midterm-solution - CSE 3451: Signals and Systems Mid—term...

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Unformatted text preview: CSE 3451: Signals and Systems Mid—term Examination Nov 3rd, 2009 (1:00 — 2:20) W _ - l . 1‘ Time Allowed: 1 hour 20 minutes J-n V SC; (bf/70 n ' Last Name: First Name: Student Number (York ID): ___________________________ York Computer Science (CS) Email address: cs INSTRUCTIONS 1. This is an 80 minutes, Close Book test. One letter size crib sheet (8 1/2” x 11”) and a non-programmable calculator may be used, but no other material will be allowed including any blank pap er. 2. Write your name, student number, email address and section on your test paper in the space provided above. Don’t turn this page until you are instructed to do so. 3. Use the test booklet for all your work (including scratch work) and you may use the back of pages. Do not tear out pages. Hand in the test booklet at the end of the examination. 4. Solve all problems. Make sure you number the solution parts according to the problem. You should show your work and explain clearly what you are doing. Answers without explanation or shown work, where appropriate, will receive low or zero points. 5. Keep your York photo ID (or other acceptable photo ID) on the desk in front of you so that the instructor may inspect it without disturbing you. 6. No questions are allowed during the exam. Good luck! — —- —- —_ - _ Problem 1 [6 points] Determine if the following signals are periodic. If yes, calculate the fundamental period in each case. (a) [3 points] x[k] = 2cos<£35+ it) + exp(j’%‘) — 2cos(”7k + (b) [3 points] x(t) = sin(%) — 5 cos(3t — 25—”) ‘ k) l<’i K3 r ‘ " kl; KL, t) ) 1:752; a“? aw erlwcfi, “X Ck] is fir/Mlle 5 Th: Wool f5 LCM uf K;,k'z,k'3 :_ 1'2 x .113? ,fi . . 1.1 (l3) 1H) ‘5'— W (’3‘) “r 5 (B‘fvrgr) Uh: 11/3 CU}: 3 3.1 ., m _ __2_._ “‘73:: lim’ 3 Z T c7 V N —--:' 3 ~— VOfiiot/WVQ j/Lu/Wlué/f‘ ‘ Tluifi, ‘I Pt) {g ml" Pat/Paola}; h copyright © F09, CSE3451, Computer Science and Engineering, York University 2 Problem 2 [9 point] A CT signal x(t) is shown in Figure P2. Figure P2: Waveform for the CT signal 510‘} Sketch and label carefully each of the following signals. (a) [3 points] x(—1~— 21‘) (b) [3 points] Even component of 360‘) m '2. (c) [3 points] 16%) 2 5(1‘ — @169” k=_m La) ‘Xll’l’) 100:?) copyright © F09, CSE3451, Computer Science and Engineering, York University copyn'ght © F09, CSE3451, Computer Science and Engineering, York University 5 Problem 3 [8 points] Suppose we are given the following information about a signal x(l) (a) x(t) is periodic real signal with period T 0 = 4. (b) Its exponential Fourier series coefficients D“: Dn = 0 for n = 0 and all n > 2 and n < -2. (c) x(z) is an even signal. (d) x(t)|t:1=‘/§- Determine x(l) and find its trigonometric Fourier series coefficients. G) Acwwciin (b) '1 V - ,, a “52%)079 "wat’» _ ‘ 7(a): D.2 5 +3245 + 1.6 + 2926, o gubS‘li‘i’vd‘L (D 41;) <07 ‘ A g t ‘7 Gy » '3 wet i , 1W” ~ 9%? 70+): 6 4’ (Grubs + al+~)b3’)c @ “1%) is om 9(ng ) bl: by?!” copyright © F09, CSE3451, Computer Science and Engineering, York University 6 Q; 3 -' i an ’0 (Gala/S copyright © F09, CS 451, Computer Science and Enginecmig, Jerk University 7 N50 (00“ V1) - Problem 4 [12 points] The following CT system consists of four different subsystems: 3 37(6) The subsystem h1(t) can be modeled by a linear differential equation dyim dt + 4y1(t)= 2x10) with zero initial conditions, x1(t)and y1(t) denote input and output signals of the subsystem. ii) iii) iv) 25(t + 2). The impulse response of the subsystem P50) is h2 (t) = exp[—2t]u(t) . The impulse response of the subsystem h3(t) is given as @(r) = eXp[—-t]u(t) . The subsystem 114 (t) is an invertible LTIC system. The impulse response of its inverse system is Compute the overall impulse response of the combined system from x(t) to y(t) . CD Wet/WM viie’iem : . hum: [huvfl—hflil* Kn+f]*-hdiy (13> ‘Deierm‘ma hive) , Solve, A \ H) cL+ aniflfl38WL 50 : A?) hOl/Mefiafimtg Shiv/1%”: at) Fined Sfii’bfl‘m qfiwu €- ,th copyrié it, C; gt: ’4’» + (-40 © F09, CSE3451, Computer Science and Engineering, York University Se) 28%) re 0:2; ‘4' 4%(4): 275”) oldie/am??? Ma H) W” WWW“ marl/M ., - l' W {n “‘Vafiér ' v 4’? MM = 5 «am 4% 1 WEI/10% hm: [hm + Mt) *kfl‘h] 4;: ht ht) - — _1{v , V : “i’ e J<@.M[H -— a .4. Eli—gH'Z) 74 fli—‘t 91C ivl‘fik ' _ . ‘ I > z [(26 + 8 ’ C MM” * ZSHvz) “'49?” t — H42.) 4(a) c :\ +fi’6 _ Law-” copyright © F09, CSE3451, Computer Science and Enginecn'ng, York University 10 ...
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midterm-solution - CSE 3451: Signals and Systems Mid—term...

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