Exam#03 - ECSE-2410 SIGNALS AND SYSTEMS SPRING 2009...

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ECSE-2410 SIGNALS AND SYSTEMS SPRING 2009 Rensselaer Polytechnic Institute EXAM #3 (110 minutes) April 15, 2009 NAME: __________________________________________ SECTION: 8:30 am 10:00 am Do all work on these sheets. One page (both sides) of handwritten crib notes allowed. Calculators allowed. Label and Scale axes on all sketches and indicate all key values Show all work for full credit Total Grade for Exam #3: Problem Points Grade 1 10 2 10 3 10 4 10 5 10 6 10 7-9 6 10-12 6 13-15 6 16-18 6 19-21 6 22-23 4 24-25 4 26 2 TOTAL 100 Exam#03 – Spring’09 – p.1
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NOTE. You must use properties and tables. Solving problems by directly integrating the defining integrals is not acceptable. 1(10). The step response of a system with transfer function () 1 1 2 2 + + = s s H has the form . Find () ( ) 0 , cos 1 + = t t Ke t y t step θ ) radian in ( s and K . Exam#03 – Spring’09 – p.2
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Exam#03 – Spring’09 – p.3 Extra page.
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- - + + () s X α + s s 2 s Y 2(10). Find such that the closed-loop poles ( i.e. , the poles of ( ) s X s Y ) have 4 3 = ζ and n ω as large as possible. Exam#03 – Spring’09 – p.4
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Exam#03 – Spring’09 – p.5 Extra page.
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3(10). A signal with spectrum () t x ( ) ω X , shown below is ideally sampled at a sampling frequency of 10 = s rad/sec and then filtered with the ideal filter shown. . Exam#03 – Spring’09 – p.6 5 5 12 12 π 2 2 2 X ( ) t y 1 5 5 ( ) H ( ) t x t x s () ( ) −∞ = = k s kT t t s δ (a) Sketch the signal spectrum s X for 25 . (b) Sketch Y , the output of the filter. In each case, scale vertical axis! ( ) s X 4 2 6 8 10 12 14 16 18 20 22 24 -2 -4 26 -6 -8 -12 -14 -16 -18 -20 -22 -24 -10 ( ) Y 4 2 6 8 10 12 14 16 18 20 22 24 -2 -4 26 -6 -8 -12 -14 -16 -18 -20 -22 -24 -10
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4(10). The circuit shown represents a second-order low-pass Butterworth filter with bandwidth equal to 2 rad/sec. Find . C Ω = 2 R L C x ( t ) + - + - y ( t) Exam#03 – Spring’09 – p.7
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5(10). Find break frequencies 2 1 ,
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Exam#03 - ECSE-2410 SIGNALS AND SYSTEMS SPRING 2009...

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