11FMT1SOL

# 11FMT1SOL - Question 1"[20 Work—out question Outcome...

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Unformatted text preview: Question 1." [20%, Work—out question, Outcome 3] \$(t) is 6(1+j)t if —2 S t S 1, and :1:(t) = 0 otherwise. Compute the expression of OO 3 5”?” was “1‘; 5w W :1; ~~~~~ w (4‘) (:3 ‘f:;,_~ 5N A}: «.43 \i 52% Cw-sxcvmsj W3 \ pt: «v :7; or: I} A I, d V (:3 C) 15.36”- ' '" 2:““E (WS3C1zwﬁzig—3;t§_§étmﬁ 04030: 33 2+ta533» .JL" at O Qifhxjm awt‘M C3 Qf‘xﬁﬁ (3‘7 M ‘ (“A 535‘ ﬂ‘jﬂw ,@ acCﬁ”\$§f"}\$ I xwg mg if‘é”‘"”%/ @Cﬁlwnﬂ W o 16' “i: "W ” “” J1 V; w v . 3‘ ,m « Tb i?» t < w 3 « ‘3; ﬂ 2 / ami s; g A? a. «A CM~C§35 C‘r3ECEL 19f \$3 Ex” 3 IQ“ ( ‘3 "99:1ng J CVV'QZZ ( t+m§k ’ (“H 3 1' {I m 0} kw / 3 ﬂ ”’ P3 3 SSW“ 735“ 7/ I 2: "7/ "1 0W6“ E W i, ( 2&3 Jeni“? "’J’E W ‘ E9 “if” W Jo ’ V t < “(:2 {f my} i a Question 2: [15%, Work—out question, Outcome 4] = 1 if 10 S n S 30, and = 0 otherwise. Compute the expression of 00 9(0)) nz—oo Hint: The geometric series formula is K E OHM—1 Ic=1 - E g 5' f3" if“: I?» DC L rx 3 “£5 :1:§"i1w§“xwmv {is} ‘f M a1(1*r 1—7’ K) 2 x[2 — Mew”. 3W“? Question 3: [10%, Work-out question, Outcome 4] Compute the following partial fractions: 1 _ a + d —2+3z+5z2 —b+c-z e+f.z' Namely, ﬁnd the real—valued coefﬁcients a, b, c, d, e, and f. Compute the following partial fractions: 1 1—2 a d g _2+3Z+522 X1+Z:b+C-z+e+f-z+(b+c-z)2' Namely, ﬁnd the real—valued coefﬁcients (1, b7 0, d, e, f , and g. EaQWi-‘a wits \$33 “\$3 \$32 ma \ \$3 \$15»? (:bnawwﬁjégii l“ m Cl “\$1 A ,l «.1234 I m WWWW Magmaai ma Kﬁ" 13:”? law mtgfawsiwt a§€§3w§3 Jib 3*”U ‘3; CXCW'?) ‘33? “V? Zcﬂ/g/ 62:. (mg: 7/5) 1‘. &[O3 3:7 (3% Eat/M? if 111;; 3 m We g} "f" 2:; “E;- ‘t ‘2'» 332°“ {a f3? :? Cl? 5/ ﬂ W‘anf \$532533; ‘ 5“} / lift]; r- 5 i ; K p a 3 w 1 —— ‘2. Q My d W :‘ Q we? ’3 5 g d 7/5") V W E 2: - d M « “wiﬂi O 3 E; if” A K 0‘ in? walla J ‘l I W Z W N 5%» We ’ wt @1% WW ‘6 5 WWW @ 2 WWW 2 "z \ a» a} (‘ﬁﬁawmjfwzﬂ “XXX/wed Aﬂggg } 75 Question 4: [15%, Work—out question, Outcome 1] We know that 30(75) is a continuous—time period signal with period 3. We also know that t+1 if—1§t<0 . :1;(t)= cos(2t) +jsin(2t) ifO S t <1 (1) 0 iflgt<2 Find the overall power of this signal. #1 ﬁrming}? mm a (Samimi g pcﬁcuéaiom ., 3 C,t°’i’\) ) ‘ :3 WW)» “’1’ :2:- i M e ﬂ )0 9E) CI (:3) «v “:37 ()QégJﬁ‘l, g, iﬂﬁkﬁﬁjﬂ Question 5: [20%, Work—out question, Outcome 1] Consider a linear system. We know that for this system if the input 33(t) is an even signal, then the output y(t) is always zero, that is, y(t) = 0. We also know that if the input m(t) is an odd signal, the output y(t) is always y(t) 2 33(73 — 2). Question: Plot the output y(t) for the range —4 g t S 4 when the input is 21H>0 t = — _ 2 m) % M<0 () If you do not know the answer to the above question, you can assume \$(t) = sin(2t) + j cos(3t) and plot the corresponding y(t). You will get still get 14 points if your answer is correct. AV www «In DC ( “M L :3 {is} o; C? . smmWWWx« ‘35 t») {IN/*3 u .Ewwwwmmclwwx? m wt”) :5 W, g W,Wrmm»swmxt¥ m“ gr on ,g C “7:5 A /.\ «g lam-imammwmw N C) (,W wwamwwwmmw wmm» \ﬁ, % 7;) 376th: 916%;me stﬁi (Afﬁl “3.5 Cilia ‘30 6%} C h‘mxcm; 35:1 s. C) "i“'°’ (2:) (:3 C 73;) v. [A 3 (WWWWV ,WMVMNWWW L (if: "im' f\m,vr 3 ‘ i‘ 4/{w jrfﬁwl w t” . \1 i‘f’féfwi s: E» ‘v as K :2 rigs: W 1% i iﬁwfaasM§ Question 6: [20%, Multiple Choices] The following questions are multiple—choice questions and there is no need to justify your answers. Consider two continuous—time signals: ffﬂfﬁﬁﬁ‘i‘wy)‘; SC‘Eairaf‘E‘iill) \$105) : 8(Cos(t)+jsin(t)) ,, “QM - or “i” :3 m 372 (t) = SID“) F t o s 25: 5 s i m “as St + e—t A. Av ' ' ' > g and two discrete~t1me Signals: t 3" 5 ﬂ «Null; C; (“44m gﬁhﬂ‘f?‘ e )6 \$3 : COS(7rn2> + Sin<7rn) 0/:3 3 2 a} i '1‘; Mr” H at") \$4lnl : 6(1+])n- a CC) 3» f n 1. [10%, Outcome 1] For \$105) to \$471], determine whether it is periodic or not, respec— tz'vely. If it is periodic, write down the fundamental period. Please state explicitly which signal is periodic and which is not. 2. [10%, Outcome 1] For 1:1(t) to 3:4[n], determine whether it is even or odd or neither of them, respectively. Please state explicitly which signal is even, which is odd, and which is neither. (I) Dim—a) We. gymnast {a h ‘T' :- Qm m 35,; (71;) m} ‘ ho M w path‘zjgi \ es». 96‘ b h :3 wws Pm \$0 a! (a. ,, /\J 1‘34 El rag} W4”? fa? W, 53‘s.} r i _ L“ @ 1.“ C t) w» W ems”: 5y (1 s3 w> Odd 3K5 [jag W”? Evﬁh ° ' )0"- 13%?“ £5»: :3 W»? I’m. flex ) ...
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11FMT1SOL - Question 1"[20 Work—out question Outcome...

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