Question

Problem 2 (30 pts) This problem has six parts that may be worked independently. Let X(e) be the Fourier transform of the discrete-time signal x[n] show below. x[n] -7 -5 -3 -2 2 -1 4 5 a) Find X(e). (5 pts) b) Determine ZX(el), the phase of X(e), (5 pts) c) Evaluate )do. (5 pts) Intel® d) Find X(el). (5 pts) e) Determine and sketch the signal whose Fourier transform is ReX(0)} (5 pts) f) Evaluate xo do. (5 pts) do

Answer 1

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It 2003wt 4Coslu at see the graph. E n= -10(-5) Discoete Fousties seguien xlesw) X(eiw) e-iw(-2) (1).e iw (2) ره نه. (1) + q.e e - (1) e iw L-] + zevwli لیا ن + 3e + Bintie-ton + (1.e-1W (6) - lelucos +10.e-jw (3) geisw ė "24 jew_it juwt3e + e - 31 = ) xleiw)= ei gw telow te getic + e و ذ۔ = 1 +i+2-1+3-1 + Fit =9 j2w +3 -j2w -jte +ze j uw j50 dzw +ze e 15 - le jzw t e acoso xcesos= edo tesotzero eto telo Itae do te je teto xleio) lycerol xceties eiz teitw erowe have evo telo {aC035w+ 96046 +4C033W -2 20 32W +3] einer can write xleting Xcelw)= (xen (xerras) maynetute O=(xcelwg phase zxleiw=2w we xell we e whese xleswie eroun dw have ㅠ sen) = 1 2T LIT #10) TT OTT l - IT IT X IT reiwgieodw lew.dw = altero) = -217 [2009 517 +26084 T +4C03BIT - 2003 271 +3] e x (edit) [-0+5] =-3 ♡ Xref m) IT ) =-3 Xce cosy w Re Excelu) - cos3w + 20035w tcosow frostw -Ite to 4 е + ze - iw I2wtze-jew Reerleiwg j3w te £e-row

2 sln-25 + 26 int3y +46(+shp) we have sin-noge eiwno بل slotho) e ev who sin) signal correspond to - (b) + $ (b)+ + (b+ 1) Reexleiwg} is xela) - X d) +123 (0-6) + I sit 6) +20 (07) + +010-2) x [erry [erw] Walt From. 3+2(-3) =-3 x[erit] Xein) mathipalafitalet 's 33 2 2 3 hlm 15 0 COLE 1 O 0.5 3 105 I-II -2 -1 a 2 - 6 - 5-6 we have baysevel thm Ź 12(6) 12-5 ZITT n=-00 we I a ceriwelow have -in e(n) # $ x lelu) Il tiny ma dor e de televing ] xjerojaw = 27° 1 nxinl co -IT 2 :. d dw ns-a TT 21T E n=-10 2T Answer 2018 1 machine -7)2 + (-6)2 + (-10)?+ M) +(-6)2 + (0) +32+ 3)2+(3)?] 21 [ 49+36 + 100 +16+36 + 4+4+9) =5087 lesw).X* (elul de ain).x (n) | E inile du I aloi 21T I creices n=-20 -NT