midterm_solution - ELECTRICAL ENGINEERING DEPARTMENT...

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Unformatted text preview: ELECTRICAL ENGINEERING DEPARTMENT CALIFORNIA POLYTECHNIC STATE UNIVERSITY EE 228 Continuous-Time Signals & Systems Name: PROBLEM #1 Simplify the following expressions: (3) “F4 — :2 )5(:.+ 3m (b) (4 — t2)(3(t + 3) (c) (4-t2)*§(z‘+3)- (d) j'exp(—10t)u(t)dt' (e)- T[t2'sin(2r) cos(2t)dt Midterm ’3 (a'tz) [#93 : ~§Srr+sy ;: CL'('E+3)L 00 —r‘oi‘ , I Q alf : a"??? _-_ "ta-'6 t'!' #97170: Winter 2007 PROBLEM #2 Consider a LTI system whose response to the signal x1(t) in the following figure is the signal y1(t). Determine and sketch the response of the system to the input x;(t). M) tie-{t} Obit): 2%.(6) -— 9<.ctv2) 31(15): 9 amt)— amt-1‘) “(UH/L 3 3 (3) Determine Whether the system 13 causal 5 (b) Determine whether the system 13 stable. HQ (0) Sketch the system response to the input x(t)- — rect(0 51‘) (.19) (d) Eepfat (a)— (c) if h(t)= 'e'“u(t—— ~1),a>0. (t , a) men—comm? (M10450 15‘” 1‘0) 'tb) 2mm { flhtffleft =5 <00) ‘00 (c) ’XH’)" 7M (05-h): U [t'f'o ‘-L{(_t'*’) , , give). as) = area “it W“) .t ' :Iutt-H) (MT-ID *[Wt'W‘ “If 33 ~ 7 (W2)— wt) 'Ht- -2)+ Ht 41-) t.( Hiltj'eofivtw) ‘I'W’l €11- <00) no .517 on —at J 6 ut’H)u£t-E+1)d’t- f e we.) «yr-r ME 4 fieflrh - )fit of??? : at e *Qffltl 3"“ e )W‘f)‘*-d~ (t «2 )ur-w) 0? fish/e ff 9'er wpbfcall/ ' . _ - I’M” Em? {:hé‘ LE;- ~w fa 2} “km-wt ’64:).- H-z‘d +qudammfla1opa 300- .0 mix} 01 1342 : '21:: «rectangle ‘5' 1:3;ij (mag,- wt) 14:“ 4‘5! _ e"? .01- I W? W) e t a u e ; hifi’ ”it 17.7.: "*t’i , “bis—«3!? 1': GMHJ was. Mr) eggs} ' H J -oE 'éla.) a )= f,::t -—q€ The! L I E i“, - H «Mt-I) -arT-H) ~12" 6": FA ~ a (-- ‘1 ' €— e < 7 W_§__mm)t ‘ .‘ I PROBLEM #3 An LTI system has impulse response 120‘) = 110‘ + 1) — u(t —3). ‘ 5 2 PROBLEM #4 Find the zero—state reSpon'se for the system described by the following differential equation. - 7 y"(1‘)+ 5V0) + 6W) = XU‘) ”2160‘ - 1) , fi‘r‘it: 3:4. 550,4 6 go: I XU) = zefiuo‘) 05 s’+5s+ 6 =0 5.: '3, 2 3 ’2 * - - ~£ ”if”; any): k’QBH 1091 , -t I _ ' — Forced 7!;st HF (t) = c. e I 3F .: _ Ce f, 3‘4: C8 {- C’S’C'téc .: 2 A) C =./ ~> 3f: 2 9:6. — ~15 ~75 golf): Eli-tines + K282 MH'Ha you» = 315(0) =0 (gm—stat mama) {”k'wfi" N, {km ‘l *Bk. —.2k2=0 "2='2 ff . -‘fi -3'L’ ~2‘é W ya“): a +3 ~26 . W (IWBE and ‘LM w'wucw'ame, 3* 3(6): yow- 99M") ' 3 (40) I 4(25) Total (1 fl ...
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