNALS AND SYSTEMS SPRING 2003...

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