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ESE_305_Notes_wk_2

# ESE_305_Notes_wk_2 - Square-wave 5H 1 M...

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Unformatted text preview: Square-wave: 5H] 1 M) ‘1i(’c-fJ~r1i(t~1j _1ﬁ/{47—3,_}, . - 3 5° Mt) w +1~((=1T]Td_?({;+lT) +2.<(¢)T;T{{,+TJ ,'J + WTJJU +3<(TJTJT(E~‘”j + X’{1T]Td‘T(£—1TJ +X{3T]T§T({c—3T)w -= His-:“(nﬂ Td—T({;‘ﬂT) Prob. 1.5m} Fiat} MW : Erna—zippy T‘fztlglﬁ, (i—lJ—lﬁ, {at—1r) 0r: : __ ﬁ_i Prob. 1.5 a}: Prob. 1.5 b): a} b} it?!) =J’t‘1} x(2t) duration = 1 If!) = 96‘?) + aft-2) - aft-4) X213) 2 I269 = - MHZ) + 2W) - aft-2) For #30, 2E0, so xf29=ﬂ f = ﬂ =3=- 2: = ﬂ f= 1X2 =3= 2t= I =3= yﬂﬂ) =xf1) f= 3K4: nyf-if) =xf3z2) f = I: yﬂ) = xfz) duration = 4 e” : Wile—t ﬁrst Tami“) = “tel” Him" : elitist Tim" : tassel") We expectthat . a _ , t‘ __ i i e ﬁe“ — lei 3‘ e‘ 2! Etwehaue A J a Emit west) : Menttdeﬂl) s (uninjth sewedeﬁne .i‘ a e} : euttdeeel: Etthen eafiﬁ' t1} :eit, eat; Self EL] :Xﬁzm : TTEW’ =TTéi‘9r 3‘ EL; :X1T3Y1 ‘ Hedel hH‘ial the” 931 : ﬁﬁﬁll’tiﬁgﬂ m ﬁﬁiﬂﬁﬂlj -- multiplying complex numbers multiplies the magnitudes, 3; adds the angles. Ex. 13.1: xﬂ) = -2 + 3 sin {0.61) - 4 epsfﬂﬁt) - 2.4 epsfz?!) xfl) is periodic with fundamental angular frequent-yr me = 0.3, since 0.5 = 2:10.31 8:. 2.? = 9:10.31 =:=- fundamental frequencyr ﬁ=mdi21tl=ﬂ3ii2nj =:=- fundamental period Te =1iﬁ = 21:!(03) In terms of amplitude 8: phase: xﬂ) = -2 epsfﬂyﬂ) - n)+ 3 cos {0.6! - n32) - 4 epsmﬁt) - 2.4 epsfzi’t) er xﬂ) = -2 epsfﬂyﬂ) - 11:)+ 5 cos {0.6t- 4:) - 2.4 epsfzﬁ) | where tan¢=-3f4 but ni2<¢ an a R=1h¥1+31 =5 ...
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