ESE_305_Notes_wk_2

ESE_305_Notes_wk_2 - 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

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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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This note was uploaded on 02/19/2012 for the course ESE 305 taught by Professor Robertazzi,t during the Spring '08 term at SUNY Stony Brook.

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ESE_305_Notes_wk_2 - 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

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