94360W00

# 94360W00 - " "'~ . ,. .' . ': ,4' CARLETON NIVERSITY U 7 t...

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"" """'~ ..' ... ... ,. ': ,4' CARLETON UNIVERSITY 7 t .[~~;~~::~~J.5'" 7 9 3 61 DURATION: HOURS N f St d t o. 0 u en s: Department Name & Course Number: Systems and Computer Engineering 94.360 G Course Instructor(s) Professor H. Yanikomeroglu AUT"O.'Z~D M~MO._D4 Closed Book, No Aid-Sheet, Non-programmable calculators Students MUST count the number of pages in this examination question paper before beginning to write. and report any discrepancy immediately to a proctor. This question paper has 5 pages. MAY This examination question peper be taken from the examination room. TOTAL MARKS: 100 + 10 bonus m []~y IEEE CarJ84~'l "'. .: ~:;11;\. .c - (,;;j;; ( . ... r " Ii ,c

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..1l1t).B\ Question 1 (6 points) Periodicity (a) (3 pts) Find the period of the function x(t) = 7cos(5t + ~). (b) (3 pts) Sketch x(t). 4 I.E~E Carlet_on Question 2 (16 points) Block Diagram Representation 1 S 1 -1 x(t) S S+T y(t) (a) (9 points) Determine the transfer function of the system given by the block diagram shown in the above figure. (b) (2 points) Write the input-output differential equation corresponding to this system. (c) (5 points) For x(t) = u(t) with jj (0-) = -1, Y (0-) = 1, and y(O-) = 2, find Y(s) in terms of the natural and forced responses; that is, find Y(s) = Ynatural(S) + Yjorced(S). (Do not solve for the time domain expression y(t).) Question 3 (14 points) Convolution x(t) y(t) Z(t) nit * -!JLt = t -2 -1 - z(t) is the convolution of the two functions x(t) and y(t); that is, z(t) = x(t) * y(t). If x(t) and z(t) are as sho\\'n in the above figure, find y(t). Help:
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## This note was uploaded on 10/15/2010 for the course SYSC 3600 taught by Professor John bryant during the Spring '08 term at Carleton CA.

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94360W00 - " "'~ . ,. .' . ': ,4' CARLETON NIVERSITY U 7 t...

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