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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; [email protected] 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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