Chen - Signals and Systems a Fresh Look - Solutions

Sie * Sffitu :l faaL. to4,tece;,A4;a tla*ual

44Yan z

,,1 Na. A ceU & cu.4 An f*;elecatais.

2.2 lo. th ,{n* A c.LcA /Lrr'

*V

fr*orn, pcir "rfl fu fb

4hafrae

u tS adLt . 7a1 ;"t^ft'd''cn)'- c/

At AAu c-ic-eca gu-'U A '

2.3 0r a dv t?fr; e/- 4,e ,ieyc.

ul ;A2, t.d

l.t /rr l. = p; / t , i't.2 ." An t-7 Z'ra'

rv6;a" zr'q*l+zt- u'Oat f;ud ?i

u, La7..to . ,rt, nl'fo';r^f to

lrrrt,),*(t"f,)'+#lf A a .*arttiâ/ stprt/,t'> 1x444' M

(htr+ fr,p) u 2tit, +u L6gaa.

YU- ,.* tn r , f|u F 4^r.( a.^fr;t/

zn**/l.u *tz.

! (*r i )=/ ' , ry=gJ /-L* l i \ -1. . t&t t? = -3.v-i ( r ' g o ) - t J o 6 a

tH:,?)=t" '?ln = #*I t i t * {a.rnrrt! {xezu

0t t f i nta 4l tz?

i du'o'iu '

J,t le corr&J a

hcfur. 't/

tt< *re.h V aa

i o , s t / o s t 3 3r t6= (

I d t<o o+4 c>J

2-6 * 0)= o,, r( 4s) = o, )f, x(r) = 4 5rt(4t)

= 6,?f , z(z)= t , r ras) = / ,2r ,7(9)=

r .d. , t (Et ) , 0 .

2 . 9 o . I t t i - t c )- 2 6 ( t - t o \

i'q t' {** f t ft, ott = cz,

"L=: '

-e

rfr/'z. J ano|1t-f le = tdtl. -,- '

6 o tt/tt:O

e

J J - a i t ' f t t - f / > ) d r = o ' k c n u '

' t=fl

ol' $fu n ln'hl a'r r/z od

dt 'W\'ertp* idu'a/

'tta >ocf

-;; fr'o-''' 6"0l' T '

oa, J- t&r! )cn(t - i ldr =o

L o , ) - - - 4 - ; o s f u t ; L,rt/ 4'&t

ef 't/t t

fe o).5'

!-Sr(tt--,t>+/at +t) at

: ' ' = t e - > t ' . + l o t t ' I r = o =

/

o_z+ I = e = |e l -- t = o

e 50 to s,'t dr =0

ot

I io ' ' e2c. { r= o0

Fsrrt'cr&t

2.s t5I

I 1 J 4

3, lA te tJ 1t=76c-T-.)ce = rccsI- d g - c - V = O

. = i l d l = x ( e - J )' t = t - J

{.(4-z\ E(.- t)& = , ,r-rrL-

ro= a ( t - t o )

z,tl Orr; chbc*tlfi.;avo lnI rl4d ,ffi

?naJV &"r*rit+ttt'&it ta ?e'- a),1*

;{ ete{ /";t;e &'b'ry Or

4 "a

/ai,&. tp/t-t "(

d*ca*'**en'

'Ttsa it- a d d+'t"e"tt/ "-o&e' '

2.15

2.t 6 TfoI

- i o- ,

-2

o t 2

x(c+t), X(e 't)

o.rt

3 , ' t f 6

2.12 xrct

q d.;cf uA<rtfiifro'. w cee't t&r Y kc)

oa tfic*trtt, Tfuro tkc) /e/t r(fl fr

*+efre '2*, atifl'ulbqf 6 t=0'o

z.tt t6u c.wta*t = ii = 2,5 . T+et'

l/rt t

x(t, TaA.a +t2,u = lQ at<r"tlo id 'taee

tr tol = '2 qilfo j n 2 itn'rl t 6, fu-3J

2.rry xth- t l

t 2

It 'oj

+ g c ' l

; t t t s d

x ( t ,

z . t & x t n T ) = e e ' + " T

= u - 4 2 n , = b *

** tv b : e 'd ' ''' tzt " 5 a"{t'

7n/ c€t "4 f = - t / 'ea5=- t / r - t

= 1 t a s O , 5 t f = q l t 4 d a a

2 e'o' t ' fn t - ' bo04 l

- l

' , (ort) + X kq )

F r y . ,

2,1( r;

TcAta

q*tu-t

5 x O.aJ

= -l-: 0.83 d4/ , 2

= 4,t! tt'ot*'& E

q o f

, (t)

,t^tl

- 2 -

dv lne b =e 'c ' )1

T,rru cercf = -t /h t = ''y''q)+) ="t'/f 'q{4

: L171 42 = c,tJ ucc"/o

3"1 InL

I

J . 5 ^ j n , 1 t 4 ^ b e t * t t -e = !I - t 4 o n . 4 d

-- 4tdz - (3,f. -1'Fr ft + Fr c. )

fnc&od ove ,lex. rxg)'= *o{'

(!,,., ri*rtI= J [*n,'i'r|'at

{ .1r, G;ur'& =J "'n'"7*2'

J,l rsw n nn */;*4

t,u = f'o i lf; -l,r- ;l=E j ; iJ'"

ttr,'l;:'|Tz:ll= t; * '1"'

Rct

^

J{

Bg nue*uttual

r = f

t , - r2 f "t,

= -12'l ' 7frj - 2 , 2 f i J

A = - 3 - i 4 t f e a t ' '

-3 = t uiI - lood = tae f,ejn

t ! t ; t.1ui'rl t *l' l = t.+d"t*. <t t i lq j ' /h'roi -' to ,t'/t, tai = Po€-

'l -i l : t.**t'i| -t rl t = l','*isr/*

€l ' ll ej'0

J,to xY i ns*P

, , t , =E t 2 " [ i l = , , t , , - ?

= r

"'r = l:y' -f -t7 = f; ,1

'-i-1t ; J I t 1 5 - I J

7a.ett f *

J 1(ft)t1

M re'I rrcle

\r/o

J " J c L = - q e J t

1.1

J-e

"ia€

rt = ! l* oV &f* n oed 6 -

J ' / fe f *=ar jp ,uq tsc o ( *d f ,n t r t / ,

4'A =(ar j F)(ar j f ) =n ' ' /32 +x 'aaf

l A t = , W , 1 A l " n ' * P '

e

* i'u""r,

t*," 11 4.A * lAt'

C d n r o ' o - ( , 4 L r r f = o a $ e A ' A = l A l

3 . 9 x = d , " i p , , { = 4 2 * 4 F z *t -y) t = (n,cr- p, f , n j (d, f , *p,nr)

= c,4t - F,f, - j fu,f , o f ,a\ >

^'{> = (ct - j ,8,) ( a, -J /gr)

t 3 o^Pr,. Xr,at =J; radt'acax

= f,t-ov)

'fi,!t = XF/i)

J. t* No. Bt,ctrq1a fu *r^rne.6itt, -o{

t " 6 + -

s.tg fAcae. u )ra di//+uncz-,

3 tG t)e ";.t".

t - I + I - I ' ? " '

-(5'+) n "- ( + - 4 ) - ( t -

= { - o - o . - o

= (5- 4) - 6-+) + rg-+)

= . : . - ( 4 ' a ) - t r - - r )

= {

- 3

: r xk) = - / ,2 -z 1€'1 ' t '

ut ' t ' ' r ,2j

t"ii'

0rl&A u*h,-oke&t<L.

P = 4 t s .

f =;,* th2 f '

uJ:2tr f=f i -o, f

,')r ̂ ^{ataoclfrA/t;u-

P =+tf s.

c - J - = L l l -J P 4 t ,

u=# =4s d/s

+r(ry3 t.2ui, + gir/z *i". ' t *i i ' / tui4't

| /, {ei49 c

+ /, f e 7'z'8 t

1,3 ai a t + *) t t t4 n{ pt 't'ozt'c

.{xê*uz. J/t ; x* e *^cEer-,?

*^&+.

Trrat Au rlzre 4z co**aL- ( ,

zn/a, Ttz TLuulczttA'?,

r'' JTr,"tlat .J*ru-a2"d, =t *u4 b o

= * ( o ' r 1 = r t < e

. r ,? x(o = 2ert'tfi

tf'A"t* t4

4, tO' X rro) =!7-ro''st) u4*""

a

= -2 f-u

t-f,:ica)t4it = :;+6o c .

er1r4"l -= )L, (a * t )7e

[ , f .r jat

-c.1'C4

+4 an jt u Trru,ztoc ,& qca.{a.tL

4az<d

fru)d.

lr.r.reo

{ / t 2

zr/g . i.2 t4 p.;a*L il,r4. etq

r ai i i ta Po--'2ry$, '16 /*k-

45 lt o F*qr&, ieaaee, r,l cttr! thft

{arc @t*on /rct;d Po =xr/rr = 2 aae&

* 1-o.r""?t/ 4 o Po ='.,')'d

ru*6/ f-f ? ,, *'a ' tn/Po - 3 '

'6'/..^.baurfr? ft*"7

^ ats

=zrr/po 'v tzJ/s-

Corrt"rrea At+t^t''z (Xc/) (

; a, 'f . rhuo dl

o.7 n$ a4 la

e )

= @ / * ' 4 ' " r

( & ' o ) -

xol= # * -0,o

:o 'o" t 'xus=ftr= #T'o')8":::;,Kki l - f f i =G74- -

z o,zt u ii'r/+ 1a f 1 -h?-b a(e vut*o*'n

xrr*)-fu=@=EEF7"= a ,o2"Jn l> -z teJ t r

rGr rd=. -hr* fu=f f i, o . a 2 e J J r / 2 = d r d Z e i f l z

16 flufuu&<.f '

z, t aa/ 2.8

l-rv,Pilr l - Po=zr/o,7

- 5 -

4,tl Xft) = f,rc>

X r-t = j fa rct I {i' nr.-r * "o r-4,

rn=J 6o).t' 'u'.Jt = dt"*l = !.t t4

fu e - lfa 6e( tt&tf c't

t n , ( np = * I I fta,) l',{ r"t = fr) .) t+' :

@ l o

- - L * ! : * = * ( o - e a t ) s a o

d4 idltreo caead ln 7'tntt''62 )

1*ncfr* J'es*'tf 2r"4a

tt/'b'd

aaa,*J o/ aunf( -

6r*tl-{-.

-- = l yr,otl

jXho) , h'' [t, Ykuflftrt ft'aol

=fu-' f,- 4,,xut1 ttk )rrtll'-4x@'

'7t; qfarf&)fut 742?)' 'fu' &4

Tnotc erttf%uh{ atru 4u P'4 t"

f4t &f,

4,1+ U xe) n 4na.( e*( xr'd=x/6)u

dOro X&> u)' ias u edd (-Aseau'

ara t-u)t -- '/dt r *t ) - Tt"4 ''6

i'?gv'*f,ta'

u+tt(tv (&,e) i dM. "/'4f

h

In Y@) = Q . '17*' XGn') = Fe Xct't) i

-,rrol egd tuuzr) ,

4, rZ-a cl)

Xdrf 1 x(Fte )e!*",(t -Iro-Or"'iuF-eua

= " -rJ +

1 ir, - r", ":t re -8

t t<o

D4* / = t- ts . 7n4 tr ita'

firut=ui*bf 7rFte,iu7o ., "i"o Xt-)

7 = t

"tkiL'ryfulxo,rrl =lu1 u'tollKu>l=

lYtw\

4Xr lwl = f e ' i * to ' r*X@)= 1X@) - uto

4./3 Xf, r(a n l&. ab+

Pe XuO =f'nrtt) eaaarf, dt+

t ' oIn Ytro,) = -J X ttl zi+, at t dt

-&

Sc.aatc uO f-g)t = @ k't, *ry ke

& )((v) =f*rro, cco r+)t dn = k X'/d kq-4,

Eo rw U) f'-ult = - 32r tt'7' & &'

&( rtct n P* itar g{&' n tiea'

i ; * . J r n * i l + 6 r

+.t 5

a , ff) "ts Zla{

, ' * - h u , 4 r = o * " 4 *J ,r"l 'a+a coat '/t =-o

t '-"'^- et<cc< 1tt'

Ttua u< a"u+, tu 713c4'v,

-**8-r,o/rro"f n t*^ n' vv'&b-

,f caWil

h G t t T

:l tx rc. zt tj

'o

' ' 5 -

[t(c -o.s84lf F - zPo

> i;. =2rr/p t rr/fo 7 a/a/2 .

xb)" E E^ ei-Aciln'<r

9 . -1 | f ' . f t ) e ' J 1 , , c " a " o t ?cn= f r " J " x ( t / e

; f c . a -, I f r'-inru!'^4rnr./'rrrt"'4-

v" I Ju rft)e c'tr ?c

'/Lu ,,^- "r<*e1V*S { o, f Xrtu-z) .tt/

t,, 11urz) 16- a., . i f-2,21, e

"/f l') "44tia&/ &'e//'re tr wtd'ql

zat e4&2& / uryh 2s**fu

uq.l eermet de c.a;(t c&)ae /

WaZ|,

O{* i = t' Pa . /fua a"c ,4au-'zPc

.?o

fr*,ea^;'h {rern)"""'7=o

_1ttO"t

'tarat- G'e - &

-,?^4 P. l tnrt I I

( r - C t = f( - t

1 , i e e " l , * & e ' Y

;* -#, t {?n,.'i''6'ntt - 1?o.-i'*:4

> o

1 m n 41r€tr sL rn - zE thttv

; = +" t t'r,r, /' ;"* f; ft) "i' ;;"*J

= i I'io, o

'i'o'" to!" n cF ' c^/z

a

l=Po

t""

J *tleE.o

Beeauaê-

(i+f) -#

,, ', C.'e/r,

n : c * 4

+, tt x k ) = € , " n e i n u c t

!,tlxp ,4, f lt -t)ntoet

t r?ltv t01, = z rr/Po c'r/ "rt E J*/j"o

dt

ytu) =1"')rot'*''d,

in-- -egf"/z -e)ntoct

o.s lx,tutol

^trJ -/gt

4 X,lu,;1ss

7hcq. .a ,r..) aw*hfr)7

4 a, t 4tcot/o) ad dt

{re "+r..catar/ /4-,'rÂ

Zi5I

4X,(rt to)"

{ o.t X,pa"+c)

larn*/ tG-c.t ' l ccnt

rttd<4a44

nfilt

Da*{ tak<Ifufrr*zt {*!t cm=;r'ooy'Pt

x tr)=l*f

"

en.t'niobcl .i ot""

-ft/t

= z ,^ {,ll"i(maao-'t)'ot

a,rlxp ntl)o,rpttu Dl

-1<tt4( xrt-q,r) ea rot.

- 7 -

=T c^ -l .-irru', -utPo/z

lrntuc"trfrlO J ' rmk;- - ; . t ) l t

e

= \i ,a z,La; ftnt,.""'a') P" /z)= lf .2 -L---

I-t -rrt

i t n tal. -- tit )J ', i . -

z n n|&a-ûc> Po/z J

4 , 1 ? L L

X r n)'fr,r.-i'rt IZ +a'in ou' u4'"n

o . L

= f , c t i * i ' n t i s " * n lZ) 1 (nu t r - . ; t t =O

= ; , 4 , . . , . ( e i ' ' * ' " u 1 t - t )- L g ' ( m t d c - ' u ) | -

, t=4,

4,& tfa T*tJ erna77 i

f = #Inlx,ot1'4u,-;h +'#4tt-3

I L

altro &e0Ottt* .of

4,21 X^r4 = o, t I t(fta-*rc) + X (o*a2;f

4 X @'te.) altl l1u rtt" ) do pt at*try-

dt,

I Y*rnt1 a a, r I lfr'a+oil * I Xftrtt 4ul1

a4/ 2(Knrartl ' o,)t[tXu 4)t"* 1Xt"'rqll

661 ryt d xnls tdct

=/;fi,Q l v C c L

t r& ./ . +4y l ( t Xu -htNoto

* I I xrt"'47cr' "';; L )*-e

.Q

-l

* !"lxr"au)l'*)-o

ztz AS./ ctagX (

/4

f .=h fittu,l1>dat'4

aa- \ t '-

/- , "ml \?4 ftQ

Es

1 6 d

o-Lf,rr*rtl'dez f i J

-&

E " = * r r x t x 4 ^ ! = + =

fu ô*r/4t/ "f

'"*? *a "*fr fut/el d' nWd/ c4,c n Y

-4=#f lXHsu" l 4 'o

.,9

rhq trc fllt'ta

E, = a,ar(E f E) ' o '5 E '

4 ,zz 4 r " t ,NFR = (F . f 1= ( - t r ,11 .

O € 2 t T - 4 f = 6 r r ( * . d 2 f )

7fur d. 24,u. x.(ar) ,/od dt a.sat-

Pf f e dk on/ A.b /"t).r{r"(

fu ,rU ofu*( xhfl:6e1e'n7)=1. /* '*?n

4.zJ 1 ,, o,{., NFR = (*, *J'f-rq, ril

&.caea zt = 6il rrc/ +tr), 4hl o'4

YrhrT /fuu* zttt* WV 2r d/'

\tnf) ,o i pwi^r"4 P

. 77, pa'rV.(

/* 4 xrrnr) q (w efinT'

Bacru<.2 4f l=O ( ' 'd ' f f ) ' Z1lnf l ' t loa

fofr7o *r/A Po>"f{fr.:,'at (d'n T) = / 7C*

aZf n ' 77t+' a* 6'm

4't &et.-f ,ufur" cto . -. '**

Xtu>2

lft)sfj: z

X(q tfit.|

l(r,.)>1i : I

TJ' z " l 0

7k .f"ut *t "/ Trc) ere let to

Xr@t

I

l\t,)l'

, t

J t =z F

tO , l lL

- 8 " -

4/+ T =o,l .. A/ffr = (-ta q. 0"/r j .

\'tnT). i=t.2, J ca. alâ *)nnrl

*7tttactr s/ orz it V.ri,+n? /.tar.

in r'- t,r6 ) oT. Of lao Â4"'/ ,Ft U' "'a oLt#.

4.26 T'A s NFK = Fz4 zrfl= C6,tq l,4Jv r a * s € ' 7 - ' -

t t . t l _ _ t T / t o/t2c81+-' x(+, *re"n xhT) adt' t ' t'- '

! - - . . \ . 1 v

t l ,ZS X(nT) =, l . t t l?nf

"y T- / . d/r' HFP' ?4 tr i= klrQ J' t*J

gcarytr- ,0 i aa*/;{c ak 'vfr / ?t'

fur{ { tzi ranf i "t€

/o E/4

to = /0 -6,2t = J,'/2 - 6ri l t - l"f/

(f ld 6,29 )

lo z ld - tl..il - - 2, f6 /*d / J,56 )

Ttsl ui rcn7 u;r/t T=a,t A ftg-1. 7!,/_ reg<fu _,- f:_'?_:r'T= 6,3 , NFR=(1 +1 = ftto-4L ta,+/tJ

ee"w to !t- nld. nt' NR- lt'r P.nT'

uiff' T:o,J, ta /4f.

la at/ a t*

fYft

4,27 7' zr/4 t/Fft 'G #, +]'G1 +7

i 0 = / o * - g = z n 4 d A )J 4 = a o - l ' / 2 - & : + t * d I )

rhT)= 2 -!tn tO nT + 4 cds-c, nT

: 2 -tu) znT * a ca +rT ( hnef(/n)

tt ls *l).rl Pf t s,/ + *rt a4

ax g+nel ..u.cry&L nlt) /*ra Xlnf) o&

T -- r/4.

4.1e /=rf/r. NFp=C#, *1.kt, f Ji o = 9 r * d / a >

2e . : /o= O f * td /a )

*(nT)= Z' 3 uA @n / ' * 4 cwJo trT

= 2 - 3 tti O,nT+ + t:t+a 6.rtT

= z -J t ' 7 r4 t l= 5 (P . * "44 / f4 'n )

0r Is {cietl /-*. O ath'ch e;aid*' 'Al

n eu{ /t'"f a. ': cs+'d a'ect**z

:r! i: i:': (::"!1:7= i/to. NF( = pre, tel

2 o = O 1 r d z z )

y hT) = 2 - 3 tt14 pnT't + e zznf

= 2 - 3 l 1 i t o n T + 4 - 6 ' t ' t ' ^ ' O n {c n+*'7{ /tra

)

T=r /a r . NFP r ( - t t 2 f j

x hr)= 2 - }.ti Pn f * /* ccb PnT (n*rriJ/a ' )

Jr l*a na e/t)tt/ Pf ' sl t* c"'

Alcc+ztot tt(t) /rtn XltrT) /*/t'' 7;rf/zf '

4'zr (t 'd F--a." = h

+(r- r ' ) o ( r -- r'l ?l= l - r

H'flyu r* -Atou .Z rn =

h=o

' e n a i - L = /

N = O . L F - = r ' - / - - - ,tr=o / -r

t n ,-.^_ fr-r)(t,t!)N = ( Z r - t t ? r ' - ;

t ' t> O

= t l r

S,rp1re.^t t +t6 ) le /r''

N ct. H

S r t I - r f l ' l'{-

, t t c , I - f

ftata H coti*t' xa I

N l l - , ( s t l

E r n = - Z a " * . n '

( rD- rnr, ) = (pc- f )

3 ) r . . . , ( r t - r ' * ' )

/ - r tJ* ' .T= o,i NF( = G/a 4 rc rrft tt/,+,Ji.+J.

i*/onT, tr.lh T-?./, 4 ,i' 7i*"2'c/

t* ca/ 44 '1laz5 ia '-/L 4Po d

- q *

h = o \ = c

Xrrul= t (o, t)n e-Jc"''=5 (o,Jy''u',

" = O

h l ,

= -/ ' 0 ' J g '

. - , o f

N & . n 4 r l r l = l a ' 3 e " * ' l ' g ' s < (

(+.6v) @rt t'< wVd-l'

pr;da sd *Xd@) s -4zao.

h , a r i t ( z , f / f . t r f i , caa u f i

a t tc l * )1 . tu l=-42tO +rrVeZto

qrl *Xotul * -o.zti + tT . Bnf '7lc

4 *i/( & tit&' * Y;r'iPlaryG r/. 7f1 , ft&o atc <t"tnfur4t ztr 6 fA

4 Xa(es) = -o' 2 co - lf

1,J5 'r*o,2

X4tD= r-_t* i" ' "J" '

r" iu, I u ir f - z ; u 'J 'xt r 1

= e ' i * ' f t 6 rn tdT -z i - ,u t r

t 2 e4t' ( * atf - t )=4 e' ft' docoT)

, a e:)rrtr-n, (, - <zz ,erf)

Eezrttt< t'-4D tc-f V o /- &( at,u" t(rtz

lXar -S l = z ( t ' c 'a te f )

{Xora,) = -br + n ( Ne rL'e( dz /Jta

Pld ,*4f 44 &h;ê/ '6 Gtr''t7)

id * m (Ltt/NT) 'n (ary'lr4', = n(a 'r/l)

o O , r c f / g - e t , 7 2 7 = P i )

(Xrro 1 , o, 1 X"0) = t7 . fleA %ar ag

cenr7*Q* 7r/.4 TXrla) = a PktL

,e,//.+r /<ên zfu ano/V&-;.,/ aza:}t '

6to p,zXr w, d.Aettt;r* ta Zht Jo '

e4'Paaadl .

I X.(tot/s>lt 2 (t - a (#' o' ) =' ft t o's)=3

S Xa(or/s) = - !-!!-ro,a + v = ?"t cr d

, N+l= Z - n r { ' l

1 - f

r - r ( '2? -

l - f

^ t t t t - N+ t p t2 tl ' r + f - f :

=

.tu ft..6 ) ; )<^-/.'/ k eV fd.Etbb * i E-'f n, -2,5 f J , cfr o,z 'i nzsat"'

t'6y+ N-

+,31 x(n72= lo ' -+c ' a n l ct t

,ti lrz{*** 'ttt'<aVcl ed P *ol-

>.r44.

432 xQT) = O,Jo" rVa cd T=a. tCtO Ac 4 . J 1 3 . &

X'rt',) " Z J'o,/tn e"tu"r' 12 k,rge t*r'- 4 i r?o h4

= 3 ,v / - O , f f e J * ' r

*,Jl Xinf)= /, 2. a= O" 2 Lc,/ /= o.2

XrraD= /, z. -* o x tJ- '* , , t" t t- '

* l , 2e lu f 6 . i ' u r * * - ) .u r )

= t,2 ea^f , z c,*4 cv f = z,+ "-"!-r,

lXrrol = lr.+ e4"''. uorurl = a.1l uo cc,Tl

4XrtuS = 4 2,+ * 4 e)t- ' * ) aa ea7

= o - c , t T . r ) O ( c ' < P t o f T oI - v

4 c n d 7 < C

T=42, NFK " (1 f J= Pr4 f,lr j

frL a,' .n l : -J,t t , a,f r t J, &? 42 id ; t

- l l 2 -

lxotu*/t)l = , (, -c+t7q/gt)= tft*es) =3

/ x' ( u''r/s' : : rT'"o l,' "I-;?

. "

J,26 'T' l, uFR a (-rr, n j

X"f4 = 4 4-t'ktr-t ) (r -ee. uT)- 2e=t

&''7D (t - ac co )

lX t r r l l= , ( r - cau)

*XnrO = -eotv

t<) = rn ('a rr/Nr) - n (atr/A)

= o, zrt/g . +r/l ,, sb |! 2

lXrrotl = o, 4 /rk)' o

I Xrer', )l ' z (t' c+z("r/l)' s ( t tqs); 3

9 X"l>rh)=V r 7' = + '- t 'df

I X"rct/g )l : z (,'b (4t/il)= s

4 Xr(ry/g) =' # * o = 3!' ='l?3'

TLtg t+o dt .+anu & ftt&' caf

h P-n/zt-, J,tf.

Alr?fi4 g

f = ,r/rt, dr= 2trh '8 3? AlFR

fA. d&d el,t*q eu A)fzh.y ,/, A rr47

ct4.e & , UettL1 * /.l-ltttr lr;ft

-up-rta xa\/z = tl{, 7.h4e a )r3

6vc't/sllr-{ , //& atz ,t/vcf'u* a/ Txnf)

a et utatb &;nl 27. or/rt{ Le't ' 7tu24r

t4 n4z /* f*^ "X

+hcutt7 or"l ax. ct n E'tt+'eL

Xutt) /*rn X1:d 3r+ 'r"t4.t'Y&L Y(A P

r(nT) *{ cfu ,r&a( '"rrt+7t{ah Ya Plrr).

5, 2 f= fi/tf, a," "zr/7 = JO. nF(

= ( ' r t r r1 .

'ftttz .,+. c**l?ff , 77u au ( atê{r

dwt7,7*7 t.t/.4

TXrtul = 2'o tr* alt k) t' krr tgJ

7ht4" . P t*n cX *&"t'i' ett I e'x ('eh'

-Y:'r:?-ta .:!!'- -7 : tTr/to , k6 = zn /T : 2^t2. UFR s (-t4 toJ

ttuu , h l*'V ok

? 'x{ a* laassT

Ut,<.ntdv tft, /4ôa XOf) '

- (- 21 24.

t o e J s g c

5.J

lxooq4 JlYt"il- ' - ' , r " l | ru- i \

lXtutt)l un -& e/,6ri'l /r*, lXt,'rsl

,i o{d, arlcc iov +(ero TX4fu) h a i

f,o,+I , r€ et ildi TrQft, t * e s

b4,+Ifa *brrr,, J>, nd .rryb mlf'/-

a1 nctt 4Z-; at 27n;A* "/'/ptc* pu 4

-1xa/co /!'2'e

tT, 4

Xforn,n'), 4 ? 't n/*t ry-,r/c, ttttt,' ,r1.1'aa) *" a4 t*"

d f r z ; ' 7 ' n & a r l P " :

't, nt ptt44 i l^'r/fi e'4"1t' 6 a'Fu*

fXaro't ,^'{'4"'4r *i2/ & 7*tt

cnPLec'ful , d'u -"f* tTtz

4pt*/ /-f*{:4;f'"4a9ry a,,,7t;';â(. h ?n*fu'7{'l'

ta 2a *af A 4<' d"t"+"/ ;71'74/

' / fur * h/* ah "/H - ry

A-rre&.

t'X@ttS *rr*'t'& o/'Ath"/ P77rr4 -rrnf A- a

6 7 8 .

tXh,) 1@d'

-4fr{EeJd rfa d tafZr{ ai4, r. r/+ +v

,.ff4y 4).rlZrf/f 38, 7"te tn '4futn

a)

TXord = flXt-+mnl,.)h r 4

hrr'nu, X,rre) n f*;*t'L t&d'2*d ot

s',4 x(tt- * f\r*r.tworcs

1a.2uc{ 6 FH T&4+, ft at *i 'dt

NFR: u-4,4) a, /D4r du f;it;t IFR

{4 +1 . )u,,, .fi2 7t+tq 2?*A':--

A.. Asr it> ,a ') f4 i7' rP iaa

T)1rre,2 ' X?) t /P -e) .,

- * ' ' *o ' , u4 'u ' i l 6o

= p - J l { t o ( t + " i t d 1

e 6 , -J . r l ro ( t t aq ' r ) >o ,€ ' - to

i l

*" = f/8I+ NFRI

. - t ' l flnr)

j\:

I

4dc, T . ) ;1 i [ (o -nr l , r / f I

= tu f )11 tQ 2 f , J ' ( c - n7 )

c.-, 14, t r f. -nrt /r 1= > _ x n r ) f f i

,tt Xto), d fr. l.l > ,t^* nd / r< n/"1*,

de, Xte)=o /* lwl > n/r > d'rtat '

, ,'/t r'dt' ) t ( t )=#J Xro)e ctb '

-n/r -iut"T- lux" f r ) z

- n/f n'4

L f "n { alnf l e-r '- - '

er- -

dc'tt l l J H

= T - L)71 izo

? oi rt-af l

uirr -of lai

ln ,&, J'(c-nT)

0eq< an *yie& i e<tt od *

- lz -

rit L )1

o 1 2 r + r'x(o), tft) , Th) x(il. xf*)

7 = { = t

d.6 Fe Ja * O , a I a , a >

't(o) t1tr) r(2,-r) x&lf) 16)

z 1 - . - { = / , 2 !f,-t 4

= l . 2 f x , f = ( 2 f 1 L : f1000 2000 3000 4000

100 1 5 0 200

L = f , s N T : f

L?rF -t -

N - l

d . T N = 62 h = 4 t , 2 , 3 4 . r

_L.46 T

Wy^ry f o, zt/r)

+ 2 n. - ' -J T

" ? ' o , t r 2 :m p , D = O + 7 '

{.to Ya

T : p i / 2 0 0 ; t : 0 : T : 4 ; N : 4 / T ;x : c o s ( 7 0 * t ) ;X : T * f f t ( x ) ;

m p : 0 : N / 2 ; D : 2 * P t / ( N * T ) ;p l o t ( m p * D , a b s ( X ( m p + 1 ) ) )

:i

r,3,Fr o. n/r)

s q u a r e

s q u a r e

,r/r j

: l t / l" l . i io , i - l l

i i r0 . r I I

i l \o'l- I \

i / ' \ l^l

'*-;-o

ro o t n to rao ra rto rE zot

FarTttttrcT ̂ o*t' m.D s O +

[a, )rrh)

9 , 8 N = fU r 2 O r r , 2 . J . 4

t n , P t O e ,

f , . fT : 0 . O O I ; t : O : T : 4 ; N : 4 / T ;

x = c o s ( 7 0 * t ) ;X : T * f f t ( x ) ;

m p = 0 : N / 2 ; D : 2 * p t / ( N * T ) ;

s u b p l o t ( 2 , 7 , I )

p l o t ( m P * D , a b s ( X ( m P + 1 ) ) ) , a x a s

s u b p l o t ( 2 , L , 2 )

p l o t ( m P * D , a b s ( X ( m P + 1 ) ) ) , a x i s

a x r s ( [ 0 2 0 0 0 f . 5 ] )

h. 7 *q€e/, d. Ttacbt l(Fft r fa.s f,O Jffa J

0

- t J -

/at, efu *tcc-46 au t-r/& fit Th., p(+{ k trqt"Lel d{

€, il

L : 5 0 ; N : 1 0 0 0 ; T : L / N ; n : 0 : N - 1 ;x : s i n ( 2 0 * n * T ) * c o s ( 2 I * n * T ) - s i n ( 4 0 * n * T ) ;X : T * f f t ( x , N ) ;m p : 0 : N / 2 ; D : 2 * p t / ( N * T ) ;p l o t ( m p * D , a b s ( X ( m p + 1 ) ) )a x i s ( [ 0 5 0 0 3 0 ] )

at

L : 5 0 ; N : l 0 0 0 ; T : L / N ; n : 0 : N - 1 ;

x : s i n ( 2 0 * n * T ) + c o s ( 2 t * n * T ) - s i n ( 4 0 * n * T ) ;

X : T * f f t ( x r 5 * N ) ;m p : 0 : 5 * N / 2 ; D : 2 * p : - / ( 5 * N * T ) ;p l o t ( m p * D , a b s ( X ( r n P + 1 ) ) )a x i s ( [ O 5 0 0 3 0 ] )

Jt' utt tv-p<;,r FFT u'+ taaa'*

( xrct /'-- €ti':to'^y;**TL*"Jt/re Fti

ntfnrl

4pt+4ta cn t(' 5 2P' 'i' o^/ 'o nt "n7&

rfu tctrv ' 8"dL fl& ; P'a64at 4t(

qld -t rz "* ,i, '*y/'rtr *t"6-

F/

ktt) t* t i fo, f,a)' * Y

tSr*--'-'

r-- ,** rggfuEi-

oeot a

4 "/ezc+ frfv c&sy r/ rrc),c/t"r.v ta du #atf 'ry,

{, t3L : 5 0 ; N : 1 0 0 0 ; T : L / N ; n : 0 : N - 1 , 'x : s i n ( 2 0 * n * T ) . * c o s ( 2 L * n * T ) . * s i n ( 4 0 * n * T ) ;X : T * f f t ( x ) ;m p = 0 : N / 2 ; D : 2 * p t / ( N * T ) ;p l o t ( m p * D , a b s ( X ( m p + 1 ) ) )

1^(t . , /*L>rtan ,'d1; t'1t4

*u,? Lft - 4/rr/P'e = ftry/'r =z'ff

.t;7a , ktwtu, zfrl c"f{*Aa*

; prrl/ra, €, f ,/itd 4otv 4,

qlar ld Enbd "tYtz

'

rtu fn( nyniâced q *;'h4r uo.vz zl, a4 lo eat te{ 'd/ /uuu'

aa*r, A&ftX 2h Ztr.u /t;/aee

6d'O / c+ -/ , lfu Po4'T

.3nein &//orlhf "*s't c'q L;tlt p= ioa'

N. Soao ?r, ..2"rt t74.4 P+ha '

5.tz

qr& /alr'/4,

cx /u<

' t (1) :o,ef Io , l ts 'aGeJf c

f w t - c3&f t t J

r'd m7irt* qn t7,r--

d c.r./.3?, 4/, or4a( A5: ,o//s .

,f'f*

&rtutt

a = gl laet xcf ,i 4 / !4 rlta

. - t 1 -

'?'t14f-{4 t*ryV %,

rtn r- 4At = 4a5- at fR ,i (-,r/r,

,rkJ = (-62,g, 6t,g), filrt dr

6,1 {d aqvact< ar dt re rqrt

u1-1 Xfrz / 1c <.€f I, flb.t 'A nXc*a

8/ i 4;/A./ ";a4t

d. lelz eo

8/*/At6 =-,qfr,( 4 44,( y'2cuOto n^f

Ttuo 'd- "/h-t,

af ht* +t ; 4'4 6

./.h.," 'rl&

Ar4{ t" f*'4 *4't*Q.rt {"-f, 42 carrfa* ff,;p"cnnZglre^,* ry

d o/r. f;-f q /^62/

4e4.f .rrt| n na&lf 7a"ttil4 f

* layrrrr**a' : f:A,rrotu n;artl^cn/ I "hJua*ct'{tt

ortt( P"-/0a, g' /o ' uJt at "71*+ tt*

aoulrI

Cnttn!,

7.= tf/atn61, -

,l/ ru r lu Pry o'ota|r/

G x z2nk'ei,;^ ; it/ f//

Jf lao lfo ./*f^ af lt -'/, ! /, +' tt / i / *14

; y'4d'

dl* d'icr apt^'LZ'n'

,aar

6.2 {(ct deq rr{ d/?oa/ a qtr

a/ 4t tlorrrtt4J / ** u;4{- 7fq dlafe nt casa^('

(.J lfrJ aaaaA av, utrft|," frfla dt fe

,; "t'{

6,7 n atpznf da7<of {orl {tlr.arla

Y ' a r-'t on ^"t{o^/(

fuaLi - , f /u af#, - t r Iutn-t7 etd 4 A'zi , & /e14 ,tof *tf'J

- ry fu^ru' 'Y' 7114t 4'rfh'

i ex-..C-

art c*taod N

anl an/ 2aaftyan

6,.f 7/tz a/73a" &t6*-/,-/ ^/7

{t) = /,r frrroil'

i *t,*.1r% -r'e*tt f,H 4:4

d{ }n u(x), fr n fi. nua^lca'f

'&c&u a' eatfra* t'r ; "eqoAtr

( c , df i ,a"/-''4+ a'zeta'u' 4

t / *g t .+ l fz ,4b++ z r .

7r*' , ,r-( uo r tt,'ot) = t'f at-ft) + l4o(/t)

+ /,f ,fr'rt) = {rfd

+ {rH + ;ttrtt)$!a)

4 $62 +'{rt*)

€,6 7U- aTeta* "tetc'*da( n'

dlo = (zt sr) utc )

; ,,,-'A?. dri r* ryY 4Pznou

il. c-4|;;"n zx;t) q e /'"''c^6;

4

d t , 4 u=4* / z ' a t *

{ t1-- / zt +t ) / a' ed } (,.Pot) = /' ltt t {'/t)

ea4l (2ttt t d 4/+' = 4 /:Nr) u'(3) = c{&)'

7t4t de qo& n 'hzaa- '

- / 5 -

6,/ ?1u naohtef,r, n/e

{ftt = (* r"r, t) uk)

; u*tt-*tyaet . ,f ;' Z; *VV

&-"aqnz dL eqt/4eut{ catectdt h I

/.","6; / z;:' , ,ty' ugz'l*uz

{tx) c ( cat uot)( ct,rtt* tl'ftt) s/'lct | {'e)

(m ar t ) rl u,(a' ot ( cA bLo) 4ttt| ' * {' (*'

6, tJ

- )TAuo f,tb ,a4ofu a 'htu a+

6,f, tlr,e Dr.<1af+ acu42.( 47

{rot = /.t (uat)z

i ttwnaryrhal, 6t z'tvPw'ual 'drd

dvrqh^tL /e

41 44ltu aza'aa*{ ca

A P-#Z"D, 6.f,.

6.f 7/u DT tTc&n "Aac'-ib/ I

{rnt = (2arD u fo 1

n runeyho.-l*'<vt* /tnl tteV*t& 'n'!7

a7 utrtl df i .b;t ,-Vrt '/*tca6ot zL'

u"//';.tt/ r2tr?r) pt a *tD^ a/ z'1

'A,' ittr , Jt i y'is+ 'tt ri ffra 6'6'

e- 'O

E"a'*, €, -' €-u e'&z itt(

€+t o

6, tO 4 o- /4 ?az. zlz+t

f t n ( t r + ' l r ' , + t = o t u ' r / + ( u " + l ' l

= { r + X / r - / * / , n { ,

Tr.a ttL cTecZJz oo nel ^&oce+ - Crt te<

J.y'i 7'f -, au( 7 - rJ , f,,h lt: tur/

{t<cntt /

= ai , '7la io c /as}u

. ui'- €+ U-, . Vo - e{_ - Yoi , = f . i

- D . , = T = V ,i , + i . - *- = o 8. .ct t . 'c-= o

h( i4. &', = - L',- fr

Rz

Z=- * * zg td - - i r ' t c )Rt fr z

dr p dt ztcnt ca (6'/?) '

Bc'n* t-= O

e = u o ' R tR ' tRz

R' g*s*ol e-t €* =4'

u< &nt< ,..= #

F, cL

L = # . , , 4

aA(,y+q^bu ha ud*reR. il. 4t /R. A=r,2,3*t = -n/R . o,t.rl irrt 4

* f , f . f- f 'o

6.t/ 2/* Va" u(()- uc ar',/ /eOellq -dc

.4 ira ,*to&, .c-v t J4-{H = R iret

7A44 d a 4t<-c Arn --r-u'"-f o7u'2q,t r

' 4 R

6s

+a

-+

'ac'

6.tS rct A

6 , i 6 .

tItt

'lllq uv i<ttC, Zro -:. q, s O, + Al

. - r6

7' | ,h i ,i o.4r"{ J< caatt {rn|a, aroflJ, tira an^h; tzcrts of

ctnfe4; ru ?4at-4t a/ arnsfl 4/

afn-21 . .l!r n fr;. ,z-"ir.rl '&'cmt

t$ ".//r;^"rr^6

.z *r/ ! *te ta cdpete&"f

td ?tte ,

/.2(1') Ce4a./, ^d. ipe.u,'^c# &f

,rarr&i"*y d.ioeu if ,re/aau te,

(2) Catua,/, hi"o,r. 'r/ 6ri. /;tn .a,

( J ) Casre/, /.ita. oql 7t ^'n^'o^f"

/,J ,hv y3ufn|, n > e ae ,1,*<

=,t tn4j -

Senzr< { to+ol '{ful t/fal = {fuf,44 lole d rol 50 .

t f*u r ('4tDI',( fouit {r-ui = a

d.il eyluo

{ r - lu |= - { r tu i = -* { r '7

77rt( eAt',n{,+tI;( bry

h *t Prrir*' o+ x7a'a;< A'A;,"P

,rat/rt+ -

7- f L ro | , 2 | r (n - tJ - +3 , rn -g j

I t a l=o Pe l l n<o6tol = t Ea kt 1 -+ ta t+J

-- o

in7 = r* l-oi '4 A kzi = 2

f r t i = r i t , 1 - 4 4 P r l s o

tu t : z to f zT -+ t " tu ! = -1

i r 4 7 = z f a t t i ' + $ n I = a

l r r | = 6 ' h n = f ' 4 " " ' '

Ttua t* iPt/"t ,utpc'ut a{

{ f o t : 2 4 { s - t l ' ' } ( f n ' 3 l

. Garnl)>P ufa'tJ

=f # 'pgtnl

77r.a * aVn, E;r* ,1222 dl /a"'rtrt',

f*/^-+, ot/ us 4*tt'2t ,1t4,,a

(qalrrlrt-nt)t - # #-rrff i2

(u,orl, g t-at)f,nnt

- ,rfn'tJ

uSaa| t tl, fa't7 ut

Tlq fu 4r'4f't" 'tacl z{ 'no'f

14 Qe rc< !./fot A 4,6 ufal,hro+

4rn7, 4' a . r(rr P * etl: pi,Tca

+".4/37azd/-.;{p tr'ia, t4 &.'4

{ r l a t : 7 / r u / ' f {' / c rg&aFefuq; rAt r 24i t : f ,v. 7aa4 '( foI= tt f YT'r/ f '

uLoI' ttf6t

Jr , r t=, ( t t " l ' i / ru ttir "( = P/ & 4 oq rt"zgt

*Jit^l

tu aaaif P'-fq

rrafiot . 7fu*+#/*t

; f u 1 o z , l t t J = - 4 * t r ( o l = a htt( z t{fr.+ nzn / nna? J ' Jrl FrR

15 f," *i& 4 /tot'z,.rurnJ; l .h7 = 2, i f" rnt = f

?,f , n=oI a n * o

,Jri F t

i'r I E'rl = *' f u rnt, atrtl +u[n-zJ+ "tn'tl

Jra a -t-pai{ ery ^-Ze

t;"14. *ff t /+ =O,af t -

'nOt J .tfr'|"

1 o ,art*.;l-.

ttri FIR

t rqot , {ttuJ 'r{t/"J'f

- l r7 -

Thtrt At taflt/"t *l'dte

.n r - . a t ( n V0

I ' rn i=2x1t ' t ) ' ' l n

lfnl=1 7- tll n <Q, &t'etztt

snlr!(- frrhiQ> ile co*t 24. eg*c,Eh ci

! rn1 = -2 d n-, 7 -26r Io a!'$otnel + 6 $ rn' l1

0e *f& *'wutti'+t, *{ {taPa, h",

n4: {&1=-z{pi-z|t-'1 -$r'zt+ 6$t'fl ;0

b t l ' I i l . -21 toJ'l f"rol ' frt- ' | t 6 f,,t 'sl : 'z

n * z: {tzl ; -z

7 t4' 2 trrt I' $tol + 6 6,,ral "

t-'rkzt

- l = f - t ' J

a= E ! (sl'-zftzl -'z$rzl - fottl+ 6 { tcJ

z(-z)x 3 t 6 ': O

n >+: {t+l = -ri", -tS tEl - $(rt '6 $ftl

= o

n>f ' {hJ z O

I,to tet {5frl = Z &tn-G7 u..te l, ..rtQ - o

v, P"/no ui&, tf or7 -J{tn-rJ = +ufnj'u

{ t l = / , r t ln - rJ +zufnJ

;aa7i&try utnl = {,rnl d4 tutl .{il'q

/.> n <o. u e+rtp*A *czPrltt"f

h:0: dt l = ,, f {krl

,t zEnfol = z

r,: l : {ft l = /,f {fol

+ 2$ftI = 1'ft2 -z

n=2 : f t z l ' / ' 5 t f t f t z57h l 5 2 r7 / ' 5 )

n ' J { t t I = t ' c { t zJ+26o taJ ' t x0 ' r ) J

u t d . f , h 7 : O / . " a 4 h ) + a ^ t l c 2 ? ' , < 0 t

Nt A-d '/ a * r, c'nt

l.rnJ=a P n ,"o trhAt /r//'fu

i ra-(1 = o /'e a4 d z tt ' 71ad tl'

&nA.*r'io6e"' tzt' /'t 'atzfia4at, , ,

{^ t=?*4t ' 'a tut lT

4e<-.tc caalt 4 r?r,f, 1,,0,'"tr'-t'"f rt'6| Fao

{ nt = t pl u rat + t (tl u i"i; : :"'iill,' o'

+ f tfl u tn't|' t A*t u tn'4'

"2:;frY:;*i"rf '

{tn| = 3 t tn| -'u "''J

r 6' ufn4+ f u fa'3J

+O, i t fr , -47 t " ' t O' ' t fA 1

= J a f t r l ' 2 t t tn ' t f + f ,u fn ' |1

Thr, 4 (y',t).

{ tn l 2x ( t . f , )

74.

zt?-

f6'"

$ ufnl = u,Frtl t ztral , /et e4/ n 1a- fu

€trl= 2i in-fr(4rtin u,16)

{ r o \

I , El fa'{l artd7i{'o

ltnt= Zia'ret 1v3 l '+

" Zlrn-61u, fQlry

= {, tnl + |rtnl

/*a lu lttttt/o4 -?w 4 lu '7At

i l{oJ;o, d ttq, 'z ,trzl= 3, *att o /*

0>rJ e td a<o , 9 fP t r - * '

/, I Cau4/cc.,'.3tJ

7' ta l = 7 &f t -4tur41l = o

Ah7,s: ,dxfl

7 ' t t l h t = f l Ln -p lu th t

h t c

,/or urtnT - afn -ar|, tkae o*r afta+-

41{nl=g f*

h€ht, Thte t r t?e'< '

(Hdhl)

l/ u+ til :

(3 it' E't 7 ' dt+

{rr,t = E

t r' -tl| u' tl1

=F Airn-01u,t61

6P

= Z fn'frl Pv,tnll=c

- t'firn? '

=p1,inl (t1)

,l fol= 3, ( nl t '2, Are1'a

- t & -

{ f "1 -Zfr"- f r Iu,reT'1=o

= Zi,rn-ftr urft-nr|fr=nt

O"/* 7= l-n,. 71ua f i=d,t{, el

a0

{,ht = Z7=a

t a - h t ' S t u r e l = { t n - h ' 1

7A4; A.tarr4 A. ycy>I,Z t2 t/ ,f at = /,dea 6*, h

, zo, dl

t,fal=a,trb> nto, zl*t 4fn-#7.1 fr4U i >n . TA.ta s,s ls<,

a , , a-t

{fi1= frlo'olatll =F P'anrs). 'utll

W {"a

7b opaodih fe h a!/ tc atd *<

Wt uuLh't -n't 'E

fanl = t, (1.wtri' ' ut61

- i=o 4-,

narf- e urrlJ

> (reaatsi' \rL'l , o

^f-h&Mf &4 c7+t,o" illfr

lnt = i0loa6:f 'autll

(=o i -n

= Y, ( r, oaa trf 'hu

tll + &eaa/t) u hJ

{oo

: t ,oootr { tntJ + ufnl

'tu;r/,o

{fnt' l 'eaotti { rn' '7 = u fn)

y',tJ 7a fr-$ nnr7 qln-leez cd

? !r, = /(t l+urn',J' "" n'[n-,zt)

g'f A; 4 ,rârt'rt.z44tq q?'-cc ?tqZan

1t nte* lf , ,,t-i aTnlu atfryu t4

f rui = {'/ro trh> n': o : hf

I o / , - r . o a r d n V l a

,,16 c.+t *4.Ad* &a?ezL u9., A

{rat = ̂ Z 4 rn-77 ufeT = a ii 't r( l2=a { = h-t'?

n- * a-:ro'ddul i'aU; 'w ds fffi

r! rU eotaE* 4e ft f"no / ,u-l! n er,./ t'se c1'3 alzlt'

- t /rh-tl + uh'zJ + "'+ ufa-F? 7

{r"',1= 6(+ufn '?al )

Tt44 pe 'lg'v , /- nr7 - ufn-/",

{ta7'l in'tJ = t(o'

-4.

€ ainl r Ut tal 'r u3 A)

Jt a batz*-t sd E;u ;tzlaurztt'+(

9nJ.<>

I

o

o

n 7'n1

r j

fl

I

I

b

, ( n

(n

{n

Llt,

'o

o

t s l

7 t l

u i

x,i

t{

J =

t :l == J '

.|t l

l l =. l

J: (

? tJ' t I

ull ;

t j

r j

iJ

r,{n'rtn

,rru

ItnY.[n

fn+t

fnl

[n a.

lntt.

fnrti

in7

ln+

tnr

fn+

fnj

[na

lntl

[nrt

tn7

7,

rz,

xJ

rftI Yrl

L+

q,

r,xJ

x

tnJ

h 1

td.

,tn 1

,(n I

h1

7-

$(n

rfnt,tt'r(n

, (n

9t't4 t ,

o

:1,z j

t L n

tt,frn l t

fqatYrh 1

xrtn)'x,tn '

\ (n )

\rd

, 3 afn l'l{l''r3ctu7

7, tf, 2.itt

Z /6 /tfnul,tth7 / r-t lEial

_ /? -

7, t7

ulhl

ray a;//'4 fu (r,/8) a*l (/, r?). r20 {En j

Jfi ss epuafiia u Ah 'to';c m zt'

tr< i+ F*lb /, /?-

41 An ntfi 4 eXaaê;a e/'c

u(n<1 utn'27 utn'Z)f,tn7 r2n7 ,.rt^1

utn-+7x*tn1

Eotr-ol z 2 ' t l -*7 ts, daat]

f, t rfirn, "' r

- J ' l

'1fu a lfo -tnorc- 4aeh ,{44f 4"1 , AIP

i/ tr* ae<FtL Ab au4baf 4 ez4 u*i7'

&lT tltt"-"f 04 Q oaI'' ttt'e/4+ at

-&Aanfi, fltn *< 44/4

4h f f t i z ( fn l

Xrfn+t\; xrtnl

Yytnrtl = /'tn )

f*r'n'l : r'fn7

!tn\,4t)(, tol + 42\tn!+a'z

xttnl

fp,rx4ofl * o:2qtn1

7,22 q rr,z "-ry

aaetal a t r.ZiZQ

x/a*ez( ef ac'o. * ry

a+ttltr'c ;f tnl= o

arr/ utnl = a h elf n <o, 7t'4 {''

d

atoJ - tîl*'Ent 'uXt*t*':T

^d/ l',tc*t4 /4 'i It r-tuPN 44ze

Yrlt - 1.eo?/5 t-' Y't| s llQ )

or (t -/,cas tt)' ' ) /rrl -tt(l)

#=fu7,23 {f,"t = ! afa-t 7 - .7 ufnl J.

,95 t@lae .uf"rJ'a€ kra €an7"G/ '*

P.s#at y', f 4e I ftJ's ' I'ttJ = -4 td/

dfn=a /*& n '4fu+ zhtv t a/"f 3 ' //'e

ttq lza<

t t n l ' 2571n- t7 - +5 " ' n ' t J - ,

-t - ' t '3':-4

- (-(l) : I rtr':l = 2J-''

: - T

ffii,:i:-m;ItrF.h<a), a* ie"<

'frlt' 2 l'tclrt t - 4lu4tls

=(zJ- , -e l '3) Ul t )

.Hu(nl

! + 0,2 rt tn7

?, lg

[';?,:,trJ" [:,' : :]E^::J. [" J' ̂'! tnl = (-,, s -r,, I yX,ItJ , .u tn7

ukaL 'bf/-:

Y2=U(ttl :#:,1.1i:::

l S a n t f l " t a o

I + a " t J l a e t o

r ' /? drnt--/ ,aso/s: /(a-tJ = afal

0"/.r4 x tnJ = { fa tJ - tAu dhI " Itn+tl

rkûa t* /rue

X{nt,! = 1,oo?/5 Xtnl -r ufo j

{fal 3 1,c?o/s' Xfnl + uftl

fli trr ss .?ttaE&, y'-a&iauar t -

U 6tj

. - 2 0 "

1'2# lht =

i(rmru[n-tJ rufntJ ru7,-rlnttr

4/fA at f fuafu *'/an""'Â';rf;/ ,*lrr.*r^tu, &

Yw I (rr p { ltrsx i?tov i'u ot . i Uo)

44 HrG) Hlil a'v A/acal f*4

an -tlew Hlil H.fp * HrpHl tt).

1.26 4 Fi, f,t4 dt /b1 <t+a.t<r of

/, tl (e) e/t

a+ ,4ns

- 51 ( r t l'' *l''rt't* l-+ I U t3)+l--+t -"t

I

rAaa ue 4*'<

Yli l - 1+l ' ' - 'J-L+l-- 2 '-

ulil ,r

7,)f Qqnzi*r. * fe4

4*4 **h

/t"'ch-- 4ry1 et llrqS. ffe 6-*

/r*e I d* 6^zc4rt arrrtuctaia 4

firt) /fu4 4 flrrst a /'r'tt/itlt'

HrG) i HG:H,IJ)- tt/'*+l*'ou t;7.4 /'ff onl 4

*:A

#=ffiI

tt 4vil"0)

&.1 ,, nd /*, tz)

*' r*u:e{ a//'/-""/'Zt ^ fu ''o/rgk'

o?Eu zb. f1/ n'a'o"a" ;'fu niSnl

t f t ) = r i d = ' h r ) + u / t )

utbry ure lee r'4t4t (&'to), 7/"1t n:6 5s

"try*'6i i-tr--;- ; o -4'-l * *, * [oo'1,,r,! * l o - 4 r r o : ' 1 ,

t o )I o " - c " f , o J

{ f t ) = f a e ' t l Y l o * a t t )

ilrt A,er at t'lafr' -7a2'L i Âz

,ulrs ae 14*), 7At -t'//*f f::

i.apeset-;'.;//M P lE rr)

_ t a l *

frihui* //rQ 4/2 t'/ oul rry

fu4 H,GlHrtt) = / l .QtH'U'- 'Y

/* stS a V&"

k cryt irn'*++te

77n- 6**'u 4 fo"'at*^ cnPcEA '

F*Ur*tO 444fu4'ffi:F*ur*loq?'maare{ ,* Arelta? /

;;-b-.'tu-'"o'tb'' 4

Ht 0) u 2x 2 P'/ '/ H'"/tl h' )^ / '

dr; Hr gl Hr(il n "u/"'uol /"2{

f,r|) Hr4) H hn{/t/"-a

82 F*,Fz],f, I(e), hK&,tff i, '

re/ ZUya ? t-, ccp.+)^{+ a .ti;t|rba ue -&ry.< , ry

(f'tS) '

I = t i t o ) ? , r t $ ' 7 2 / * )= E r -/ OJ trc) + ox uro)/ G4/- ao 7x z d'4 4-{L H&tHtr>

- 2 t -

fAi n 'fu *cfy*f c Vafioi' . 06 4e4

lffr-; h dt "une & r&/*) ct 2*

anl ; P.plh 8, /.

" 'J;. ' , ]L.a,v;, A( w et/tcf at

e.f*;Av w{afu 4,zra, tfi

r*t*ltd er z *t .

tt/ Al idtt*h'

A l l x , = u - ( r ' + z ' ) / z

= - * r t ' * r , * ! "

6 u = r y + 7 J n i t

ry t r ' l t4 td ' i& 4" 2 i '=x '

(b ) + - rF " f t - l

T"{

tI

xt

J

2.J \

'flu wz6fta& it z-St axt&*

i t , t x z . f b

;6 e*ttt+n'f ;

7 t,+ za) /z -

2.

Xt

ry-lru#I:I,"9 '; .f , '$ui nr lfi

"fl:L

('xitxr)f z

4t ,cdla

.: 'tt

A+ ft.dtastuaf d en*;aal - 72 , At, )6

,n{ASz d f ir', ^;d /rh,v? y .,dz loa,u'u)Gz' iftu 'uer:afi eo&d

xt - 5'k2 , Bdf ;Q

-lA )rz

"o44a,+yf ot U"f4 Xt.

, { . 7 2 .

! = xz . 774td 4t atfu'uif a4l w ,u.bd t6 ca+t"af x", Tlh Alo

ntOtr" e,t vrd fu to-o 'rt)t6--

ie-(z u ilsta - 7A2 z-lL"azh' l"et

*qn*q-f ai, + x, eu{ wef tt-7t '

&p ee.htf et w&.ry (*4e* 't,f

eztofAaoa

w &i,v6te , 77t+, dt *walr fetV

etaryl * 2-s 44;rfi'' /; (tt-7t>/z'

AVllft lu KCL ad Mcb A fI'{'

, * , - r y - x z*'Arttl tmp0<za

i , = - * r , ' * x , * t n44.+ry zfu Rlt ^tnX fi' r{-la"t

/.tV N/4-f.r, = /, - to Xz

u'hcl i"f^fu

i r = ! x , ' 2 Y z

lle ret

,lacA^/te'

ita = trc). t t

"1' t /z -t l

'/2 oJ

, c, I

- t- 2

l t v

/ 4 f

frtlrI o' r o

' * r =

BeJ lr

'it-/

Pt4 = l - t

II l

r^t 3 f.

dt.,

a

v.1",'lu(t)L , J

+ O 'q f t )trb,Tfu)

8 , 4 a : [ - 0 . 2 5 - 0 . 5 ; 0 . 2 - 2 ) ; b : [ 0 . 2 5 ; O ] ;c : [ 1 - 1 0 ] ; d : 0 ; d o g : s s ( a , b , c , d ) ;t 1 : O : 0 . 0 1 : 3 0 ;u 1 : 1 + e x p ( - 0 . 2 * t 1 ) .y 1 : l s i m ( d o g , u 1 , t 1 )f 1 - n . n n n 1 . ? n .L L - W . V . V W L . J w t

u 2 : I + e x p ( - 0 . 2 * L 2 ) .y 2 : I s i m ( d o g , u 2 , t 2 )p l o t ( t 1 , y l , 1 2 , y 2 , '

( 1 0 * L 2 ) ;

I0

* c i n / i n * j - ' 1 \u r l r \ f v v L L

;

* s l n

: t )

,J i*ii;r *^ a "aa6"nje/ Q/

'dx'iIII/t'fl,^n

,r,r,-.-..ÎL

20 2t rl

[i:'i' l*: : : ] t:;:J - [ ":'J u "'{(*t= rr -,"1[::,,:J f oxu/t)

-:1. -

Te 7r+t7t'*r, /**A ran V&e-aru *d7v,ef arz e,e/ (.rcL)/ 4A) ead A. .JU

h*t d.ee1 (d&zf Az), rat t3o

St&to aaq*1b. rt*ld d. u"4aAL +a,af a'u14dPnrr7rrl" al *ff-Q1raat 6 ehar 6 At *xaaferq-.

a : [ - 0 . 2 5 - 0 . 5 ; 0 . 2 - 2 1 ; b : [ 0 . 2 5 ; 0 ) ;c : [ 1 - 1 0 ] ; d : 0 ; d o g : s s ( a r b , c , d ) , 's u b p l o t ( 2 , I , L )q ] - o r r / r l n a \

\ s v Y /

s u b p J - o t ( 2 , I , 2 )i m n u l s e { c l o o iv v \ g v Y /

TIL f'r€/Lnayaaa"Qa

,f t C/t t,e ,czf 6 tjznr i daf ot" ,*f

u7*) = 8/c) /-;Z? tl+ar< lfu ,u6a? tfu,6

/*r, z(t)) =O A a/a)= b - olades/. "Au

;f?,rr"*t^ { (g./a) y,;//", l/* € -o,

t

J ,,.t clr = y (s) - t/a)o

/ 6 , t= J 4 ) r z ) d c r J t u r z ) d rt-

: L

- 4 f x , r Q t f c 7

' ' 2 X z { = X , f / O 7 2

Y: = -tFi x; -L#?ir * orJ) Urzt '-o.f, ̂ ; -o,r xr - iJ

i t = o , 5 / r . , { " t ' ,

g,g rtz-l,aie fu4 ,*aga'a' 'o f-atd 4r'rc)

tao J ,r&/ead (e.ol zz*lo 2 tP ory). 2

atle-ox&o (ea ri zs& 2 e? e/41v)- J

2rrl* 4"rrra (eoci tzztda r ? a*V) a't/

J alnTua f* ( 4J "t&

t 'T a/af )'

Tlqa alc *d7"an '*vltza " ut/'/

t ? a-? aafl -

g.ro e-=€* - -o. or z # -

t * ;= #

ir' #

eu+trtr /% /fr zb af>or

,a6 t* .;wtEy Aa,r44" ; c' Tlua av

t b a a 4 E r ' - 9 ! . n C , ; = o# . ; T - R

' v ; - - i ? ( a q r t r y + c \ )

h=425 1a

xt t 42 x ' t

X , t z u

- + 4

| = 1 , ax r l _+J

7 ' 2 9 u

+ 5

x2

z 8 t

1-. 1, J

1 J

' , 1

lJ :

X r 1

t +- 2

6 ,

xt

l

-(,

J

o

* , = -

i r = I

{ = x

x = IL

{ = rTlza r:b ntfaZz eof 4 rc'rc) aal

(t, tr) ",r/L d = O ( arfYf erc'61 a7

4/t) = ,f H a*d-'x/a) =o ) "f& alc P'o-

'/N ft"rfr erc)fol /7 ud=tt

h "41 >) a a*J x/a) = I .)

o l

6r

=A .lJ fte)dt2

- 2 l -

,$ fc= t , d tn g,/3 tu) z A

%s 53

z A

,-[-*T +l.u?? il=* Yas

I I . Jg

., s f/ol o s ' ' * 2 o s r I

,15 uo

)j-zs'+ |'=

t ) J:J r zs-+l

V o

t l ts )

Urs)

/ ) 6 \

t 0

; - = - ( c q r b y z t c l )

F, t I J/ a.v ua.-aa 7/a, aa<:f4zf u -ft(t) dot.o d ' - f /UB)

+(

' I

YttT

dz at+aaaf /h;y fu 4t a,tuf'/ ta"fa

& .arcztV Z*mr)n/ 'i P cikt' 7*4

ar ,tgry

q 4 i ' 4n ' +R R

4 , * f R C = 1 ,

i = 4 r ; 1 6 4 . / c r y

8,/2 F-,on, F-f,g,t'7 ae{ rV r& at<<ZA

La P*d-/&rrrr t p a.r/ &, / /, /tr/ /(at<

- , = a , 2 f l t / a , t ( - X - r + o , z f ( - f ' )

f , = - ( a , z ( . - v , ) + 2 r t ) )

t = -( -xr .r o x,)

oL i, = -o,Zi x, - o,5 Xt 7 O' 25- u

i , = o .2 k t ' ' 2xz

{ = Y / - toXz-

an ,litzztz,ad ', Pâ{- A,t // a/

6

* ' ( ia ' t t )znnts)=a6

2 s . , '

c v,J

R- C X - 7 O v^rss=#rtt)= /osr+z6.tJ _ g 6,1

. f s r t c ttasl sli * I

J,s.r to i l fsS= -""* /2

\ -. fs' 5s " ftt"!-l: ,, u,tt

Yo= f f i Voui=; ; f2ost r l5s r /z*

€'- tl rc )= f f i i r / 2Tku e,e rr,*t/'.t P lfu

Ll 6 gru

d-s

1tt

u6)

T4oo *f 4 T*Z-"/ k &e'nd*? & 74? z s r ! = - 2 s

2 5 + ) l - ' 2 5 ^ + |

citz t/t na/lZn F, J lo2 , 'Tluca lu 4

'ry

eiuriy' a A..f rf ".f,&rw.6

Zfu ss - - z x ( * ' z e a ) =L c o ' Z r t n Z e B

cq4aZal uo V*4r?o, ,f,Jk) "'4 k4tt 4

L ^-^t ot ^/4 - n.- o,ezzo/t-?r'v i nfbpta-E "f " 4

Ob ss' e7a/'aa H 'Cf-'

4a a 6alec- /,4a( '/ 'J"a"" a'+y'- 1*'

/,c/^L4. 7V

/a,tc' nL"t*r ''/ 6 'r ''ry

ulu.it ny&d'*6/;;L. 6b'n '/ 4't'4'M

t*B=

- z ( 8 s " + t )

t 2 s ' t i g s ' t 5 s r I

V ro = Z .o 'U ts )

zns yYtt.vot) =

{r zau ,*

t 2 g '

/ z s ) + # s + 6 s + 1

A t L 2 ( & s 2 + t )- -F ; / z s t * t s z + 6 s + rTIz4 4a-ar' * nr*/ Da/'4 /ry?i

aa st' offzanA uaiyt T -"'"f e)tt"'4 - I^-

T ' S

Panoi^-, on tfa"bl nzatrj At d'tcz

r/va at lia's/n /- {7 fu

u 6 /'o,rt&i*{ utt; 7* .onathi/ dt"'/p'' 4

Hr,)=#,'=

r ' 2 5 ' n l r 6 t ' \' ( 3 5 l z s " r r \ /

*>f,zttr& ,

- 2 # -

f f i r ' t 1 / ' j + /

8.t+ .-/ a ,' W_ l,.f"r-fr._z s \ )

fr ,l/r'z?|v-L

z s ' . t

Tt ry.4<ru"P+

7h; Zl;tl -n"4* a.flt*.*fio/ u/n."fq?/

dacruiga {,i/ c.+rx.a/ ia Fa1 f, /+ (6).

g, lg tJt.\= fJ a- 2f ,g

zsL+ t

T e64-czf pryL

8 , t I J " . r f l = / , f , r L + o , f

l ' t r ( s ) = ^ ^ - . _ = - \ ; - (z s ) + 4 s + { J ' r 2 t ' r ) , t

: 7;l,.UJ ,o a , r J x ' r o ' z t

f. is .eV at {aV/'-rz A,e/uf1.* d!*f

W -:*fu e.cr4aafr.ri o. *ris'o 41 t(a'"

s'X/s) = 'a/t5S'rU/s)

/ n ) = & X t s ) + d U t s )

E-r1 ab Vaaf *fi'o/t'', /-4 /4^4

(sra) x4 = t'/ /') Lv xtt=h ttu

T/ttta uq r{ttry

a- (trs) .r d u/s) ,- (* + a)tlrslYr i= # t lu ) ' rdUrs

a^d de r,4r4tf,L- /a"'af"/*t fu u 6zY a

/ /r,s=W = _!_+aLfrsS t'r 4

l / u 2 = # - = " , 1 5 , r . ,tas-.rAfs * /2 d^+ 2,af S * 6,6

rlt ^q Zart, t-//*u4 /farh ez

an< u, P4a4 4 t fa) a,v t{..ntct.qa-

sf*;'zhl a4/./ttott/.. d, a-atu frLC

c+.r..t.tf . 74t rurtn/eU 4 uTai^fr+ *J

? -Tu u'tto/ A Aa n/r&z,snZJ'a- ad

k e, // ,tu zL aaeta il'"t'na tfu /att*t'

ttaz4 8 atlafaa d' /t&v utzt ttt'u'U< f<*la

'ftt etct 'au'a'/'(a, o) P'oa/ 'S' J k) a'tz

a'oa*oi^6"f /;'7L /fu "ftz'h

w/{'7rz

ffu m.4c& ctz+'ttilf, 7/" n'on*g d

,fta-fe va+rz/r4n /'t t74; '')74n''z+t'{a/'h

" l o,--1,I a

{ = 7 o

e./6

8'/? y('/rl + ary'rt + arle + a+f/r) = burc)-

def ea 'Irt^. zrtt) = X)r2. rrlt). {nl- 7r/r)=d/c)//

f/It, te t{naua -

i, tt) ={ td = 7, (t)

i , r r= i ' t ts =x, /c)

i,d =ilt= - o'i -ori - aa{ 'L u

t 1 L = ' 4 ' 7 t ' L g X t - o * / ' t l u

oL f f , ru1 f 'a '

'ar 'a*7fx ' rc t f f b l

lu"',7,1= 1 , b o ll *', l* lo lurttL4rctl I o t oJl^r,"J LoJ

* {.ftL =:- | o-

-o r./-o : !:'//?)

t 1 s )

6 -

,z s t* gtn G^r.t I

( t t sr t Ps-n 6s+ / ) Yrs) = / ts 'Uts)

/ , s t ( r r ' ) + & , t 'Y ts )+ /5 ' f f l 'Y ' ) = /2 ( 'UA l

, ( J ) . r t "/ r { ' i l , ,8 j ' , t t + / j r t + d / r ) = 1 t u6 l

4alat*+ rt,r? ze{ i{"aV"'tc"{

- 'Zf , -

,r=i,/* uo ,*/*u x,k;={rD,4@1rZ r"t4=itt)TAa ure 4m

i,txl =!r+S = Tl,1')

irttl-Xto= xtft)

ilA = 7i*) = - q2xJft) - qrtzft) - o+r,k) + b urc)

TA4o at ,(su

/ , t u l l o r o l [ ' , * ' 1 [ 01

l r,trt I= I o o r llx,itt l. lt l"ttL+,, J l-o* -qr -o'JL*''il lt J

{ t *S= f t o t ' 1 { t+S + O ' t t / r )

Y t ' { , aa,l ri'{. 4

6,*C u4/,+

120

DLI"L

7lv.n

Ys)- 7

U(r)

9 , =Ylt)

n< /*t'<

#=# #r= l ' s ' i l ' ' s+ ls (z )

'ab ankda-*'a'L, tt) a4 (z) /'zan'aa

,'"t*) + 4rirr) *arf't1 t 4+rr(c) = utt)

{ft) = l, irtt + 6rtrt1 r b" r/t)

6r* lr, AhL ct4' t34'r na h;r+ rac \2{z

Y r = { r r / ' l = { ,

a4( ,'.,{ryT; "js + J l f , - r s z 7 s r r 6

s t r %

A/< e.Tt'L

4 ( , ) = t * f + f + 6 * O

-,t,r!/-3;'r &/'3) 'l

Q hll ; FJ) 'r) t'J'/

z 1 e o= - ) 7 ' t 4 5 - 2 4 ' * 1

v,ru Q/s) ltt Ftt */ -J ad tr1'/e anl 4tt)

- ^4 r,.t^,..- /c t-z'f&

br t -n .6rs , LJ

J' '* e, st* 4,t t + 4+

g ) + 4 r t t + f r J s n 4 7

Zn

l,elap t

D* t a / i ' : t / , 72= v a t = u , T n e a N

4 * l J + ui , ' i ) ' , = ' Q z x t - 4 " -

i r ' i ' ' / ,

i r = f ' X z

{ = b , r , r l t l t r l t } t

; 7 + 8 s t ot t ' s {

? t ' { 6

- 1 7u ' - [ z ' ) )ort^*or'

n 4 tfi 'u ^'-( nt e /'7af'P6

Tltu4 tP tl'toY

H,u)='ffi=#H, t't 4'+t lcXtu't'

".'::,: rf :7.)*l1uf'o* 4'nL "*tnztttq*n

'r "

ht rx'"'"/ "/&/''Z)t"- : /l'*{

u, r;':J,'l iJ,

c+ o=[": | : '),,u),t t = [ 1 , b , L J l Zi - / r r r l 4 r l { t c

+vlzu- l=fx, )(2 x'J ' Ntu

,r,/).+tpr ro aa*Q *nn/t ry (?'tt;

t', ^ r ''At c, onlrrtfih ''ffi;

o/''tr t's', tat st efar'"a'2

{+ ct*a' at ""i"t|"*'*f

'/n6'cot" a'"

{o, il ett ncf ^f,nq"ehf- 'fectr /4n'

F,ad &, tf . '(

[,=S7 a"/ lt=o,' 4'a' t"e 'ite

_./

ff ts) =

il-rk1 r{4"

s3 = N ' ' 4s ' ]+zs - r DJs )

4e6 4 4 o, )\/o rl.c" r-, aotd

- 2 6 -

et O /rcaat 4lats-t + P, -fAua Nrk) a*/

D2G) au c.Flu'e 44 /lr/9 r/a &ynez.l.

q,u

t c) Ys1= -!/c,'/;ft,0'5u/s)

ll, rs) = o, { ,td/4 nrf c'le+"tZn"7* "-*J/

tfu c*i<Y<J ,

uf.;& t*Tagz 4'.)2t'u i5 aan tfzpe'tt"l"

,,2 du €f ol 't'& O. Az V*iz'arr '

,'v ';r,64âr ; i;'* ( *y'f;;')/t{)

c&f, oâ '*'^'<-'/a'/n4/ ' 7"4 )/u aaa<tt"

'ta atr ft f'a* a d a 'uy'/e eru /"/

'tf, aryc.at o ; ;

&-/ * ^nifc/*"

b r l

. - r o T ' 1 . - . ' + r - t )t,, JloJ $>v)sr/o

. I - . ). t ' r 2sr /o

2- 2 g ' - s - i 6

s - + l s r / e

s.23 k) y6;= # Llt:2 = o, r L/t:)

J4 fawf,- /+ois2 = ?,J- ltat 'tf- 0 a*{

e *r,e*6r^t *t/ff d'i"'at'- /a )c? eatlf

46'r% t(er*'t lr - 7/ra -At

l't+-<)/c"'

t1

,*';tetr cJaa-cQ'ur* 47 t^6 a'

fu&*it, Yr, =

# t//s) = ct'f //r:)

Hn tg = o, f ,l*ct nir ctl'nac/ct'trs"

cr.Lu14,{

Ileeaatc ala sa,1a{a,er7r

2r&A ; a.4,a6," Ut)'xo

naZ/4 a/ar Z,til k,

l ' - | I r rba ty ' z ,&o*?

fudufu , G f,,ef,t*//*{ ' ;"Ju

u . f-', -': J, r [;J-

t = E l + l Y ' z u r r )

8.a+z t A Z t

Utsl

Qit)zr 1,

(rs1= 6

= f l

- = E J

6 z - A ) a

-tfi

"t[: JJ s r 4 _

zt naa/ c-;Z( nal da(;lt 7fu wf"u ^&;f

' z t ' q 4ca la t i oLa 'u ' / / e+ C * : *

Ac"u? /uacfiir*-

o*/( zo{ cltuo&uf

M6&Zr4 lfu d^cal ' 'f" '2oa'T'Q .'"a-- -'/' - /

2 tct-' h roltt'tl o'ia"J) '-Ahrqo/t/ -4Lf Z,/r)= O (atlt

S * zs 'r/o

"fu tdfepz *'ot'cd4

Dc{a e tt"f B A"fuy

t/k) , Thuo zt o4/'l

afiu4, ta At 2'4'*

/"*rfun- fr- u 'Q f, ^ {' 7/Y4 d z'

c.z+tat*t L at'//o- C ,4ftu at ftaay'*

/o^rt* ,ril/ zl *1u'-"6"'/-

*'/e{/

tfu u-+et'L , A" /t" rt'€" '

'* 'u{a"/'/

&f Z =q2 (qztt ,t*""'l') '

8 '2 r A za

< 2 1 -

" - e ' i t 3 ;-

5 y - r z

; , * x * f ' ,

l = z ; = l r t r * j u

r . - j - ' - - ! '

= s 2 t = ' 5 '

oAB J - , . -L -

- 2+ ls 2 5 z S

- Jls

\u= ff i i l ts)=# =fi iuoty q = # = # u 6 )T/u a.t'4f4' ft'(fu't'

. o -zs/t 3srt) . v(

det za{ cta*6-l'4e{4 T- t tr/tPc ,

ct*c.cif /<'cetat. -rf iot ltr /"

s' 3' 'c4' o 'EnE lLnls/a

dc c'+cv.if -l,qn 6a e&ff *T

q = * , r i r , X r * t i ,

i, ' -!x, - trr* t u

z i t ' x ,

)i, - o'57,

[ ' r '

f+ + 1" ,li| ,L * o J [ o( o t l x

J

zs I - '/.,srz> i) lst

6 s z + . i 2 - s f t - ' '

2s

6 s ' z + 2 s " t

(t) atl rz) /{M- t L '

i , . i - * , = * r , + r i - ; i l= i ' , ' uJ '

Thtro u+ lnuc

, l o h o l l t ' 1 .u ' l o - 2 , l ^ * l o l 'l' -/t o ) L'r' )

{ = i ' : E o - ) t ' l ^

Jr t4 nc{ a tfu sfo'tlea't/ P Taut'e y'

il:.,: ! ":'/!t ' t r rz le A' ) r , ' a1i ' i r ) + tz

F F i , = 4 r , * - * i

(q) 7at u/f.f4"'.1 -u/rt

@,ttVAeta

Xs " X l ' }xz

?7- P/f-tnnl - L'o&/,

4uf<au = * t + l J

i , = ' * , , + f r z r t )( 2 )

v n g - - z a ' 4 , ,T n " a g

5 + a- @ 11ts t

I - t ' 'z

5 z s ) 4 t + l

- ,f'/s-rz) 7t u)Js )s5s + /

9 ,28

7 'l'

* 2 u'> !'t

,&tYtss

frtn lde A, ae 'hw

i , i , , * ,

i , ' * x ' * ! i

{ i ' }

!L-

;' 7 j -

t ;t a

x1

d -l - j' e,fr-/I,rt,,/- /;e laf

z @ ' r , )

( 9 i " ft - J ' J J

(s +z) r ;l'- - l J r 1 t ' 2 5 s l z ._ _ =e 8 - - r ) 2 * + - r ;

fr 2s'+4si l

* r t u - l t ' z X z

ti:J,l:, (:J.,[1"(4'X

= L't '2J 7 + Lt

*I. I T YQ'= ,,/ i i , ;ttut, C * y r l

' t + s r ' i 1 + Ut'i ,td /. dt sfatlod f -

+

Y').=Jr6^* f-f,,n

11/ tS =6 r - + z s . t /

-tat dtg-trt z a'4 dazr r.dafu"t@,

%ee( aL a)a'i/ /*cat4 ab aiaaf

tu

8,21 (4) ,1-;. ;l l t s t n ' X t

t --r ir- l -a-L<

I

L* ' L

u ' x t

f a t Slra'eae e'6r'/',$

- z & _

Y , r ) = * v r r ' # r t t ' )

eJ-.1â4 lzfrtz 2 4../ /aet rutf c/.eart-^6rftfu fioz4a?+ /z'ncErn ";

l ' ^ , _

c . ! ' + i ' s - r a ' s ' r a ' r 2 f

ry dr at;q;^rr.,tf4 't enz4r{ "hf+hru+il '

Hrq = f f i .s?&3zrf

- + d , / - l {

9."?= f f i r s , o r f

(Ort'+ 4r f a)(S,s ,8o)= 4'8,s- r /Dzlar\], ) s

* ( 48o + Dn\, )s ' , 48n

( u"t'. N, s + Nc)/Att '' ,4)= N'A,s'" 1"1'4onV'4'y

7/"<4 d' ^Cq./t+ ?^{r;^ '.t ata a)zJzt

Hb) =. ,ra

_--J s - * 6 s - r t

s t d ,4t (

f,u Bo.7 /'/., ltu tL Do Bn - No Ao

4 Eo t DnT, = N, Ao'+ Ne At

er D,gn ' NrLo r Oo8'

t , l / n = f e r O a , t 2 3 - J

< l = ( t o l 2 0 , 1 1 J - o . a < t J

;1 e, Ps;:

6 ; ) ( s 'o , ' )

cte.a'ttzt t(f

"!6 /4 ! ' 7/u /&h*'"'/;?"'2-

t/ T/tz

ir .eyafilz- /4 J '' & /Ttttr r{zno aesz'

,, l, 7-/u- dv ss "fo&fu

/t4 4?7nz

drf"ha'rY ( ataad /'e /'&' caTt//d/{"

at+4 oA*-'tla ) oud i n't rtnzJ 't*

r( M,Ar'r NaLr)s t :Uo

O'

,f,rry ot, *t*;*6 of tl'rr' s-o""/

- N o A , ' = o

DrBo + 4 8, t lv24o+ N, /t1

or JtEo - f{'Lo n D' 8i '' N' 4t = O

0.0, = Nz|t c* D'Lt - NtA' =O

D

Ttutz ft. rytf*;* z*r y''z aryPaza'gz{ ur

8. t z , . ( i- { r t t = 1 { t r - z ) 4 ( z ) d z

Az,/rru z = :-z . ^/e6 t74a.r t i f:!

aqc! z i Iu Yo'nn'(4 ' 71tn z=t'z'

cad'( cl 7 = '' d c lht/'4 /44 iot<

o

I t ) = ! "1(e )u rc-z)Gai)7 ' t t

, t I Arq q f f -z)J z=J "t ( 7 )u rc'2)d t =/=:' - '- '- ' '

t=oqJJ /r; {nttl {,c 4t eulwf z'ri64 A7

4/r)= ffa)= / h tVd'

'n/4""t/st<

/ t '

^ . ' - , . ' l

{ * )

drr* l ! n,4. . t Jx 4" f r t )= T€ = 0

aan laqtz+ zlPrrt c'rr/4a

fit y'rtntzd aa i2e4 '

noll*i fu ad

ffl:?tlf|\lf ,Jo

\Xt = xa

' i , = o , f 7 7

4 i r = t t - x t

; . . t = V' J 5

i, -- -0, txJ r 4

q i ( 4 , ' / . * - { t , a a

"(pztntf . 8e-.oo44

' fo o )x :

f . - q f o

L O o

3 = x t = ( a:.1,,F:1,( ) r l x

c.4z tv)tzz,{ i olt"'''-'("t't ftt

L a

Wq cr tTI rVfn'u,

t, ,9a r,on,/r" ?"f""l - i l r l=H,=; ;v

,9.i, ;{-l z. l-r

\1*J+i,;!,f ' t - r jl< -x r1 " r ' | ,

- 2 q -

f . t%a"r_

s- - |tl, ts) =

. l ( s ' r s ' 2 )

- - s f lJ (s rz7

2 s r f - Z P + 2 ' 5 ) -[lrts) =

Wz) -

J g.str )prz)

llrtst ito 61 fN af -)'s' 'z*( 7a4a er

-l at4 .-2 .

. z s /_2s . f {H s l s ) = k + s + t J )

.= (-r-t )zr *

(sro,9[g.4'r fJ

= - (s' ' t r J 'zX'r '- t ' i z)

(s+ P, rS t"*r, I I I f t ' r) ' l - 3 )

- (s a)(s -r '

J (ssz)(s' ' t2

Ai'h 4u=Yl*) = o

, - zs^ - / t , s+ l I =+ .o , f1= A f f i l r . -n - z

f,

f,//,r5i ,lat a, pt 4.f -/ a,/ o /& d -2.g r ) o + l = t r / t 5

+ f t , { " ' ' l t vo

' J q = 4 t - r j €

?.: rk /;'f4hz { /}t't i {''fur';JTfu .{af .1e/par,4z "/. ;gr<1 i ,/''[tttrtl,lJ

= g -'[#tnJ .

7/u; 4,4or^,a dtt aoatarEir* ,

Uri)

/1'4 t(z'<',tf l,u 4uz.

7,4at ar -o'9

I oct/ .tti )

,*af a?t .tt*t

q f r e i z

? . 2 f t k > = f f i ,

Y:) = flb, t = ] i^-/{!-'r,t:'('s rr ) ('s'r t)

= { o . + - *axh /Vn=f ta,)= 2

. o - 2 s 4 1 1 = 2 { ! ! - - t sE t '= Gz l r - , . _ r

, z ; - q o J r t | - 8 + z c t r l = - 2 f( r =

t ' / t l s = - z - ' - z r t

. u f t * l t ' 2 5 c ) + t 3 € - t ' z f e ' " '

ft

,t?rtQa, .' u t t) = Er *) " Ll ts2 ' t

t z o .

JEf : 4(f) = t. 6 Za, tlul=

Yrrl = 11'19 ' /L = 2€ ' -r e'sJ' i' .r /s.rrXstz)

at-., f, , ttt ao ' i . t + t s - ) ' z

to (s-r )

?,4 4V,A'4z-V n .tay'act ^;z.rzVl-'r-'- F*J.,

uu7 (8,+t ) ,

5 Y/, '{k) "t a, aaalYt') =

(s; a, aap t ) Yrs) e f(a)

= 9o

PaYrs) =

' S -2' O'PP?/

q ulcS = o, flil '= fu, {n/'-

ort dtu.t+t /o/ott T"t"t/*

ta

- o .aae/ t

g U i l = ' t u e

drr t, lo fu t"+* fu Xrrd 6 'laâP t

/a , //-a'{ n,

-\z,ead/f/

7a := 9'7 e

T/21 ae 'r(4t< o) . -o,t J *

' o, Qaa/ tt = h ('/dft

cr i, = / 3+o J a1- zz tta ;2<2 'Jtc'

?,f J E/e 4nrarr'12,

JJ

Yrst=\il:)' -L =(s):tfo) :s -

r ro*/f,(s r a r)J"

t , * - f r - ^ n ' F , = * 4 . * #4r

= Tt ' f i t *16 - .rso,t ' . -$

{ rr l = f , e- ' , 6rt. ' t * {r ' t 'e- ' *(+' 'o ' ' t ' l t '

h t 2o. btiL it- =fl rd= #

1 -7tD .

- J 6 -

?'6 Ytil =N(s)

' -" - 6+t)+( ' . , o.z)(su +js)(sn i i ls

{H=4,"'"* 6rte.'" + SrcL'"* 4*zre-)'

; 4 , * ' F '22 * f i t

" - t * , (a t+ fn ) 'n 4t , ,

/,a> cZa, a'ifft-'

6e=/ l (o)=#=f f i=&' ior '7Y ls)= f f i f f i=#

- / - + ' - l

J g+/

{ r 0 = , - * - : t 7 . o

/t, /& ar +/ ,/ rtot q tutf tv"rtJ

<7 ar" W r, fa.ac,t:'* , al; +V

c( u^rz/?af'n"'' nt^t4r et/o4/"'1 o'n/

,<e4z,t 4 Pts) ''iA & "s''GZ/'

?-F r/,e *ofu,/cA. - naf tuz+fu-a

'fv PQna*"?/4 CT a'{e/'O -

?./l rar.,rr*t * 4os+4, ,q 'ar/ao , gh'i

4 s a + 3 s t + z s ' ' + s t /

t ' t l I s Is* l + z , Eo 1 ,5- o . l r jt.t, l t ' t o,,f, [ o a.s t 1' -

lo ' t | [o -z. j? ' ): lz,.tzrl t l

T dfo/,& 'laanaa a/' dd *f"t'r *n/a'

r J ) : ^ t +

,/++/z.f

z,s/0,8

Nrt C

r r , s+J '

t/e S+ey'r.J s r

rqJ/to,l S ".t

,

t z 3 i T

6 J'2 >o

tt,3 ro,7

Jq , l zo

4trf3 O

t t,3 S'e'il

J a , , I z a j

qBf )

(o

Eo(a

leuttz h *V 4f.zl4 or Pnafa/&

7'A**, kQ ar"r/*'-6to y'o/ "

'fu/*'

ryh / n/*4 rl 4 odo:::paz[* *

"tt;': :*

-/ do 4*4 {tt

e't' ,'/ d",:'4' de*-oi'-)' 'cr {q4

Grrorb )1t1= 4o s' * Q, 5 r Qt ui//' oaT o

s t l 4 a 4 2 -

4,/4/ ; I o" (o 4'1

I | 6 -

4 o,ro, n,i, j'"' o:: r':f#: ;L

ord ar, o , fu*zsat 'Jorg n "'-:' ),n *rrr&4

a*(t d \ors) i cT t'/'q'/'o 'o *1

Dntc) u cT 'or4/'c / */ ^# 4

o''i=o 2'

^" "/ & 'orxt uf '

"tM k4r*,4. *xo'61 q fuoad"(

e'";,

ad a/|zr,n t4t P.44,?,7, 'ftra 'n'*f"*

ry\g- -ha*.{e/ r'rptf uQrcdg- l r

?.? N.t'&r2,. A,,ttt d.4&o "xeff o^z

tib ir^:d' d. e{-ry ;-y'aeo" tu

H h {

? J O , O S i . r 3 " l r 2 5 ' + s * r i n a f c T

trtl4 1êea44 A'' f"A"' t* I lYff

,,> ia ;;;"i(,- /;,;; ;r',h, o ,ttgzz'u

?,r z

'/a,

.t '+ 4, s-+ Qzs a d3

, ' l / 4 >s ' 1 4 , 4 r f o 4 ,.S l4'4'

-aa

, l r i" 4 J

T a^ t "44 + 4 ,2o ,4 t74

4 i 4 . r - 4 t Z O

* o r r o , 4 r 7 o , 4 , o t

-tt=roT)

o aJ 20 .t'J

a t 7 o

-31 -

-fl,,00 dv 5u,4/4 /ne:n f u'6 g a

4u'=;f f i6 aorcrw'ta'(n't' 'o c:T 'a'ft/4 leu'tzz

fu ,uafi+,>+tc 6 'ta'+( 46/'f Pno'

f'/6 flrst= # C$t .6ez ai*ur&f '; /s.

Ys)=il(s) ! = #* = * -# - h"- #

t {n) = t -i'x- 7.-" - o, f,t'e-t

Yr/a = 4, €-", f.te''t* (rd'e-t'* gotte:ti

n {.e 'a.2t + Qs e'tJn tst + {, )

H tsl a ohi& a'-/ '6 t* eg*lflnr D;

t/o,, = f .r, '7h4/ i/' fafua '15 azcaada

'lrrtr) = /")e

{ t f t )=- ( t ' r r +o' f ' t - )e

ac. ptar l{nrol i du 7'a/'-t'^6r

0.8

zAB J:+ o,o t )' i'g +o,al r i [

_ t +aa l-

+5 ' ' f e ,o4S l I

Y, t1 =ZU' t l ts t

+

Yst

B

,,6 T/r',22 turff'*"fr ::#;%i?.r iS Tfuu H,O a-4t dca

T fIt t;ft'Ja"cz c/zAe

Yl F^"//t( PtszE'h' a/

i s u l r o ; f f i .7/rq aQlftz<'

t o s . t

z = , - r r O E . . = ?b A r t a s T ^ 7 o t 2 - + J t t o'ffi - 4't

&t- t; tr-*L(t ,

- f

7,rrl- /lrg=rffi

A4 4Jorrt1",a P.'*4. ?.{-A 4^q arysatil n

l@= 4, e-t* Al e ' t+ 4""^"-(* t 'o ' '- / A V , , t V O

{r/t) = !* {ro

= -7ro

/r. ltt = {re-+ {rtc-ca 4t tTt r l 'e'Aft

H*l a .&4A vnd iil t'u eatu/*nr P

,/o,t =tQ . TItt, ;f 6'A'q 'rd "u'qrnelt

o 5 1 0 1 5

0#'t4ê t $rC)l = o,tJ5' a'4 l {rrttll = s,e?"6'

7h/4 /v Qaruenf -tzctc'rLld tW

cr' +4 ^,;76 t ?o 4 )6 pn$ '7a1/ta tt+

tuL 6b c*abt4.

?,t7 Can4dtL /-lts; = # ttA a'rf0

0.6

0.4

0.2

0

h Oo a*rctnf a a/<'c caf a4

{c-, dv 25 '-a"'L 4 *a4^'

f. t5 //ri [email protected]

fu alan<t n P+r{ /. e. c,* *fitu

fl!tt=&; {/d = /oc44t

ar4

i ir/z=o, | €

- 3 1 -

iHs'dl

TI

n/,

a 4l lQv)

- t f

'n/t

y'c& fu ,,a7itfr& Azfl" P 4c4/l

atd & /on lafnu a ad/- 'r/' y''tz

aguror*{za r/z 'd' ad Eo"s'dP

?, r8 4 i r=# , / / r4= f t

Ir/,q',sl=1.fu\= #l f t , r t i u t t ' t f r t ' f f i " = J f f ir,lut ee lsc l/4"i*ll= | H'riol 1'au

?.rf Hre :

? , t o / / u ) = ) u - i c r t c i u , | l t u c

I o lal >ut' '

, f "' jors tlz:

f.r') = # J Haol6''-o d, = *l "'-+.i'uta,,,U,tZ' h)=<lo tJ

=fi{'"*r(c-tiudro = ffie'-Uc.

;rc-d>ul

s'tf s r roQ

/18) a 4f,ei6 , in ato/"a' tE *fl$ 7tu'en'L

7,5 , to< *+rn7t'c"6'

' r ( f - 4 )

/* e( r i ('-F),ce), Brnaa t{t0 i x*t

ideaÂ;tan? Itu /* aA t10, ah ;e4^(

laxtyaa He

; 'Td ca"zof '*{ c24a'{

'{n /*t;tr tt' Ât 4't'? "'-n/a/'

F.2/ ltrst = -5 + re

/|tu) = + , tHtetl: tht/a =: ilnur

-rt-- i ,->=-L, : ; ; frH d o l = f i a = T , r j i . ' t t

= o,le/ ( i /a) P'Jtr/ t

s - o 2

^ t'(t-Go) t'tu 'J (t4) K'.-e - - < € ' -

Tirl'(t -c" )

** f 1s-ro2 rorr l

ttlqe.,l

2.1'4.tn ft-tolru.1

zr j t*- t - l

- o . 2//(p) = ff'

=' ' o,oo 2

i ta - o ;

= Ot tC,2 € t f r

+ j t o - o ' z '

- ' io *ito r /aollQ'to) =Arf +d'lo + ro4

r O. 7 / o - = 1 = / € l

-* 5

d

' 1 ' /ao ' 0 '2 x

H(l'/oo) -- fr;itoo + tao

- t o o t i n ! ' = , o . o I eI o a o d e -

Vru ilL onorlr -sta'& 'v4Pet'u ( /tts I(/

qru'64 4rt 'uf*l

= Z+ ea/at - tta PatI

t4

{ r r / t )= 2x ( -o ,ac 'o) ) '+ | x c ' to ( to t * 0 )

- a ,o / o ta ( / {o t . - fy 'z )

& C & o i o t -

lHgetl = o:loI lfit/ a = o'/?'/ /l 't"r

l / lqwll +O 't4 d n&l l Tq t , / l

' u

- ' ' 4a ' ^ l / i t t l t t l ao / "w , '' rrr& *qrr,ru 7 "'-''Tlrrtrrhk,lnafn'' ' tttrLE , ..., l-,/f ia,

dtto tt lnfaut #G-

I t . ' a.----1OtzQ0

i o/t'

r+vfl> 3'1 B 4a*ntct"/l'

a . 4 o 'o , , Hk ) t c

nd)'l-a'/4 at"{ ea;lV

(s 1q uq'/ oo o

/bll fs; a&en ra&t g^td+ dc o+c/ i.rt - 6 a l q u a r { a t a f -

i. nt k ztVf,c<,tYjra*lf n3;:fuf-rf +inttoct&, frrre. td q /.da/Vaaa

-J3 -

;;7", r*4.tu* a*' /'/7'

?,t2 7t' Aarf+ /a'cfr'a "/ % f.-Ltta) q

/-l, rs) = i/at 's

' ' i + r / 4 t . 5 o , t ^ t + t , t + r o

'l.t ) a/ eL fu u* P..,1. r,21 . 7lu4 Lf

u r'.zspaa ,ut//u J -./8 AA2r..lrt' /a. dc

u"{rrr"6

/ t ,U ' o , t ) = f t r - 4= /

lHrrPt l* Stdt/a 'x o'

t i b ,

fu *t t;* at uJ 4J "/'4f

'/{

pa.fri,t, i;Vat rc*:::"Y,r{ R e_ z

tt,

R, rf,R , = ?P

ll,riroo) = ,#,

T/t4t4 Att "Eadt/'lfa&.(/

x /o : t7, l " - t ' rA

_ J,ILry

4t74f7n'U t4

{rrn, = tui P,/t + o, / ai (tcos -rt/z )

rutu /*)L -t*f'y t''*t"t*o( a ofu"afrl

€r= t- = ous lro = Lf

- uc, - e+ Y" - 9,5Uto

" t = f - = T

_ o , r l b = yR R

{ ' = - i , = - F u ' = - R i: e a t / a ' * = q

ua& ahr tw ttetY uaz'l '-=

' "J r*rl=J

*roru'uoot, ="for"''ti'u'tu

?,23 rtu 6*ay''t /4ao6'o' 4 '.F,! zr (J) a

H^r r1=# , r '= ; f f i - ' #]N

Hr/i*) = ffi x.a./ _dar=o /.trn/z

ilrla) = O, Httb-' ) -'

;ffi - /

. . .i)t' = i- - ti"(iO =o,7 "i*il,+i")= w:,7

/t,g)w)=ff ir:+Ft

Jt i firtpaa^t rir|, J'/B /*1fu| *?

/*fr*,f '' d/' , Ltt4 Yta/'aa'/

t'

Etrt, at), rtu4'6 t'*ol'^{il' i h' 7l'

*-f'r-G.Ca ru'tPn*P tc

{"1"''1" o, t'u/'/t (a, r t +o/') + 'tt}' (pet)

t z -Q l t: 'Q

{?"u-iu*4t* rn Gr,41 Ed ,(0

D z / t u - f ' ' t , n t s u T f u, d

J o ^r.?'*d, 'J'r!- il ei'"'E 1-li)

&@rld,

t = 4 4 .A)

?,24 6e.c.ctto<

It"trri,t l '

Ia,rsuS | '-+

l+- tv 'O

h u,r +a

ryO /'- t"t -- O

l* u: f4i

f* ut + tct

l t ' r ' 'o '1u tft jft

utt a,

= [*x1t) ui';,t{ /it""r "drJ

7=o i 20

'{ fx-, -rt l" =r,,

7,2f 4 X'rs1 ion . .tr?6 7& ar s:o. { (?tr

{< ryp*trled aa

Xr4 = + . fua dtct'fo *ilt-t p"&4

t*ttl" fi, = x'ts,', lr., o

4 e// erle* p&z art 4t<da d' a'ft"q

"'F* eu'i'aar *'f? A'-/ Po4)fu'ZZn

VLrt" z:rn. nepfit4z4 ^Z( tV7>tt*c4 Q q

/ lHq'l I

- 1 1 -

!8, I

l/og- -- ,=1':,;; * #llts)= Vr,6 = -,s

*roo / /

Jr u .&,,wyaa ,ui//o puoZcn,t fa,'1"'J Joz Fud"

?,2 | J"* argnah ct4|t'11 4ee6d ?V ''u'& Q rutJ-

/16'l car, le -aphud at /'- t/"nacn h'ou* 'd z*t

t*u pruradltrt //ri qa W olt'af Att-"884"d{

/0,2 roRt 'w E- = e- = o , i*" o

4ul = A rs) [e* t'l ' fi-FtJ

-#[uo,-VuiJ

6,,f f i )ry,)=#v,ot

: - v i - * = - L' t - R t R t

, ' - W t - = 4 ' ,- z - - t o F r t a R t

-e' - -Ya-

Rt -

rcK1

Tl*u tut /^cc< 4@ = '/o 4' ft) il/

l/otrl= -/o 4rrl - rtraa aIt A*f

't"l-= --:,t,.,o= AH [Ero - E-@f - # Ertst

et, f , r tst=# /ot :1

. t/,;r,t - I",e 4rrl = w.

I*tsya7,(s)= -t ,

$til + Irls1 ' -frfs) = o '" $/t)= -Ir/s)

J!2AJZa - i/atl-Er/t)

Pc'(et ,|Pc aqcfit'e ^t4 fo4'4 '

da, x(A+ 0 ao t*&. fo lfu) eB12

fu ef.-Ea',' "ZU f'{A &zY'znz

-Lit4( /4 ,t<, pc& ( Xtrl d ceauy' s a'd

!m; sX'65= ps+0

Il XG) 4a4 a?u '+ 2424/ &" tn/"

pnfufu .<en? yru.S , tu afz'"6/ P"1'

* t =0.. €rttr* lXt*ll*to ao t +6t '

$ Xrtt fad r4q& pe&t e" 4t i+t 'a^t4'

&^ xft) ca/4/"4*' *tfui"/ dt'&/aftaL

ola-rtxomtb, 4 Xts)= ;rr""

x (o) = c(h ta t , A ez./ta,V/L ks Xb) =a

ttp do 2d ta/e k,xt+s =o" 7h'a L

,4r;rt dz eaa'<f,ottt- ,,4 k'z/f /tt*f

.""1 dl' ya4t4/42{'*d12fu '

uo

o) z' ot .+1-

Rt to Rr

h' /o l/r: /s) - /t1 ErG) = -l,itsl t Erts)

,,... rrGr$2ySg/e VG) = - ;k) r // Etrg = -l'lrqt

7

=t,ut[!# -,J=f r,t/'ffiV,at aP fr&

/Jk)= 4!L = ''l . ta&

,L(t) r / , f +J-t),3-7 *

,PV

Jt> "O ,a fa. raoo ) H k) anol /frts2 ,1rue

- 3 s -

neraêf "Ze, fri.r-( @3 W P

' o e / o ell (7'u)= ffi

'- # = -/ o = $ti,,:)

fea aa, /t@ corr.n*t & -udz*/ 6 'to ft

% e/,irru/ 4rurttz //rg d l'af da/4 '

ab+ oxa*, dl q 44upaa { tto'

fta* u-&a"t/4; ntfz.aa . f,t ,6/

4/Va?'oz / Hrf"2 o -/o.ha//rvo.7atu

du cA4',/i/ utt*r+{ 4'e att4 la oa Ptt

raRt

4k)=ffi

4

!(tt=/rl/.r'tt

I/orsS = AGt I enrtl - E_ro] o"/L

4rs1 = # . E*a' ll, /<). 5-1q= j ?ot

(s *so, J)yots) = /or 46) -

{ U"S

ol4 :.r z7"t'+z .va/'7L6<;n i

itrt= -'fl t(A + u/c)

{(tl = '?bo tk) + 4a Urz)

Jr u't 4t 'o/'Z'nPt-6/ a'

uaoktl l , 2 = r r f z J ? f 1 44 1r '2 z a; l

2.+, t.,e 4fa* '4t at7?'nd" *'ry= € t = O- ; -

= L z r ^l l e at -aldrtn'

2V ; = P r = p = *

Xtol =/ | !,(c),

oo5 1 . 5aqoo 1f=r r r A K6', ..-

k+ ro .J , /oV, ) 46) > /o ' ( " t '

fl,a At fi,att/+> /*f^ '

ic24 _

H,n=#, ; f f i^ ; f f iJf to..n6& u''t/o Ei" eaahtd '/oo

o.3/ /x/o 'a =/ , / 'P-6. Jra !A*r ' :

7:r':r*;-; te ,)v,i '-'t'/" c:/'41

{q ""rrr+r*ul

a'/ '6 e//"tfi'-4 ff

+en1e . ]c> r--'r'/FF*7 n/'"2 *t '6

l'<,;ttt /nz uu - 7: *"* u'&at+ "of A*

/{'"{ taueb ci 'a7" 1' /lre e*' /'z

-o 2 r,."fi"n"v t,Xol,l

E 'u

Fat mot.pnd 't =z, 4 f = ',2. zi'c't' fu

ay* tu?f r rc7 y ' {ar i * " , -h//X.,L n zfu leywf , tu 'ry a.tt,4.o)'

Qr a .o',,rr'(tt 'i' f/'25' e) ei{eid fu

h=/ , t f : d ,2 ad {= a '6J

oo

5 1 . 5oa0)

o 1o=co 0. i

,.Udtt ,ztl a' | / '

- H s = 4 ? * ' 8 o os r 2 O t f 2 0

. t =o,t

t,4

/d'+ HGI=fu

e 36 ' '

Th& ?va41,g q fiChul /'- "rt=/,( =a.oz aqd zta+."ita f , ,l/ f =42,'v{t

fe,'aA;n-?/uft'T *W 'i dt ,

laf€n, ,hr'i *ry'/ f a,?, a) a"l'J"

a' ,laytzz ZAa4r. f t.sf e) t4&a/ k

t r= / ea , l I to ,2 -

ua6ne catt h u'&,ke, vfutd ird naf( - / - t t L - t j

{"*tr;/" 6" za/r nnVaD'* /*d}-erb

con o{o/,4 q 1i/46ab'

@ aal Hz=#e' t r t r t ,

/q 7 tJ = JL aad /1, = -2 oa a^{a/4 ., , f - s . f l , t d . / o ,

t 1 ' _ _ 6 = S t ' =

l= f f i={zr?2) :+7

= lo = u{ ["i&s - t ? .

T1uu ttu znTa^6u /-OP / f,uo *t:

Jd ctsl= fr a"4 P k) = z/s(.s+ Q, &*- 1 2

Htkt=f f t= , (#0 6

( at" p{e4 { Hy', o" /*o'fi( al'4rtit"

dill ,6 d*ran;oc'G' 'Udtld "{&

(s'r 4 r'/' ))(5 * o, f + J' 2) = 5- 2+ 5 r Ltf

'T/rt4d 4

2( = 4'23- /77' ( t'1't'?f' db4' dl

.*f{ /'//-44 lf'e'r 4* V&d

ar -o'{

!t__t)i dt N* 4 ilfr) au 0'c"'b'/ al'/ y'J'' '

dtla 16 aap*)^.h a/a'Zl etr4

(.rrt -jrX" + t +iz) = 5zr1 t + f,

r'a L Lx/i'6 6' 'tz''Q r'-t 't '- t | = szt 2J 'tt '

fru 4 Cts)=i, a' cffiat^b d a*7no' a '

a* w.umf p/o* dL Vo!'a / 'to' at

_i tJ'2.

to, t t $ CO = #r:,

q dtgrtL,a,wpsn.t-

$ A7"., t. rfu+t'N-st Nc' 2

I t 4 ' 1 = 4 %t r

D , s+2o t6 ' f l )

: 2

H =

- z ( s - Z )'.='" ^t

s'f,t.ilaS ' + J 5 ' f r O

aq dafa/,.&Xu a *

Z (rVt.s; Na )

(qt, 2r,)s (s tr) t z U4s'rNo)= 7 1 .

/o./ r/11 oatgur e ,{ * ?t:*3_o/

arTrf th Ftr. ,o, /J (c) ro ' 4 Rf =R/F '

€ = - # r - ' f i f = ' / o 4 - / o F {

= - t a ( u r p { )

Fntttt %, ro./3 /;;,' '* '(on '4

-/ ='/o'

€ ' - A f u t l s t ) = - l o 1 u + P / ) -

= a. z(/'/' s"f Na )

7t Dr 5t "r (oo+4 )s-n (Dr'tztt, )s *zuo

et A, p{- { H{) oq lnaH cr -z adl

-t l1'z , tl/.L ,'6 /cnot"'ltalat' '/'v'(4N

G+z)k r/ -) z)(srt/ i4 - (r*z)(r"+2s +5)

= . t ? ' f + s ' t ? 5 f / o

Ef't6/? dz wt//i;rt Yu/'/o

4 . / , D n f 4 = + * D o = 3

D n + a N r . ? ' + N t - J ,

z l o : / O + N a = f

Tfu 4 CG,)=#, tlpru

Thq'.fu 7fu, a.ttzl f.;tu

,o,io rrq f.caa/+ /r^fft" / Ef,/4/4 t4f s

, t . C(_t) Pls )i {q=lr- t+ CrrsPtls)

= -t ' - / / , / / , r -

:@

" - ,t-t S'2 (.t-/)(s-z)

/ / t - - T = , , - ' , ' = : : 3 ' / ' : , : 6

- 3 1 -

f / - r r = r e . J L t ' r l s - )t s , t r + s ' + f s f t o

uk ,laa f "dJ 4f -z qrd -r -t12

t/(t)=o,, h t-Za- A{r, du ,*ly/ W"

/ltb)' a ( ne4'13rrL f.5) , Tfuaa a( 4/f4'

HfP)- l ' *=A

=. /

&rt cr.[.,e,v t rwLctt , ttc, d?e/+z,

i ruoz.(e/, Aald

ecfzae/.A. ar|/ aln'7bT L

Mif "/ .*tr M( ,ut/t-t^*zet i77u'r'

8eeo4 I-=O, d/-

-auta ctt.*V,nlt Z pd4;?

dr"r/f z, eal z, *4

- . - - ? o ' / ;L ' z , r z z

Zinq E- ,< f Zt + l/;

= /o ' l / t . 2 .+ 14. = i14 tLzz

l n Z z ' L r I r c

z r + Z -

4 = A ( E r - E - ) = - 4 t r - . = - /

(2 , ; z t )U = - lZ r 4 - / |Z rn

( 2 , + z z * A Z , ) l / , = - A 2 , 4

Thqa /€. .kua,

llht = llrtt =l/; r t)

anA Fzs r4t/(d)o

Becea<" tl*ts) J; dfe/4, V

,r* f*

^42^

Z , ' r z z r A Z ,

l/o tst -n({) z,*2,

= - Z z

z,rzz

A

l . + . = ' AZ ' r Z z

A (2, + Zz) - A Z z

V f Z , + Z ,A 2 , . 7 r+A Z ,

/o. tJ =, = R, Z,= / rz K . . A,= /at-

. , - / o " ' . t O R = - / c 6

H'/') = FraR + rosB :/{'-

= -i2i2T = - ?, ??r?

4 Ar= 2r/or, 'a|z.n

Hrrs; =- 2J /asr/oR

R rtoR 't 2x/o 6 ribizx/of,,\-ZoAoO a O = ' f , ? ? F s2 e o o / l

6- 2 X t O-<

6a 7oa %

,,,/*cJ le/fa b /u

7fu dFr, - dry f,e*zza ,*t/f- 4

lryl$'rrtu .6'*t'* /rtcac-Eaio,

ttu, d.//2, &{

I i l r 'H, | - o ctPe(i .aa6 tn- Q,aa6 f

I+ l =

f f i=o '€Fose - - v '

That r''b ry ft*trfrst t< i,tnufrk

p dt u-^;/Z;n- a/ A '

lo, l f sJ + z,t /+ . t + / + A

r ' 3 | r t

V z r ] | z l r 4r ' l , -A

l z| | i ' e

to r -(r+A)/,1

4frn4 1=> r+A >0

- t < 4 < l

o!.Hr' t=ff iA

4ro=@-5-+zs rs'

Trw Nfn'"t/ ; c:-T

a 'd t ' -A>O <>

A (s '+>s+ f , )o r 4 d = -

g>+zf -+ f + A G'+t )o

'!-t oleaa,r'ta,tfu lza '/ztrt't'u' z.*n/ :

':

ol-o//t 7 *tl n'o, h' " -f,tn1r:f/.Tt ad o/t |fr")' * 2tr"

'+4'u '+I 1<< Altr 'u ' t r l

r/1u rt' /'oct/'-"4 qfffffi^+aa r iz t tPa 4 Hb' b

-L4tr:r;r&.- 4 H r s ) = ; : # t , l t h t t

' , - . A - A ( s ' + 2 s + f ) ' '

/ tSst = f4prs1 -r-+2st{

r A(t4 )

- 3 9 -

' a + H o r s 1 = Wt (zan)s + (fq

m qa&t u u*{ ifalt& '"/

TtLr u-ttp'qe c{ /lrs) cqadd

( R,+ 9rt(RCs + (\>

f t , (pcs*r)-- R,RCs(P ' r f lz1 ' '+ t )2

-

R,(Fcs)'+ 7zR1-Rr)Bcs + B,

,1,6 eon eti,nafaz i tfit, ,.nrn-e .24 de. c*zt-

Ln (ta,*r), Tfu ccz-{.Zatn rt- P9 6 4'"v

p*. a.f tlro= 'i (# ) '* zKt ' f, , nai

Auzff ; ârz 4.d.nc' a4 d,e axz &tni* "'

,tcdtj* /a,1

tr* r1.i423

Ei. ,o eo ( b)

k cats aa

eri@r|., 7/u

4 >f,, Tlaa

/4 ;f4,

lqtz- -

14/6 t/6)= #'/4 auratu lt-'B) =

# h rcl ada^442

J/ ir ,a ,a7&*rz+,t/ cz ; E/ /a'/4'

v l a A Ak* r )e-" /u ' l : ,#=;t+Afr;

/ f A ' 7 r t

= 4 G+r )( A + r ) s + ( r - z A )

Hrrs) ; ,,er ifal'Q P A ?alf ''*

?

t/.tq^4t o( /1rc5 u*t*r{ & ttaf/e "//''6t/

aa ab f.'-//,a44 @

naftt' A 'uV

Q4 ur FzZ. 1A, /6 .

/ a, / 7 pl/rzrf ^zZ4AZ{'c"

, - RR cs'r t

frCs+l7 -

R '

6 * / * / * e f i E 6 F t l

.1t4 4 a"f ,

A-t + A'm, ,, .. -+ o, .rttt

^,ltd, rn'*')" fi'rR)/Rr aa *-* o',

{X.at ;f, t) t'rztneyett ar'/') olooT 6/4'

,Yn **iL iV&'n"tr*Li;* tl

totta.t4J f

6r* '/i'tttzt/o- Ft'f, td't6'

'7ku 8u 4/fr( dt'i7a'n Aucanz

Rz- z r = n r *

Z+= f t r *

Llet t&.? ,rdzt

Z-= 0., I, = o

Cs

.E-= E, ,zt E+ z4

Jvu

: # n

R, 4 - R,z.t

J'tt frrutok, /*e%b4 '=+zr l ' 4 , " + r - 7 T ; a

(f , ' t) 4=

F-1rr'z+) - R'zt - P , Z I

- ( R,n Fr).=z?R, Z. ' /(t oJ

f**, a' -A(z ,14taf 4d dur a*t cAf urt/ "'

f..r/. /O. ig.

/4/f

&8tF,

4 W-F- #,- 3 ? -

WZ ab S-tra*/ha 6 (?,rtt 7<?.4Ytlt - l'Ytt) = o.o-r [Uttt - |--Urt)

|,-l-' ) Y rls = aa,r(, - l-*) Ult)

7l4a ,rx -t(*<

t t . - . - YZ ^ a,or(r - l -*)

4ttF6 t j-/

" O f h u ' - ' > -= -)-] , t t u _ , )

Neo lr,nr Hre) =ft,(g) #

T/'z/ lntz

4z anq 4t4 4 p/n aa1;z*a *l aaz

/,tL;&/4 fu et*u- .Ju- prod t/,6'.( / '/ t .e

_Ye) = z l \ * rJ+ g _ z -?t - t - t + J l -2

U t P 4 l t + t l n t 4 - r a J - , . t

(+r ) Jn+ l'')Yt2s=12+rl'rtl', tllt)696 d)//e4a4<z eVafzo'z "a

4{rnt n3 d ta-D rxtn-4=;1:::r:utn_t1

r / , f 711 #rql= " ! - , , =:+:)-2J^, 2l r t 2 (r'* 3t a,r)

t ' r Qt+ z)-

( ]ro,g)z + 12,2r

/.rl]+r)

ffir+iar )(l ra,rio,r)

/ /, t Hret=] ttatl = A

p, eaa tr)' J. o

AU

=Z (Lea ' t r l - ' ) ' = In=O A ' /

t - l ,oao/f | - |

t=

J- l , seaE.

/1,2 trl Wfy aA g-6qqa/Lurz- a,

z { t 'nJ ' } g t r t - t J '= l t 'u fn1

ffu "tYgt -jl -'Y6t = 4 t//,)-rlu du tr"e,ra4!e>

?rcEi* ,a

y t t _ 4 _ - _ L - _ z J, t ry : f f i , ,=77=F ' f l r

J% ab4^41 S-fuata/ar- n. At4 *i7t/<-t r&1rht,.t

iAl , 2y (r.-r) n, o ? oZ ZR . Jaar( 'ro /r.a/( 'l t (r), Pta( . t /. ) (z) a Pg +t

/t.J {er {ar7 8d urd 41 Taat* tu,

at S-n/-'*, 6 (/ n) ?r'/4y41 = 4-ar[u rgt ri'h6) +{bo* "' * s'

t I tt rp'l

.=o,af (t*l-/. i-'*.,.*t''t ) t/ry)

7t4 ar tha

//,6 40 olCa "U pee4 ef l'0, 4 4."2a6/

rfu rdt, xt%Vha't7 tr' h'6/ 4

cwV{ta1 fu .gzta o/ ll/ip '/dz/$' /"-/r)

/-/,Afff = oa'r( r +l-'t J -+'r'o'

UlilYrt)

t l t ? t s + . , , + J + )o-ptr /t " / 2'-1- "' ' + I + t 't

l ' ' , l- '

l ' l

zx" f4rfra*r^-,/ l'Lt /'tr 22 n#' fut/

a v d l d t * ' 1 e o t +

l * = , , i h ' o o r l ' e i l " r l o , ' ! t

& a'a d,t6'td ^*A f

; = -f ,lo ; tut "'' "tr"0,nfod tt, 2infi n & r"'l

Ac,Q na zlozot' "47'nf"ndtlo rz/. a+ t7o, tJz'eaaz

414^frt { I =t ,, e-r ) u cn"tLJ lA fu

/ac^b ea) A 4t d/4,t4.444 C /60,

g. I tt rurt 4 7on 2d 4 4 ( Hrltl, A//

b{fu* tf .azt& o/ I'o-t cu- 4tz rc 6 //Jt)

lttQ) rlat au y.n ef -2 oe/ A* 2ah ar

- o,r tja,f,

( z ) H 1 7 t = f f i = #- - ( J ' J ) Q ? z )

l / t+ t1 '

l-t'til fu fto t4 at't atl -z ad /f"tz

p4" et o, -tt d -r ,

llrtl) =i t t l g - t )

- 1t-

oa-d H, @ . Alr' t 7 pr"&n ,,/ /1, e ) c.ut ft, lp

aU /r*u.t ( ef t=O

& = c ' ? e I =rz (trr)(l-r) jn,*=o

f ir=ff ir lr.,=o-

Tlal are /aaz

- Y G ' = _ P . ) - | - - ' I

t . v7? -2 f r t 42 r f

* yt,.=-o,Lrh -, h+.tr h

Vtt'tt AL 4+ 'ut/o>t"u at

{rn'. = 'a,trht)n - z(4&f 'o'2/' hv o

/i,,& l4r1t=#" =fu ,

urnj=rt;t 4tn

lJq= l 'a t t ta . t - -?" f fe f

lt- ,(aoat)g + t -

lt- i,lrl 'r I

_ a.of fg 3 , ,=:' lS -etu'') (l 'e-Ja't)

/r., ){:: rft*:::r74Yr72= llil U6s = -

a,f x a,0 4= € . 2

18x(-o,z)

a ' ? = g ' ) f

z x l , 8I r,7

f/&l = J!I-*-" 'r ' Q+t )/s 'qt)

?i.fl/4e,tafa,lu ufo| = $ tn /, ll (S) - 1

yh)= HraStlQ) = ,

+---o,i- 9 =o,r

i , &

fr /-"! ,X trrrt a2fl:44q *t"il'":"k/'

6 rt Uarq f -/,rar4/bt/?,*

ry=.tlil =orf

Q +D0'4e)

= { , + 0 , h n ( r '

] -o,t

',iL h,- f pS = o

tz,= ft:l ,r"o=fr,= #ls-o*-o

7ha "c lt*c

V_r ' . -# "#&

o{ucl */*

ylt t=-l t h+o'r h

Tfuu dfu u"ry'/u lo

- !ryr -= :",'-1 ll -!:r (o'8 ): n vo

s6f c, t fnl=l ,n>, 4n:F

Ytt=Hrt)UW= %^ t' t - Gtr) t l 'q i l 9- t

lde orp^( YW/l a4

f at=o . Q *

()u) Q -4t)Q -r)

= o " r l , h + r t ^ r t j t f r t,;ifr ho'=f ra,) = Ot - a , ! $ | - _ ' a f - r - a 2 s'(t ( I a?,OG -t ) llrt n ?r!) (-z)

' , ltrl = -a,3'/? ?r,zf )n'2 4u*-ei

Lt+zr1Et't')"

t o, +tu e ir' 4?5,' 't" o")n

'= -4 ?er (lzt)'*q&r ''ro'o ''''f,\ ,';tren'r"r!

: -q) / tL 'z ' f )n + e '9t eq (4lh ' t ' t ' f )

.= -ot t?r //.2t)Q r o, ?t 4'; ( /'/" - /'/-t s nl't)

= -t2, J2.t (/.zr)o + o'?/ 44; k7;/ h 't o'+2)' n to-

Ya - -4Jr'tz *

t J-n"f

J i , l ( y ' t

o,*svrs!"'-u -QE.>-/==+a-luin'' I - e " o ' '

1 #t " - *

- p f ' ,Yrt)4.

&

t t , ? t l es=#

He oppaad f+rA/e 44

-AJEL- -!! l ! b: =-fio r u, /

,d I ( l-P

; - biltbal =kilL ft, = o. Qt ' t-P ll=,

I _ b , t tbc l - hPtbatrz- ] I l+to P

Tktt r.v */alq ^ L. b.-/t^ ,- b a / q r ' 7 +

Hre=v * ' r y t - rarrtil,*y'*

* 4 1 -

t-'tus,I =? {ot * Y r', n)o /t./? arlgr,rt.A(; cT.r6i4 4eA

tl.lo ufnT =lt n7 O, l,l/71 = #

.4qA tlag ayhc ,ra( pa.$ . Jr i A r

6/14 4 a/( n 4aZ 4'4" *trZ*Lat At* t . a 7/X"a""-'( "-i

t' '{tft^tt(

/^ ,,a-rLnL ,,. i , x, * &au .

x t qf D c7 ar/ OT 45'64' ,

x + 2 ; c7 tfr/ft n"r "JOf

o{t7'4'

x -4f 'o 07 rfr44 '*'f *'rCTo6/4'

x -2 D ntCT'ft/4 nât D7 af"'/4'

Yct = H rD Lltp = J/ l ' *z) +t )

Q -, fb- a r I a t /g - er-jal ),*"ar"f4r,a aye a/,f.Lpdfu ",t+putt4 ;* F&,L /*r, 4t* 4

//. /31t2 f l , t1 t =

Ylt = N(t) I

/1. 4 e:)J (7 - o, r)U', 7' *6) 7

, t* l+o,6t = (J+a.5 t io 'aXlro ' f ' ia 'e )

= ( l - cq f . i z . z r r ( l - o ,7e e i ' ' ' 1 )

7a/4 *,e. (,ate

{nJ , fr6o hl ,1,,G0,, f '4"n (-o,et'4i co'ol

r (r(a,f) 's l"(o, l t)D*t (z.zf n r(t) + lult)"

Tbncryil&etc '/ dt feb 4r 'o'8'jo'6 u

@r=,[ff i-,f f=!.,9f n ,rt !./d doa /, 774/ H'ttl a' z+{

tatd.(L)

HrQ) = l

Bzpntz. dt'nt'a"t't'^h' 3/7'z) *Iz4 Au

4+N /Lo6'r-

a ott *"itn"h" fu le

o/ t l rOl oJ( ' 'o 'z , o i l l47 ( 2 " Y -

p& ). rb ny'ifr& / o'tx;'o'7 Q

Itmrlltat'' ' 7t44 H' n afrnc'

"sH,te)=fu0t144 fr/"l

ar 4 o' ad'o'?J' T-ftt't"'

na{nifuA; *tt fu4 rttd' t ' Tt'&t Ht rc

&l-a&.

'h7dzQ fu z*ATc a4 ,6 y'n*,lrdab

n', /uV-t7, rtaa,/? d-e,( e lil4.aaqu'{

T=| u/i6 /<t

tt,7,t-lVC d ?41f 7. Ae

ft*. o,g *1 o,n = orre tio'tt. 71"d atr'

tM fo / aL "4,tttf>tu a

Trrl"llurn1 t Q,'(/, n {t b,/s)n 'i (o'flfn * 'l+)

/* n as, P&' atf fu H'L4'4 fu ao

dt4 e at,/f./4 ,"L af I't 4 Jtlt6

lfrryWop tS' 46 X I + a,e 1 qa)

/ t , t 4 t r ) g , * F l t + o , ; , z

O z4 t 4 , s 2 / 1 " 2

i + l

q-,( f: b*l= fiot h | ++1,(')n'Lrn(t )ot L ( I - t ) '

fl 't rrr,rtl /*, ; no';( 44'al '6 fr'Q

at ayot u a4 n *n. ,J

ah; 4e' fu

tr)* ,foEot I tr'u/ /*/4/t4'

S r d l e o 7 ' * A o 7 o ,

l * o Z o t d l A o ' t l ( t ) = / a ,

lt 'ti -+ 1O c'-t n +rn

7r2t ttgtt:<.t.V/;un"z '/ f t!'^ A1 '2. 77uq

t +Z A

- 3

a nqafi.e t'aly ryW-Trtu4e

t

fr? o)t/ ^ nô{ D

: 4fa//2

Itt ) = c. {ft|= 1 /::f-:4::

-4.2 -

f , D - Q ) = 1 3 - r ' - 2 7 - a 7

/ - l 2 - O , a

. - a , ? 2 - / , 4 r . - 4 ?

t .3 O

ors-l frr=r. l/b,s1 = 2,2 f

-D:'!,3y37 *e-,.a) orrs)=21.4+/,e l l , t , fs i '146+J te,32

2 / ,6 t , /2 o ,6 4 o .J2

4 i 2 o , 6 4 l , q z i , 6 2

l,g) r,f i '62 o' tl o

o.l8 t,4z /,-r /,F

1 ,2 r .3 J a

t , 2 t , ?

yg!'td .J t

u)t uzTz"6. // /e/o') -= tlrJ; ' --e '14 '+ 48

a t = o . e t b ' t 4 H r D = f f i = o

ao,, rt/a' el*" 4 ? r4 a. / + H(/4) = 4/rJ'a"J -/

= -r.2,i4? = d./;1ei:f =- o7,'J:^1;:t/.d+jt',7 t,66 6'ta+

u :tr,/z, "iurj

=> //0) = #

= ::#

= / , o f a i t " * o

t()e .a.ez- tirrf -Ln/ ,+n1n dartt',. t4 ))<A'{

"*rrr/A4 , fu "-frtt/

''n&'aa a't t<t'= tf/+'

= O,7& and 4t : rT/2 = /,f,? 4'1'( c</7'14f441

a,ihu lk /f. lhatet'ta. nL ylaa' a/2' tJ =o

ti n/z t , r4z Pb/, ru4 "aa1 le r*Pbou/

an /,*(/./rr/1 , )" .42 uet{ '*mo/( t

t^'rt '{rua

elu >t r l 'h) art l l l iel ia)- ' f f i

= t',o , = I . Tl*a )6 plaat ,a ld n *

/ ,e , i , ' - / . t

ni/z ( ra4 )

.!?ee"J/ r/14f a< tl'a'/a tz'uqap'<l T = I

tincf ht nf f."r /'ttruaf no-f

:' "(-rr/r,'a/f 7= Gn. riJ, Tlat z* &'Y"taf

fuf^t{ /4 f , Frurtn 7/u nhf,n'hil '

'.lzaptmu .dta,*+t,, lerc '4/1 t'/taf A" 'fh

ti a "ari*1.paaa '/ZA

"

t/'/7 F"al drz /s/r'{ t-, P"t'{. tl' /6', k< ca'+L

-t-ead .*r/3 /-/@J' 1= H(r):zQ ' (t't/z

llr e t'4,)l= o."o 6 eJ'' 6 oo{ //leJJ)

= 8. +et "' '

Thu 74'- t6'aQ/';icfr' atfau' t;' uow

flz*ttt, /1, 4 ,

f r , i r \ = 0x z r 0 ,o6 A) (o. ih +/ '6 )

+ g , * / b 4 ( J , t + a , 6 )

d &,q a.n (Jn r o,6 )

a,J& oo,ff6

f ir= a'r?"f

fiX =O,6t

p*= a.l&l

a^"r+ ca{ a rzzTattu eztF";rt rl . )/ '

lowrv-t DT aFe,a(,|, 4<eaaar '?6

tv'*6 a/tt

t o,g aift, neTz<fi"t1d" -(tot 4tr:__

t/. t'r *v 4f ,ra^"'*( l''46+ -l'v 4 il

r /. /6 // i,tt = # . 7/v llA rLA B pta7e*n

n : [ 1 - 1 ] ; d : [ 1 0 . 8 ] ;

w : O : 0 . 0 0 1 : P i ;H : f r e q z ( n , d , w ) ;p l o t ( w , a b s ( H ) , w , a n g l e ( H ) . t \

gat^"rfia

,i p oilaq.r( o:*V,-.fH":eft ui6rc ' T7ut4 D111 n '

1 0

ltrei',l

4 H(d'J t

- | 3 -

Jr r"t4u7rf,L-ftFo.r7 u)ti{ qv'(

aI6n <â&,, p o fq Z*, frtr*" 7Hr't-- e-,)l(;+a,s) "lao

4 -r, f&

4.f - e,,*

L . =

04 a*I

esre.fa.ttf ot

'= 4r4I

-Tiz V4"n rf'r{'t )o, "/ru 4 fu f&

d/ //rA) , and r+a fu 'z+Pan -/ /2r

rt, cat h rT , Ti44 if i { '4t'utott'{ adl

atL, frf4fr4f P"uo'l& iy'r7'zaet7

Jr ,.,rrl/ hpr 'zc/' Y att/

Th.p*ter-r /1.4 dsed '24/ 4t4/-

1at | < at6.

k , " " lw l ( t t

-g;, ( A,8)

ztwo V ALt" ^*fl+ fh"= a2.+ 'twr/&

fr *ac/, i6t/{ :6t" , ,Pn rafl/ ttraT 't't

lunqaad Z,|c /.cf 7n4f 7.2(t 2p,/'au(

aof i t wpt & an ) t f r7:+,4<'ca4a<' 4te

au ur,6ua^/tz/ t t o/g e*r At{t't't"'('

/r,rg H,(r)=rffi, t#f)=fuTo a'lau lH,ret'"t l'= ll'lrle''usJ ,,

c<'c 'dL'n"r

lia et't!- g l t 1 ee

t'u-'ia I

//.2o /./ rcl-) = Ir:si/4't2c

t't)e-'rl"Qr<'

flr,t = *I"1-1,ui*, e ruort *-fl nlc

t ( u' ' -L L,/u(n'he),.tfr

J (. to'n'e4'a"!a7 -;Ju da'

:d" -crlc

I icr(r,'hd lttc= G76,r* lu,---"

U.itn-n")k|c _ u1/h-ao) t lc,

! ta cro taz s7 /o o: ' g I2rr j (n-no)

I te e a'"' '9 | ' lo (to tcz '{'o -=

;-;--: 2

= I ue c:;0' 4'aazt'io) .orh f (n'no> '" '"1t t )

tle csdtilrt'

l f e / r t - / a l , = 1 " / " o { 8 ' / o t t * ' I

= l*' gt'ro I i rc e-jn'- t I = 1 toe'i'{- r I

: l ra wu) - i ' od ' i " :

- s l

= f f ,a t-+r) 4t ''6t)'* (-ta ati u)

wt ,i l zTorrtb (r ) - ftul Hft) aul Ot':. '

rfe* c/lt 'ttt'tru nr{ uTuc& */T''*:

n*n2^7*'^ uê $y''u{

/ / /? / l f l l=#

tteu yr& ar l"-l orta/ u '/ am'/A '"t6

ahrtoQ aÊr6 4^14{"44 e-va6/ '47 'o*r a6'nd

ti t$ t/',c f*^ t,6.t

;,;; ' ! , , , ,*to1I oat (o'6n r4Hleioi '

T r / ' t G t ) ' L

- lr (n''na )

a/( n-

r / '22 HqYfu=t+ f f iI tn+ t i = t ,oaa/ {X [aJ + u fn )

{ r f i = / ,oao t { x fuJ t u tn l

f/y .tza<1.1 at alz loarnt-

r r z J H G t = k = f t , r6 ao-r&am+tirna,( a, ntrJ+t,e?'u.o/gito+ t"

l fnn l = o ,8 X tnJ +u0t )

It ' t l = a,t x tq'l + tt (nJ

/ / ,2 / H+)= 1 i i * . r l t l =ow+ l ' * JJn I l ' *2 , /37+a ,s f

= o,r + -a'!7f, 3-! o'* r

l ' , ql ' r l + q2t

[';,';,:','-,J= [- o',"'''' i J[:::'). [: ] "^'

,d iil = (o,er/v d,6 rtT [::';,1rJ

+o'rutnl

- 4 4 -

7" /ad a l-/*+*tazaa^/ .unh7,ahir.

un ,r*n .!O, (

,w F,cQ a corctl G1) o.r{ H 4&4

/+e)=,e ' * ( l -a ' r ) - * ,(l- q s)Q-e,r ,t

= o ' & J - o ' 4 - I /l ' - /,J, + e,+

't4 <ahtr1i"ta; k;

f+rn+ttl=[,, t - a,Y f,?|,4;Juh)

!r,r,*nJ'L / a J[x"hj

I rrl = f o, & -o,1 ,

ft,r;'rJ+ a tn 1

&*: x hl = A.i (l-t)X/t) =oh+o l+t

4 XOI ,let aru aLrtat-f'/- aq/' nV';e

hy'* A&, / e't' ^"?t*1'.4 f& erl=1'7ln

)r(a14 e a. n '>F , J/ X lil Au ufr

uryr&l ,nfte A& 221 4a u";'f*t&'

dt4 xtal arnfet'no aaafrzid aact//af"zn'

eni aU Lff46tu i n{afre ' fu l4 '

//.2 (2) ,4rr&f az S -n'aa/-.''n a

{f"1 ^r t / to', J = '2 .( fit 't J'tt fit 'zi r 6 utu's I

Ylt * tJ-' YG )' -s{' tl/r- / -'u0*ll'rurt)

l/,24 At W ab-rs/.faft > ,4 M, //.r/

oL X,h+tJ = -4/fx,f"l -4zfxrfnl + ufnl

XrtTr+rJ = r,tnl

f rn l =a, t4d 4t r tJ + o.62f xrb l+4dqtn l

//.?d $ X6t ,|ao a e,.ye p& ef /=/, cfcltt {K ryfaaelzd aa

Xfr> : $' + + O-vno otctt 6 e7rtu F%t

;8"4 = l/'v, Xtll'+ = f'h /\'t)X'tl

l - t -

l * ,

4 e( iL,t* tJa. '*!zs noTnifi'{a' /44

d.c4r t. dn A/u+ ^6b anfat?ac't c&(

eflr-raaql JflO do r7 '+c7' . 77144 r,r* lrut

lr-_xfni = l, i tt-,)Xtp- i hrungtn^ + e l + t

4 Xtl, tltt zto 2,4 al l=/ ottl eP&

&H nryt r'G/", ?lu Z'Aaa t , dnt '6 L"t

,ttf+ttttct X[ol+A 64 n'+@. ,.h', azt ca4'

aU ,tV"fto>, ^/.A lf & fuast XA; lct

v,u i6 kwn/f:{:1,-,Y P

- 2 1 ' " t r o t :l/U'ffi =-* 'r',

- t & . - ' t l + J - ' t i

l ' ( r r z t t = ' z i ' ' 3 '

{.$ tnuau< l-Eaa7la"- o' tfu utf>a62 af&b

#ro|'o. t lSJ='4 l l tJ=l 'wo( (rnl=o

{.n ,rU t edt-+' 'rrtam '' 1 a*tl 2 ' 4l{ ta f tR '

t/-

fie ulrc{/ tu zfu <"tnt 'to Poel 7' 8 /2) -

22 J - l + 6

/ t n t l '

xt[nal fn!'PL

- + f -

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