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quiz3su07soln - GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of...

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Unformatted text preview: GEORGIA INSTITUTE OF TECHNOLOGY SCHOOL of ELECTRICAL 3.: COMPUTER ENGINEERING QUIZ #3 DATE: 20—.Iu1y—0? COURSE: EOE 2025 gr“- NAME: :3 O STUDENT e: 1.AST,' ' I FIRST Recitation Section: Circle the day 85 time when your Recitation Section meets: L01: 2:40—4:30 (’l‘aylor} 1.03: 10-11150(Taylor] L05: 273:50 (Chang) L02: 4:40—6:30f1‘ayior) 1.04: [2:00-1:5{1{Tayior) L06: 45:50 (Chang) You will receive a 5 point penalty if you fail to circle your recitation. 0 Write your name on the front page ONLY. DO NOT unstaple the test. 0 Closed book but a rah 111at01 is permitted However, one page (81" x 11”} of HAND— WRITTEN noth permitted OK to write on both sides. 1: Unless stated otherwise, J USTIFY your reasoning clearly to receive any partial credit. Explanations are also required to receive full credit for any answer. a You must write your answer in the space provided on the exam paper itself. Only these answers will be graded. Circle your answers, or write them in the boxes provided. If space is needed for scratch work, use the backs of previous pages. Problem Q1.1: Suppose a discrete-time LTI system has the system function ”‘5 -5 5’05): W 1"” g (t- IteUGV > (a)( (5 pts) )Find the difference equation that relates the output y[n] to the generic input :8 Lin]% Ll}: 1'“ng‘331" Zj+ 7962]}th (b) ( 15 pts) Find the output of the system, y[n], if the input is the specific signal fin] = 517: — 3] — iéin — 4]) X (Z) 2 ?“33 (Hint: Factor the denominator of the system function.) Problem 01.2: Pole-Zero Plot 1 Pole-Zero Plot 2 Pole-Zero Plot 3 1; i ' ' 2 X E 0.5 _. HE. E O. _: Q E 09- r e? e F. - e E415 -; E _ .T o 1' Healpan Pole-Zero Plot 4 1mglnary pan Real part ( ) Whlch of the above pole-zero plots represents the system whose frequency response is given in the following graph? FREQ RESPONSE OF UNKNOWN SYSTEM —1II 418:: 4161: —0.4Ir -0 21 . D 0.21: 0.41: 0.611: 0.81: 1: Normalized Frequency 5: System # I (1)) Now assume that each of the systems represented by the above polezero plots has impulse response hfln], where k is the index shown in the title of the pole~zero plot (1) In the table below1 indicate with an X which of the systems are FIR systems _----- (11) In the table below, indicate with an X each of the systems for which have] :0: elm = 0 where a: denotes convolution. 'l Problem Q13: Siioomplfyfilwinresgexp m I mp sz'abl 'lhe *soenymbld (Jest Gas—MSW) $th u(t+2)}= 510118.63 g(.t+z +3;ch :u(~t+Z m~1m.wa_.._... .__w. _m___._”-_,.‘...m .m- "an“ "h.“‘_h ’ m 5a +2>+ BEL/aw) ‘) XV ”530% r:— «63 “(“80 Problem 01.4: (5 pts each) In thefollowing figure, m(t) is the input and Mt) is the impulse response of an LTI system, whose output is yft): /l\ \ 1/ l“ x0) (3. ) What IS the complete set of values of t for which y( t}: G? 623) 1:4 3 3&0 (b) For what value of it does y(t) have is largest positive value? ((1) Is h(t) the impulse response of a causal system? Briefly explain. N D -- {here as? Wfleew value; an “Use. (53 (J: will 3M9 Problem Q1.5: x(t) Continuous~Time ”Hm LTI System h(t) and Han) The LTI system shown above has an impulse response given by Mt) = 5[u(t + 3) - u(t — 7)] and a frequency response given by sin(5w) How) a 10 expt—jzw) _ (a) (5 pts) Sketch fihfi), the derivative of Mt) with respect to t. %h Ct) ~.:, ggédws) egg-7) its} 5 w3‘%wTWf hp]: *3 (b) (5 pts) Find the input 37(t} that would result in the output 3,:(t) = —30[u(t + 14) — u(t +4)]. I; -. i: If. . ”III; "N Us". M {-3 ‘~_“&" + I! (e) (10 pts) Find the input :t:[t) that would result in the output y(t) = 4cos (%t) ...
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