ece340_exam_1_fall2007_solution

ece340_exam_1_fall2007_solution - ECE340 (Engineering...

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FALL 2007 (09/25/07) ECE340 (Engineering Systems Analysis) Name: M r. C;o/l;1f(~~ Exam I I. (20 pts) For the periodic signals x(t) and y(t) shown, the signal z(t) is given by z(t) = x(t) + y(t) x(t) -4 -2 -I yet) 1 ,--- - -4 -2 0 1 2 4 a) (5 pts) Find the period of z(t) l.ll) LC,V1 o Pe}~ool 0,- ';;(\:t- '= 2) ? r-rl d r noq of ~({;) =Lj- b) (10 pts) Find the power of z(t) 2. 2 c) (5 pts) [s z(t) a power signal? S I h (E. . f\"L po vl ~ at ..:eft-) \) ~~11- r~ ;Z (-t) ., <, 0- pJVle--r 1,IJ n.J. 1/6
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2. (15 pts) Decompose the following signals into odd and even components. ll a) (5 pts) xCt) = e-l . sin (t + ~ ) - _ ("11) _) - (0)) I-l;i e - ( Sitfl (4;) (o~ ~ .f- cos. (-t-/ S,Y] '3 - e-I-t-I (OS (;!). SIY1l+-) -+ et~\7J1(?\ - LOS (+) t ) i l' / l' o)J e veJVl e- veN1 b) (5 pts) x(t) = r(t) t~O t<O 1 udd tt-} == l A- i evU' (+-j == {I +1 ."). (-17) = X oJ t! C~-) + r;( e.,~ (+) c) (5 pts) x(t) = ell (0) (+-) -t-; ~ (11 i-b) L--v--'" ~ /\ e~ (-b) X.. ."f.L H;-). 2/6
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ece340_exam_1_fall2007_solution - ECE340 (Engineering...

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