This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 = (Hlenﬂ ~ (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. cowd. 1A lacM, a. «4le 6M 3‘;ch ﬁﬂ
\M5 k M'vdud’ 2AM symH'i c Fem, ﬂ,e_. Wm egwﬂ° XCeJ”) 4;" 'mAaa no
compol: 40 a. PV\L 4M by no S‘Mfle—S. Hm] 9th] nus+ 905m: a. Poi/H er? cvM. syMM4~I7, wok 41nd— ixlvHm] 15 em sym+c<o a‘ONI— +1,» 2/1.
Can 44,... {3&3le Sianqls (001(5) ad. (4) Sad3557 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. cobaltz. l—Hé’”) Suda M
W = L T ow
1w,\¢.mn N; we )[TJLww.)+'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, (dzw
_ ..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 netEM
.__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 oddindexed 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 oddindexed 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 evenindexed 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' ~— ConvolulNoN 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, + «@323 + (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) Jan2]
+ («ZL‘ + m) Sin33 + 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 DTFT' +v giglam \{Ln] = Mn] *9 ’Xbﬂ . Ev‘w 04 erirt; «HMS (Droqcrﬁ cal7 MAS who» .14». DT‘PT“,
9A9, egos—b, or who» rxm .wt uh] m cm can sowR47
MK) supMum. ...
View
Full Document
 Spring '09

Click to edit the document details