Midterm1Solution - ELECTRICAL ENGINEERING DEPARTMENT...

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Unformatted text preview: .. ELECTRICAL ENGINEERING DEPARTMENT CALIFORNIA POLYTECHNIC STATE UNIVERSITY EE 228 Continuous-Time Signals & Systems EXAM 1 Fall 2005 Name: _ . Last 4 digits of Student ID: PROBLEM #1 For the following signal xfl), sketch: ' (a) Xfi-U (b) x(0.50 (c) x(1-0.519 (d) x80) (its even part) (3) x06? (its odd part) SIM-ft :efgby I, expand tinge. by l, averse imp. PROBLEM #2 Sketch the following signals. (a) rect(20 (b) WWW-U ‘ (c) 2rect(t-0. 5) (d) r(0-2r(t—J) +r(t—2) (e) 5(101‘+10) 1011' (2t) wt) 01 u- t) :‘t mat tt—O- SJJC orctl- .ZT(‘t-I) 1' 111-2) 44; lot-H0) 8( [(0010 PROBLEM #3 Find the response 320 tfor the system described by the following differential equation. Use the given initial conditions. y"(r)+3y'(r)+2y(r)=2x'a) x(r)=4e-3'u(r) ‘y(0)=0, y'_(0)=1 21R; g'itnag'm’rzjttlw with 21mm, 310)?! ‘ 5+ 2:0 CE. $+i 4 —2t 3‘13 = “I6 +K2€ Shut mm at 3"(t)f53{f)f25(t) 46-; - w‘tk gto)=gi’to)=o Hpi‘t)— ca 31': 8t age)- — ace: ’jP"(’c) , ‘ice at ‘ich-fi'cucw ~>C=2 ~> ypft); 22 {- -2t -51- glzt)= k.e Hoe + 2e kmkuz = a _’ k.=2 "K'Zkz-ézo 2.="q' 4 -t e-et. flu): 1e {gel +2 - t = (t 325‘) 13:! —2't -3‘t = we tube -/22 09 PROBLEM #4 A causal LTI system is described by the following differential equation: 5959—) - SW) = x0) dt (a) Calculate the impulse response Mt) of the system by solving the differential equation. (1)) Based on Mt), determine if the system is stable or not. (c) If the input is x0“) = 5(1‘ + 5) + 110‘), calculate the output y(t). (0:) Mt)- Shit) =0 we, 14(0):; 14(16): estwt) (b) [thfll .m mt mm (C) git) = _ 9m) ar- hm) =1 [5min + m0] *‘ emu”) are; lit : e )mus) + '59“ ")“W 57(- w 51' i 7 A. utf)* e at?) ; woe we) (Mt-c.) cl gt : fie alt - . 6'? 'l' _ _;_ 5f: " a; (C -r) PROBLEM #5 Let the impulse response km of a continuous-time LTI system be h(r)— 0 r<0, _1 :20. Thus, the impulse response is simply the unit step function. For this system, suppose the input signal is 0 ~00 < t S 0, x(t)=t 0<ISL 1 1 < t < 00. (a) Sketch x69 and Mt), (b) Find the output yft) using graphical convolution, and sketch it. for at) A 1m; ! i "7:“: wt 0 i ‘0 when tw = m _. . Haj : I 9; (‘3) Mb?) Ohm) ...
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