HW7 solution - . ,_ I 08% convulufioa (fife—fiy’...

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Unformatted text preview: . ,_ I 08% convulufioa (fife—fiy’ X(C"N) 7" (Cow’é)( I—Le'5”> W JV x. (aw) 466») Run flu look: '- e' L? ’X‘ [n] = 5Lfl’l] " chS'ZV‘] «2m = (aw m mm: xm = 9M x xzm = (Hlen-fl ~ (J5 WUZHJ Mote: 4m om own = (é)""‘u[n-.1 r (3% “1 um Le») 4&3ch W75 “‘0 Afar'wc W5 wwu‘. Vnum 2 f—‘__—_ As we. cow-d. 1A lac-M, a. «4le 6M 3‘;ch fifl \M5 k M'vdud’ 2AM sym-H'i c Fem, -fl,e_. Wm egwfl° XCeJ”) 4;" 'mA-aa- no compo-l: 40 a. -P|V\-L 4M by no S‘Mfle—S. Hm] 9th] nus+ 905m: a. Poi/H- er? cv-M. syMM4~I7, wok 41nd— ixlvH-m] 15 em sym+c<o a‘ONI— +1,» 2/1. Can 44,... {3&3le Sianqls (001(5) ad. (4) Sad-3557 M Code. 1—-—\_’——\_‘) Rum 3 — r. M For M LT‘I ' WSW Hl‘h’v ‘Nvlw (two/LR, [Ar/q, W luwc, Cos bo,n ——» w. as w”; DNA] as (—w.n> = as (can) Wk, us(-o~gn) ~—9 wows Hm fDT'FT we. cobalt-z. l—Hé’”) Suda- M W = -L T ow 1w,\¢.mn N; we )[TJLw-w.)+'1TJCw+w.)]elenAw of 0'" 00°“ = ;[H(e~°- em“ + H(€9“’°)€Jw°“] = HCebw') wsoo,r\. 4_ . WSQ Mafia, H(e,°"°)=lwl , ~7r<oo<Tf (a. T’ QwL T o um] m = $5 \wl aw“ A. Jr _ .L V Mon ° _‘ w _|__ own J— 0 New) 21" _wtowndw z £17}, °_Nlé.ow’r\a( I Jr W to I vol/wt, (dz-w _ ..L T I 'vo’ — 2."— o h) e.” not»! Wm 00’ w'~l4« ‘ 00 M ' ‘ Numb/w, m+o eater-£55104 5r (AL/1]: 0 "f net-EM .__L .L 1r -r L) MU “79"” - 00 ‘ WL nsmwn‘o _._ Jo sthwn Am] 0: use“; 4): N o 7T'n2- TH," 94% 003 ‘9 NADA]: Siam ((9575:. -—'l) the frequency shift and linearity properties, Xtejiw‘fl) + me”) was} 2 2 Let y[n] = v[2n}. Then m new) = Z genie—m. 112—00 {Since the odd-indexed samples of she] are zero, we may put m. = 2?: in the above equation to get new) = i esteem” = V[ei“’f2}. m=—co (Note that the substitution of n by 27?: is 1valid only if the odd-indexed samples in the "summation are zero.) feIZn] is a new sequence which consists of only the even indexed samples of e[n] is I - hisequence Whose even-indexed samples are equal to .eln]. The odd- indexed samples of she] are zero. 1.1211] is a new sequence which consists of only the men indexed samples of sh]. This implies that own} is a sequence which censists of only the even indexed sanipl of ache]. This idea is illustrated in Figure 35.43. me part {a}, memes) + X(ej“”2) eta“) = 2 E11404 '5' ~— Convolu-l-NoN A X(2)=ao+4.% +q22” mm = bu + ht + $92}?- ‘(LZ’)= X(2)H(£) = (41222 4—«(2 4—4,)(52‘ + (9,; Ha.) Y6?) = azbzfiq + (azb, + [email protected] + (alto + «39, +— dual) 22 4' (alb° 4' 40L: )2— + qol’o BX ‘1[n'\= 9%] mm Gmwuuj, «’2‘: f. 47. L 7L4}: “chug-[n] 4' (qlbo + qo‘°u> 51""1 +' (alto 4' qlkl 4' ak‘bZ) Jan-2] + («ZL‘ + m) Sin-33 + qzbz 5 [NH] - w \ C) :E? v“- f'cdwe, i=6”, 4%» X(€""°)= Z. «(flefdwh “S—A path 15 um N'W DT‘FI’ a? wa'k, 1w wv. cm Wot ‘((e9“’)= R(é°°)x(e9°°3 u; use in 1mm DTF-T' +v gig-lam \{Ln] = Mn] *9 ’Xbfl . Ev‘w 04 erirt; «HMS (Droqcrfi cal-7 MAS who» .14». DT‘PT“, 9A9, egos—b, or who» rxm .wt uh] m cm can sow-R47 MK) sup-Mum. ...
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HW7 solution - . ,_ I 08% convulufioa (fife—fiy’...

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