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SignalsExam3S02 - ECSE 2410 SIGNALS AND SYSTEMS EXAM#3...

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ECSE 2410 SIGNALS AND SYSTEMS EXAM #3 APRIL 3, 2002 ECSE 2410 SIGNALS AND SYSTEMS, SPRING 2002 EXAM #3 (1 hour, 50 minutes) April 3, 2002 Check One: Sect. 1 10am (Wozny) Sect. 2 12:30pm (Desrochers) NAME: __________________________________________ Sect. 3 2pm (Wen) Do all work on these pages. 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 PART I Problem Points Grade 1 15 2 20 TOTAL 35 Total Grades for Exam #3: Grades for Points Score Part I 35 Part II 35 Part III 30 Total 100 1
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ECSE 2410 SIGNALS AND SYSTEMS EXAM #3 APRIL 3, 2002 1. (15 points) a. (5 points) Is ( ) sin 20 cos(30 ) 4 x t t t π = + - bandlimited? (i.e., is there some M ϖ such that ( ) 0 X ϖ = for M ϖ ϖ ?) Sketch ( ) X ϖ on the graph below and label the amplitude. b. (5 points) The signal x(t) in part (a) is sampled with an impulse train with period / 40 π sec. Denote the sampled signal by y(t) . Sketch ( ) Y ϖ . c. (5 points) The sampled signal y(t) is passed through an ideal low pass filter with cut- off frequency at 40rad/sec and unity gain (gain = 1). Denote the output signal by
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