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Cf}.,) Tr~J AM If;"~.e rf.
7.1
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;-L +t~rf~ fu.<P.o. ()f. ~CUR l' tf6.Je
f//f-erJlcti b-e .eCU'~ d.£feJ-"',vol 6;
1 . ~.".~~ \j-
I-/a. ~I~)::: H (e M ~ )~IT'G II
II
-I
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II ' ~Tr'
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TJu de~'1hll v.: I/oli/ef ~ ~<JfM.r f 110 . D,.
th. ro-fp+j?~ a., J f:h ~ tv-/: of f/lf-erJ
J2. _ 0 J.. 1'1-1T<"- /-/ /
c~ h-e 'f I~ h,.q" -t~ J 114; 'J ~ If v:~ ~II FTII
6; ~
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~Lf (w) =11-1,W) ~ I--/Hp (t.)) =c Hi W~' -zH z ~ /«1
::: Hew-IT)
Q.-bt01d flfe~ baJ.
I (h t ~Ii-JLP (~ UO[.]
L \~(1--J v, cd ". h'5h P~f$ ~"'p'
for}lh
low I' oJ} C:i)h-()
TLJ ./
11 PO
II-pll (~)" H0) '" EkJ h [,,] 2-"II
H*' IJ Yl
H p:: (i) ~ (- "t) ~) (-I) h [h J t..-IJ ~-I.>Q
U.r'"3 '* Ilfo/~f~aJe d.eC-o#trf,"';"O"> We hal/€.J)o
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/
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oJ II iJ<q. IA) eS; '" f /d htt II-e -h, 1-'" f I~,::I"
St.<llbft /f-er s EfIJ(z ~ ) R
~~tJr
;;-/ (? 01) S'.e f
-e.r-ft:\t hJ 4
~J .rIAb'/Y~ ~ ~tJ.r
J>o
HHf () = Tk> h [2",J Z-2:- L h [2h1-1 J .z
-2111+1
hi =-Po,
-----...r-
E (12);L
i £"-,(i )
[ HH
-/ Ep> (]2)
I -/ lC -I(2;z)
Po
E\6 (~-') : L h[n.] 2->'"»0. )
. "1 -= - bot:>o
1:--- } (~ :J) =- Z h [1 h1 -J] Z-2 J?1
h1 '::.- Po
wJ<w
c#v,J
Th/s CCM,I
Eji 0') + r f-J (~o)
€ rh-f/ r1~ J ~J' ;; II()f.1)J :
-;> L)o [nJ
~h1pIV~i1+C1-1/iJ 1
('
!)J
+~-~ VI Cn]
fo~ pI, ~~ I, /-f.erJ',eM= 2)
r- - .I .= X Cl>h1J) ! "" .
J LfI
E91 (~~) ::
'-'0
L h [2 hi] 2 -.2111
) .2
Ej (2 ) =-
.Jfh =-tJo
/)tJ -2h1
~ h [2n,+J] i J
"" :;- -lxJ
/-1 (?) ::1>0
h-.2h1 ~ }hJ-J
[JWlJ 2 + ~ h [.2~+1 J l:
Po
h [II J i.-fJ
h1::-t,.o
-I J
Z Ej{il)
/ -/ ,/
/-hp(Z) 1= II Hr?) = f% (22) -I- i! £, (?2)
/ I H (/.2 -I I
/iHp(OI= II -?) = EIJ (? ) - i E) (?')
~Jw. J ,/
H-Jh,~ ;I
1/ /f~r
Th roe..!
~f
fr~.J' f~
-
-I ~
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-,
I[h~ ~J [,It'
0LI-~'(t)\
IwDavl
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~ Uo [i1 J
~ [11 J
c.f2AJ / c..R. J of p7) 17/ pkJ'f2
( cv... b-e j ~ ycJ,- 2 (J d 1;, ~ 6th.)
f' ! rlA.R ,) ba-.. 01 f aJ'f {'lI ~ r f vJ 11.
(VJ
c.:P, 'i) It .r
1-4 (~):: I-J ( ~k t) ..)
~--~~--- - --
Ar~ - () I ~ . M... J,... - .,) -> -
h'rJt~1 ~~ ('Gt?, ck.G;:;h?foJ'(? /-!(~J
,' fJ pi0 !~I?h.:N u,;" f (j "...,,:h- :t11-1 l)
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/-11
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~
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T~pr1~
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Po
E~.e (i M) =L
m:::-lx1
~h
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.,
. AH~ (i)::: 1-1 (Wf1 i)
, ~/ )( ~.Q - ,111 il'1- L- ~ WM E:~ (~ WM )
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Ii ~Ji M
i IAJI1 E_; (2 )
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::- L11:::0
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e v;.;;- 'I -I. -.-
~J' / ;~a
Q. h1~/
f> lie r I-/~ (~) c~ b< w~/'-IfB/Jt i/!.;...t
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I-I~ (~I) - [I i J ~LA 11 '" w;1>1-/}RrJ
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f';!i: E --I (~ )
.:>""../r- / .. f4 "\.'... }
w-.e CO/>1.
cJ)J ;;,/ f.erJJ
H* (i)./ ~ =0,.;1." \ 1V/--},,~If 0-f ~Ii
F()~;'-e r Md~/- ~
Ii c~ bvh, f I~-t j aJ
Iv flow f ..
f)( [ i) II] --.
I~ -~I~II~ t>FTI
f
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-
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;> I I-?J UN-jChJ",------ /.
t1 li ( I I. I
lr' E. (t:)? l )
Hi (ii) I =
t IN/1 -- ' ,W/'1"-/I it-I (t )
I \'
\
l ,j
1-1('1-/(i) III
I 1'4-1 I,.}.({1-1) j'
L 11' 9 -I t (i J11 - -M+/
~
'>([n]
TCf2
cp
~~ (if )
Hii, (i\1)-
H1,-/ ("iJ
/
E.;. ('7M) -
//
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WI1 '
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W (N-I)11
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~
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~ £:"""-1
IJ
I IN /'1-1f1 .
w
~I1t ::::- /)(J
-11~h [Nn-, 1-)] ~
DFT
..)
n::l>/ ".1'1-1)( ... ,..j ,/
..~ Ut) [II]
...
"
.) VI [n ]
~ U [h]11-1~
rnf I~ :
E--k (:z <f)
"II
~r fA) cuJf -to ck CA>'" f ~J,€ tt .J; dh J/n + M= tf- frJll'-' '(j CD J>, f iJ ~.r .
II
f\h " J C ~ be. oLv >tR b'J J<-v () S :',J
iTTot F Ifo..r w) '-tfl ft-" 1u;" ';/ \ rL"( () Me.
~ Hj. (w)" H (t.)- ~f) > :fOl-1k 6.) I.) 2./ 3 .
II, Jlo~?aP ro~-Iyf-€ ~-/fer C'a»z.
vi...t.l!r o(! r-€..? 0 " J.e ( l1.AJ " ctUt J,Ji ./
J' r 7r n..]S"t" -;;;::- fA) CII] )
7Th
h [I) J .-
wen] /.f tle '¥ 1)11) r /J 1:- tJ J--. ek <J
j
f,ILr P"~ t~aJe c()h,fiJ~J
1'- I/'IYI, /, (J tf6? -f::v f4"J f (?J- f. J, nr- 4Jl
A l4j)-~ J z
S't"fJ [~( 4-Jl-~ ) J 11 -4-P.. w[49-r<J-2
rr (4-»- ~)
~ -6 . f v<{.r ~ tIbc f~f.ed
fi Hen b~J W, 11 J"u/fqJ
U;h dif,'b 11 .¥'J-- t~fedf Nconrtrucf);~" ,'.f tlltifr
th. J'wmll olv JP 8'hi;J-r ()J ~ flfe~. b~
~ I'd. ~J ¥'I tJhffi' J. sidn J ')( [;] .
. W.(z UtJ
II
[3 UJ h J -!rIA j), (} IJ
n~ /,an, cP I I' I - Ii .cM,cfJ h' Iff! /(I
~ I ~o~l",) fA>[11 J
,)[ HI I'C) J :) VI [11 J
..."
'" \,.
;> r ~M-I (ieJ~ tJ,.,-;[bJ J
I
~ ~ -f..A ,. ht~ /0 ? ;'-r ~J't <I t;& (,.i)'\ ct. -h'0i1.
!V1- /
[n] ~ L:.. Uk [jJ J-If<:: f)
~I'S+S>
:rh ~il fW,.. e9 ~ 'M oltJ i?1 ~. () d - ./
M-f'- !l I
I
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~
Xrr.J}
[)TF- T (o; ellJJ
--1-4 (~) X(!.J) ~ -IL ... 0 I '" M-IR- /..J -'
TIu. C{)"V;-/' L Iv ;- p~ f J r~ U11 s Iru ci-,IJ"
ca" b.{!.
CttOVf!
S'v. eX a
I, Ih
{VI-I
Li-:: ()
CCJ'
IJ:::oH (iJ - ~!!! ) = I .
M
Jd; sf; '-'CY tI0c t~ {J N CD.A. did"
6 e rJJ!.t J a h ('1- band;; 1ft?r.
i d er h IN ;tb h I/o l.J'~ g. Pro /H-'" h-~J .
J?6UJVt,(f clo rn~ :
(~ ,- 2.7T~)tV M =/
d. If]
II
111A~ dgh,~ :II
h dMp = ;} Sf.] .
proof' 'I II
I '
I t' f11 -I
,h f,n J ==1 - DTF T { r 1-1 ( w -I ~==()
'JIT-A--I \.1 -11
e /11 h [t1]--
-
7/)]
, , h ,[ M n ] '::- M" h [1'117 J11= D
~!I h
1,
[n] -= IDTFT {/-I (/.J - 2';'~) J'2rr~J-n
h:: e 1'1 en ]
s:'i It Cfl..
~
/ , f'v/-I
[h) ~ IDTFT { L..g,-=. ()
:: IDTFT{ I}
= ~ [n ]II
h II (M h J -=I I /n h en] -:
1-1 (fA) - ~~~)J
-L ten]M
3 In tI&.~ -i;dorn~ "
! XI J- I
Ep (z) = . ~ M,f[ ~ J - H~M -I M
H w:: &; (~ ) +- i 5 (r ) +II
-(M-I)
.. \ I + £: E ( 2111 )/1-/
pt()~ f : /XJ
E.J (t) ==j, [h M1-i J z- ~
0= D ,.,. /\A-I.A ~..I ./ f rf
TL.r /
(\1-1~ -..R M
~ ~ Ell (~ )
..(~()
IPMJ 1'/-1..>- v i-tit bf7/h dwlJ~
tVYt (V)- b~ d ~. / f~ / b.e c tNUJ:e
[0 - /:; (?!!) ] -:: /I' fI1
Ex~/! :
c&.+ fVJ= 4.
~ J-,'()J?
~OJe~ /::7R Ii /f~ fA);-t!<.- ~1Mt.r f~
f-III jl ,- 2 - :J - S!(i r::: O. l J~ 1- i'l + :f. 2 Z - 2, J' z + /.s i
-f, ~? -10-I-i -~ + r
Exle :
Iin ,'o&cd
W -.2Lc. - (VJ I
M-VA,
-
~;
1.
II
If (J) 1II
1-1 (-z)I
v'fA)~::: e
, . \ -: J',J c..J ' ~ /;,)u ~ v -v
- t).2J+ e 1- ~.2 e -2.d' eII -J'Jt.j - '6t.J -V'?t.J -".;'100II f I.J e -I- e \.j "- e -I- e
!- 'I - .J7T. It"" Ii f II H (I,) -' f J + H (t-,) - 7T J+ H (4J - 7" )
l) II. -v "v..;Ie $' {! h v' 17~ ..; J.;!~J- , "h [~] e [,,1"+ e ~ e ~ e
- h [8:] e-,;i-J~ I - e27T~
'if'
I - ev 7~
-0 II \ k
-& rJ [R] e -~ l.J 1- S [ ~ - Hn ] .)n,~ t).; J ~ 3 ",.j J .I
-.... h r~J x 1- :::-
4- X O,~S :: I
h J] Ii I c.
][4,~ ::~4 ~}1.
II
f:j5 (~) 11'0
E ~ II
-, ('J) II~
f~ (~) ~
d.
3
EJ (~)I
::
Z { h f 4-h ) J -: Jr!t {h «[.O~I]J :-J.+ ", ;?_I
Z [h [4_+>J) = d.l + 2>-1 +- i>
Z {J, [ </.0+n ] :- - ,<,g. - z - I
J~ 4eo (z ) :-
I
[I (~4-) = / if I,S- ;Z-4
4- II - 4- -8E1 (t ):: 3 ' :: 2 + -2 J--2
11 1-
EJ (i <F-) ":= ,[
- 211 8 - ~-, II
II
II
-' -l f -I
H(z ) ~ (), 'l i.f t if]. I. z - 2.j i- -I- / I S ZJ; I
') ,
~
- JI. M~ ~ ' [; (~ )
12 ::: '
- 6 "-?-;+i --i- f-i
/-/ ~ U( H ~~ ) II cCVYI fo yoma 4- b fMt 01 f,- /I-~ 6~~.
7.3 (YJ'
,'
'~II D.eM/1J J.ed DfT F," /f-8v /3..,..) s-ax/ /11 '()
-I II () I. I~ rA / t'l I~'" I p'.&?( € y-J
.I" tR..e ~~ '-Ih~;j cb","h,aJ~J CM~ ~ -I:h C¥hJy.r;.r
C0Jd SJJ1 t.
i 1.
I"J M-fiAJ ..kJ ck Mt dt><?) ~{}V-vla1PJtff~ r-Je a J cie D/J-R J b~,.J:
II r
Q( [fl ]
~r-
~. ~ (jl~
. ~I'f~\---~j ~ .
, ~~[Gln)}-)(+
II .:
~!~?~}{HQ ) . ~ I!MJ~I~;Q)~
ZJ~ w,.;/ ,Ju,'~ ~ I~f ,&>1 7h, fAf~ re-..h,
J11cux; IfJcJ2Pv; cb. ~'/11J-f J ' f-; J1~ b~ .r ~. . -tl II
FJ 1 . ~ {JFT tM.~r.:r ;,y}<.)~~1: ~O-<~"C
; Ve-,.. s s '" c1 tJ cd-
1-11 ~t.J)" f--f «J- 2;:) ~= 0> 1/ ,., M-i
t'.delUivJ~ Co !h ~~brf S'hLVh :~0,"
tJlR ~J"f~ fh Jl,'O ~ I 'J" w~J~-f.f~~s
~ a)::- £? (iM) -I-? E-t (lit) + .. + ?IIT~T'/ .,
~ L£,d~~j1 )/ I~ Vo[it]
~ ~~-} I~!!J}
XCii
;J 1.1[it J
DFT
\
\
E-}~} -J Lh.., [17)---
FJ2.
Va [ill -:
VM-I(>1J
Fcu2J.
XD1=TII
II DFTII
If+ fII
S"1 ~ f:t.r; Or vJ <J 0 I> k t.J ,. tJ. t£,\
~t{v< (0) ::
(J (fA) - ? rrl<)11 ,;
11 - 0 J'vI!-"7f- --I"""'" 4
IS II ef" f vaAl 1;.;, -th h.£.t J.,) 0 ~ k S' he, «> hII J 11- J. .~ f.Jl .~ /1
tJUt Tr~J! Jl" Fh r7i'" it I of l"JI'-,'rre,,1IJ
b
.. {lip.. _I l'1li. -(1'1
fll:z):' ~ ( ~ ) f ~ h (~ ) +,.. + ~ i?r,~f
@J -.,) ~ ~j-{~J~{~!~..
~~~f1EJ-4C~.
J [h)
.
" l'l~ ,IT";;] -. l?I
~ ~~/~~GJ-J
a J' S'h.;yt,JJfb~w ~0&./1} f./h Ia. ~ )
X[~JI Ii
~J~ ~
~..1 ) r:iMl!" L-4 ~
Iw
1Io [~] =- /)( [Y} N ]
~ (/1] = ~ (YJ11 + I]
II.
F~4.
~-.) ~-j [~] :; ~ [I) 1'1 +- (1'1-/) ]
'Xc. J -;{ s/p l~~ f.q,r It? U;' ~J' t;{ ~ b./h of
I
.
OC1
J
'JJ' Va(.J '
.
0 [n] . ..
I JM C
.
'I Jtt . ; . > ,Vh-/
. 1~/(M,i.J' ~ .J-RJVth.+'~ ,.~-f.o,.Jj, ~ JU r.A tI<d-
0.'" d
fr~,-".,Jt,
II
II
II r-;Nlu,~] H!:!J
II
V, ct.] ii-7@II
ff [iJ l1- ~ J:- 14 [n J f
I' K--:r)}TV"" '. ~ """,
/'1- I
.,IIII '
UI1-i f~J II-? Cr 1'1 1- ~~
!!}
dC~)-j PI. /J.
---,)
MO/X,' ht~ j)RA.;,-Jn J oR cI f)FT h' /f~ /l~.r
, .,? ,"vJ. "',,;
;" to f'1 fr ""juJHo if
-erAcf(, J{~ btJ 1'1/
"j" I' ~' '
I
r -L., : 'f"' ,.,.1...! ~J € " "
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