HW3solution - 2-57(a RealiZing that w2[n = ydn we may eliminate these from the we given difference equations This would give us y2'n =

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Unformatted text preview: 2-57- (a) RealiZing that w2[n] = ydn], we may eliminate these from the we given difference equations. This would give us y2['n] = —-ay2[n " 1] + b0$1[fl] + b1$1[n ~ i This is the same as the overall difference equation. (1‘) 2.59. (a) Integrating the given differential equation once and simplifying, we get ‘ b t b y(t) = 11° germ + 1/ zde + Am). (11 _oo (11 —oo (11 Therefore, A = —ao/a1, B = bl/a1,C I: [Jo/(1,1. (b) Realizing that x2(t) = y1(t), we may eliminate these from the two given integral equa- tions. This would give us t t y2(t) = A1 y2(T)dT 1111(7')d7‘ +Blm1(t). SW9 L16“ 1 £26?qu :xk) l-l‘) D .t CH? 2 (L enomem 0r 9’; MS) : 5 LC + \ :3 +\ t 3 T (when 3.352 1593 Foam 2.93) - 3 Homagewews Saifiaon {S 6% ¥9rrm Kg ; + ‘426 0- W‘ngre 3‘ 52 are (0015 QC SQLCHWV I l ROOJVS 0% 32:4 :0 are SoMJflevxS \‘o 57'; -\ “23’ 5'2) )S2= -J . v W“ “as W \<er W‘Zéfiflfivm m _ t , _ g I“) {~ - A330 '2 k‘ed + be”)? 3 w“w7“\ . SWQ Mafie “J (“We‘d a“) WA) \(Ktk21k30 fluff 0(er i‘erlm t§ Ccmflex (Owjusafi‘e G-f fine Ofi‘er Q;ch KYeJti'e—fi]? k‘Zcos’E : zksmktfl/z) i) i ‘ 4" ,L > fl ) y(5)€wf::($) 15(2):“5): i3;— = it :5 Ni»: fH ‘ “WWW => (?+‘)?I%):XH)‘> Wyamm Héflcel Vovwcjeneeufi 34) Denommder of HE): 3+1 1 Qt HVW‘OSQWOLLS Sowfixon ti» 6'? ’Form \<C I WM??? 3 (S o; 30\u‘h<m +9 5*170 Z) §;—| "éhW: ke' I We” 9 a: @ XI’C):’L+ eosfigt) + 'fsév: gig-t) g . _ J 72+[M1+LV€J%V£~CJ3JC “c 'Wt L mt 7‘5 2. Jam: = ‘l “J' 1 ‘ ‘ - \ ' 1* 3 2J6 3’ +56 5 +2+3e3§t+§§€ @‘Sa (I)? We am} ES; ‘1 Y‘Au‘f’}?§€? (if? We w . .4“ . ‘7 § ° 2 K ~_"‘ ~Tr Q We. « fléémefl mmwm (imgw C5» @331 Mg ‘3? 2 3d 3CJ(ZS)_3(.):% Mme ~J5W0t \ ~‘2u1t ngt ’5 t — . , J ° “ .L ° , J “’0 WW 2J9, +2€ +2+ze fie , _ H \ )f 1? 60‘?) aquvz‘i ) (15:0’; 2’2J \ f‘n’it \ IL « Kit ‘Fm L470} OH“ éBlSQJ &t dQBLg J 14,6 ! :: fiyg’Jkn-r]‘ , 1.5[E'Jkflt Z -' 1 1 f. .Q/kfi ‘0 Z UM? {:4 ‘ h5‘ e'Jk" ”‘ ‘5 Q'Jkfl“ e") 2 ‘Jle’ .1 -Jk‘rr I /. V \ é“ 36$,Vdue 6, [5‘4ng :[nogafléfi Saw (€336? "mag + lmeM'Jrf W0?” \)Se+!ME»€ev€(§a‘i ism ~‘r «5%{Hmfl {nag (figs? 920$, 2 4. ‘* g ' 2W Lg? 53%;}: KM“) ’gbfi‘ harms 6f? Wmoéfi wé’fi Fezcm} T5: 33‘ ‘ $3 #3933 §é>§§ +33va T; @WQHQJW‘EZfl‘h W 'X'({;—l Ada—794%; 3 F13. Mamet, «germ; a“? gum k {imarwflgggfi .Qhfiz/Qci 3an X §£E~> (Ag) th“) age-Jim); g‘ (13“) Qq‘kg‘ u). .ft)~7 a": F5 )flkwi Xl’tj:xl(t_l)+ Y(t»\)<QKH1*K)€ ...
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This note was uploaded on 02/13/2012 for the course ECE 301 taught by Professor V."ragu"balakrishnan during the Spring '06 term at Purdue University-West Lafayette.

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HW3solution - 2-57(a RealiZing that w2[n = ydn we may eliminate these from the we given difference equations This would give us y2'n =

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