quiz02_sol

quiz02_sol - ECE 108 Signals and Systems Spring 2007,...

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Unformatted text preview: ECE 108 Signals and Systems Spring 2007, Instructor: Tiffany Li QUIZ 2 (50 minutes) Name: 50 (14+?th 1. (10 points) Write an equation which gives the total response of the systems using the input f (t), the unit impulse response Mt) and the zero—input response yo(t). 49+”; Waspgme Lint) ‘9' (fight) + fifia‘ M76) M—W W 23]“6’”;V\Pu+— 2M0 — Sfa‘b; e 3/0 2. (30 points) For each of the systems specified by the equations below, plot its characteristic roots in the complex plane and determine whether it is asymptotically stable, marginally stable or unstable" (3) (10 points) 132(1) + 3)y(t) m 3f(t)l Alt” I )szl .>\33'5 9”: ,1 ta 6+“ , 124* M ~91» ,\1ttx> um 54-4502 (b) (10 points) (D + 5)(D2 —— 4.0 —§— 10)y(t) = (D —- 3)f(t). 4il' u to, J\J‘; "5—) Ifizlst l ’6 49:2i&.16 ~51: 2t a £51791: (2 "9&0 m n 5+MC¢ (c) (10 points) D(DA~ 3)(D - 1)y(t) = (I)2 + 3 A9120, _)\L:l l‘kaLj at Q 'f Qt, 63+ \f" w “No *9 es) 3. (30 points) Find the unit impulse response of a LT 1C system specified by the equation (D2 + 613 + 9)y(t) fl (217 + 9)f(t). W259: bn 6%) + D7617) Qnmflw/t) Wm 07*aw’571x'g qwa‘kén : 21% é /\+f_) 2:49 I 3" '3 )1: "'3 “"319 w. +41% @ 3t" )an(2é.):aa€ mfer COM/ffiéns‘: '9,“ (3(3) 5 a: 5: 0 ~ . ._, we _, amp-15m we female) .1 t %£,30,Q2:)19n(t)37t€*3t ea PCD)‘9,,I£):bDfi)90(r):291(75)7L7? (f) 4" (30 points) The unit impulse response of an LTIC system is h(t) fl e“u(t). (a) (15 points) Find this system’s zero—state response y(t) for the input f(t) : e‘ztufi). u + —Z a 75" tam).— htthftflfifg é ~e’2c wait) by; x O '2: Q_2t[ gut-’1] / 767/0 } W) W (b) (15 points) What is the zero~state response y(t) if the input is delayed by 2 seconds? jCut): gflctulhxt (ltd) ) 1L TOO ...2(_Zf-v2 “L 9W .. Jcmwmu a M .e wmye mm) dz ’Ci’n— 753/3 6 at z 7’7/2. N 4/2: 1‘: wt we L6 dz s?— 752/; "—1 P" e 4m2t+ebtj act-a2.) Ai‘kécfmfllv’dg / Qua Viz/w SyS‘f’em is “flit/MIA; war/mt i flue {Tu/m7” 91 920mm; gféer/gly My; 6@ 9247'?qu by at Sienna/st 8 “13511771177” \ i- Lor‘fié, “.2 12-; 1%; [brat/n; or; /’ 2 "gt/(1 ...
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quiz02_sol - ECE 108 Signals and Systems Spring 2007,...

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