Chen Chi-Tsong - Signals and Systems-A Fresh Look-Solutions

Prévia do material em texto

Sie * Sffitu :l faaL. to4
,tece;,A4;a tla*ual
44Yan z
,,1 Na. A ceU & cu.4 An f*;e
lecatais.
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 .*artti^a/ 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=g
J /-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
0
t 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/t
t: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 '
o
a, 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= o
0
Fsrrt'cr&t
2.s t5
I
I 1 J 4
3, lA te t
J 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 - ' bo0
4 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 In
L
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"'
Rc
t
^
J
{
Bg nue*uttual
r = f
t , - r2 f "
t,
= -12'l ' 7fr
j - 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-1
t ; 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 =;,* th
2 f '
uJ:2tr f=f i -o, f
,')r ^ ^{atao
clfrA/t;u-
P =+tf s.
c - J - = L l l -J P 4 t ,
u=# =4s d/s
+r(ry
3 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
.{x^e*uz. J/t ; x* e *^cEer-,?
*^&+.
Trrat Au rlzre 4z co**aL
- ( ,
zn/a, Ttz TLuulczttA'?,
r'' 
JTr,"tlat .J*ru-a2"d, =t *u
4 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 = :;+6
o 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-eu
a
= 
" 
-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'ryfu
lxo,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 ' o
In 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.s8 4lf F - zPo > i;. =2rr/p t rr/fo 7 a/a/2 .
xb)" E E^ ei-Ac
iln'<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 *tle
E.o
Beeaua^e-
(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-- -eg f"/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-,'r^A
Z
i5
I
4X,(rt to)"
{ o.t X,pa"+c)
larn*/ tG-c.t ' l ccn
t
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-^uc> 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* .o
f
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 td
ct
=/;fi,Q l v C c Lt 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 '
- /- , "m
l \?4 ftQ
Es
1 6 d
o-Lf,rr*rtl'de
z f i J
-&
E " = * r r x t x 4 ^ ! = + =
fu ^o*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. al^a *)nnrl
*7tttactr s/ orz it V.ri,+n? /.tar.
in r'- t,r6 ) oT. Of lao ^A4"'/ ,Ft U' "'a oLt#.
4.26 T'A s NFK = Fz4 zrfl= C6,tq l,4J
v 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 J
i 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 +rr
VeZto
qrl 
*Xotul * -o.zti + tT . Bnf 
'7lc
4 *i/( & tit&' * Y;r'iPlary
G 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;^e/ 
'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 /<^en 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.Etb b * 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. t
CtO 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 o
I - 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 ( at^e{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, /4^oa XOf) '
- (- 21 24.
t o e J s g c
5.J
lxooq4 J
lYt"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'"4a9
ry a,,,7t;';^a(. 
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"/ P
77rr4 -rrnf A
- a
6 7 8 .
tXh,) 1@d'
-4fr{Ee
Jd 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+ NFR
I
. 
- t ' l flnr)
j\
:
I
4
dc, 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't
t 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 J
a * 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 : f
1000 2000 3000 4000
100 1 5 0 200
L = f , s N T : f
L
?rF -
t - N - l
d . T N = 6
2 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,F
r 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 li 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 = f
U r 2 O r r , 2 . J . 4
t n , P t O e ,
f , . f
T : 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,
{, t3
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 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( nyni^aced q *;'h
4r 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'2cuO
to 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*
aoulr
I
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|," fr
fla 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 I utn-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 $62 +'{rt*)
€,6 7U- aTeta* 
"tetc'*da( n'
dlo = (zt sr) utc )
; ,,,-'A?. dri r* ryY 4Pznou
il. c-4|;;"n zx;t) q e /'"''c^6; 4
d t , 4 u=4* / z ' 
a t *
{ t1-- / zt +t ) / a' 
ed } (,.Pot) = /' ltt t {'/t)
ea4l (2ttt t d 4/+' = 4 /:Nr) u'(3) = c{&)'
7t4t de qo& n 'hzaa- '
- / 5 
-
6,/ ?1u naohtef,r, n/e
{ftt = (* r"r, t) uk)
; u*tt-*tyaet 
. 
,f ;' Z; *VV
&-"aqnz dL eqt/4eut{ catectdt h I
/.","6; / z;:' , ,ty' 
ugz'l*uz
{tx) c ( cat uot)( ct,rtt* tl'ftt) 
s/'lct | {'e)
(m ar t ) rl u,(a' ot ( cA bLo) 4ttt| ' 
* {' (*'
6, tJ
- )
TAuo f,tb ,a4ofu a 'htu 
a+
6,f, tlr,e Dr.<1af+ acu42.( 47
{rot = /.t (uat)z
i ttwnaryrhal, 6t z'tvPw'ual 'drdd
vrqh^tL /e 41 44ltu 
aza'aa*{ ca
A P-#Z"D, 6.f,.
6.f 7/u DT tTc&n 
"Aac'-ib/ I
{rnt = (2arD u fo 1
n runeyho.-l*'<vt* /tnl tteV*t& 
'n'!7
a7 utrtl df i .b;t ,-Vrt '/*tca6ot 
zL'
u"//';.tt/ r2tr?r) pt a *tD^ 
a/ z'1
'A,' ittr , Jt i y'is+ 'tt ri ffra 
6'6'
e- 'O
E"a'*, €, -' €-
u e'&z itt(
€+t o
6, tO 4 o- /4 ?az. zlz+t
f t n ( t r + ' l r ' , + t 
= o t u ' r / + ( u " + l ' l
= { r + X / r - / * / , n { ,
Tr.a ttL cTecZJz oo nel ^&oce+ - Crt te<
J.y'i 7'f -, au( 7 - rJ , f,,h lt: tur/
{t<cntt / = ai , 
'7la io c /as}u
. 
ui'- 
€+ U-, . Vo - e{_ - Yoi , = f . i 
- D . , = T = V ,
i , + i . - *- = o 8. .ct t . 'c-= o
h( i4. &', = - L',- fr
Rz
Z=- * * zg td - - i r ' t c )Rt fr z
dr p dt ztcnt ca (6'/?) '
Bc'n* t-= O
e = 
u o 
' R t
R ' tRz
R' g*s*ol e-t €* =4'
u< &nt< ,..= 
# 
F, cL
L = # . , , 4
aA(,y+q^bu ha ud*re
R. il. 4t /R. A=r,2,3
*t = -n/R 
. 
o,t.rl irrt 4
* f , f . f- f 'o
6.t/ 2/* Va" u(()- uc ar',/ /eOellq -dc
.4 ira ,*to&, .c-v t J4
-{H = R iret
7A44 d a 4t<-c Arn --r-u'"-f o7u'2q,
t r
' 4 R
6s
+
a
-+
'ac'
6.tS rct A
6 , i 6 .
t
Itt
'lllq 
uv i<ttC, Zro -:. q, s O, + Al
. - r6
7' | ,h i ,i o.4r"{ J< caatt {rn|
a, aroflJ, tira an^h; tzcrts of
ctnfe4; ru ?4at-4t a/ arnsfl 4/
afn-21 
. .l!r n fr;. ,z-"ir.rl '&'cmt
t$ 
".//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<o
6tol = 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 i
2(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 24
i t : f ,v. 7aa4 '( foI= tt f YT'r/ f '
uLoI' ttf6t
Jr , r t=, ( t t " l ' i / ru t
tir 
"( = 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 h
tt( z t{fr.+ nzn / nna? J ' Jrl FrR
15 f," *i& 4 /tot'z,.rurnJ
; l .h7 = 2, i f" rnt = f 
?,f , n=o
I 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. *f
f 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!(- frrhi
Q> 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 $ftl 
= o
n>f ' {hJ z O
I,to tet {5frl = Z &tn-G7 u..te l, ..rt
Q - o
v, P"/no ui&, tf or7 -J{tn-rJ = +ufnj
'u { t l = / , r t ln - rJ +zufnJ
;aa7i&try utnl = {,rnl d4 tutl 
.{il'q
/.> n <o. u e+rtp*A *czPrltt"f
h:0: 
dt l = ,, f {krl ,t zEnfol 
= z
r,: l : {ft l = /,f {fol + 2$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| F
ao
{ 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 artd7
i{'o
ltnt= Zia'ret 1v3 
l '+
" Zlrn-61u, fQ
lry
= {, 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 -4tur41
l = 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,tnl
l=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 = Z
7=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 fr
4U 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 uuL
h'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 ,r^art'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 u
9., A
{rat = ^ Z 4 rn-77 ufeT = a ii 't r( l
2=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
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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
ul
l ;
t j
r j
iJ
r,{n
'rtn
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Itn
Y.[n
fn+t
fnl
[n a.
lntt.
fnrti
in7
ln+
tnr
fn+
fnj
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lntl
[nrt
tn7
7,
rz,
xJ
r
ft
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L+
q,
r,
xJ
x
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h 1
td.
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7-
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rfn
t,tt
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9t't4 t ,
o
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z j
t L n
tt,fr
n l t
fqat
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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 eXaa^e;a 
e/'c
u(n<1 utn'27 utn'Z)
f,tn7 r2n7 ,.rt^1
utn-+7
x*tn1
Eotr-ol z 2 ' t l -*
7 ts, daat]
f, t rfirn, "' r
- J ' l
'1fu 
a lfo -tnorc- 4aeh ,{44f4"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 - t^il*'Ent 'uXt*t*':T
^d/ l',tc*t4 /4 'i It r-tuP
N 44ze
Yrlt - 1.eo?/5 t-' Y't| 
s llQ )
or (t -/,cas tt)' ' ) /rrl -tt(l)
#=fu
7,23 {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
rk^ua 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""'^A'
;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
#=ffi Itt 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 
^Az
,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?'m
aare{ ,* 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{af
u 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"
{
tIxt
J
2.
J \
'flu wz6ft
a& it z-St axt&*
i t , t x z . f b
;6 e*ttt+n'f ;
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2.
Xt
ry-lru#I:I,
"9 '; .f , '$ui nr lfi 
"fl:L
('xitxr)f z
4t ,cdl
a
.: '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 Al
o
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 n
44.+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
frtlr
I
o' r o
' * r =
BeJ lr
'it-/
Pt
4 = l - t
I
I 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 ) ;
I
0
* c i n / i n * j - ' 1 \
u r l r \ f v v L L
;
* s l n
: t )
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'dx'
i
I
I
I/t'fl,^n ,r,r,-.-..^
I
L
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 r
t-
: L
- 4 f x , r Q t f c 7
' ' 2 X z { = X , f / O 7 2
Y: = -tFi x; -L#?ir * orJ) U
rzt '-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 1
a
xt t 42 x ' t
X , t z u
- + 4
| = 1 , a
x r l _+J
7 ' 2 9 u
+ 5
x2
z 8 t
1
-. 1
, J
1 J
' , 1
l
J :
X r 1
t +
- 2
6 ,
xt
l
-(,
J
o
* , = -
i r = I
{ = x
x = I
L
{ = 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-
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h "41 >) a a*J x/a) = I .)
o l
6
r
=A .lJ fte)dt
2
- 2 l -
,$ fc= t , d tn g,/3 tu) z A
%s 53
z A
,-[-*T +l.
u?? il=* YasI I . J
g
., s f/o
l 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 ' 4
n ' +
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<
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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 ', P^a{- A,t // a/
6
* ' ( ia ' t t )znnts)=a6
2 s . , '
c v,JR
- C X - 7 O v^rss=#rtt)= /osr+z6.tJ _ g 6,1
. f s r t c t
tasl sli * I
J,s.r to i l fsS= 
-""* /2
\ -. fs' 5s " ftt"!-l: ,, u,ttYo= f f i Voui=; ; f2ost r l5s 
r /z*
€'- tl rc )= f f i i r / 2
Tku 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-'
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/,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 y
Ytt.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 = _!_+a
LfrsS 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{nau
a -
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 lurtt
L4rctl 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 [ 01l r,trt I= I o o r llx,itt l. lt l"tt
L+,, 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; 
"j
s + 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,ela
p t
D* t a / i ' : t / 
, 72
= v a t = u , T n e a N
4 * l J + u
i , ' 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 o
t t ' s {
? t ' { 6
- 1 7
u ' - [ 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 Z
i 
- / 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 ' ' 4
s ' ]+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,64^ar ; i;'* ( *y'f;;')/t{)
c&f, o^a '*'^'<-'/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[: J
J 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+ l
s 2 5 z S
- J
ls
\u= ff i i l ts)=# =fi iuot
y 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
@,ttVAet
a
Xs 
" 
X l ' }xz
?7- P/f-tnnl - L'o&
/,
4uf<a
u = * 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
,&t
Ytss
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 " f t - 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
t
u
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-.1^a4 lzfrtz 2 4../ /aet rutf c/.eart-^6rf
tfu 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?&3zr
f 
- + 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=o
qJJ /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|\l
f ,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 l
J (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';J
Tfu .{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
Pa
Yrs) =' 
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 'la^aP 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,
J
J
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=&' io
r '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 I
s* l + z , Eo 1 ,5- o . l r j
t.t, l t ' t o,,f, [ o a.s t 1
' - 
lo ' t | [o -z. j? ' )
: lz,.tzr
l 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
4trf
3 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 1^eea44 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'=;ff i
6 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#'t4^e 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 =
@x.ct-i32
fu alan<t n P+r{ /. e. c,* *fitu
fl!tt=&; {/d = /o
c44t
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 i
r,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
idea^A;tan? Itu /* 
aA t10, ah ;e4^(
laxtyaa He ; 
'Td ca"zof '*{ c24a'{
'{n /*t;tr tt' ^At 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 xH(l'/oo) -- fr;itoo + tao
- 
t o o t i n ! ' = , o . o I e
I o a o d e -
Vru ilL onorlr -sta'& 'v4Pet'u ( /tts I(/
qru'64 4rt 
'uf*l 
= Z+ ea/at - tta Pat
I
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 
= y
R 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 j
ft 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*tsya
7,(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= p
s+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 '
u
o
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/'ffi
V,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 -
nera^ef 
"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'
uao
ktl l , 2 = r r f z J ? f 1 44 1r '2z a; l
2.+, t.,e 4fa* '4t at7?'nd" *'ry= € t = O- ; -
= L z r ^
l l e at -aldrtn'
2
V ; = P r = p = *
Xtol =/ | !,(c),
oo
5 1 . 5
a
q
o
o 1
f
=
r r r A K
6', ..-
k+ ro .J , /oV, ) 46) > /o ' ( " t '
fl,a At fi,att/+> /*f^ 
' 
ic24 _
H,n=#, ; f f i^ ; f f i
Jf 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
o
o
5 1 . 5
o
a
0)
o 1
o
=
c
o 0. i
,.Udtt ,ztl a' 
| / '
- 
H s 
= 4 ? * ' 8 o o
s 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.ila
S ' + 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 
t4
f s
, t . C(_t) Pls )i {q=l
r- 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 . + . = ' A
Z ' 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 s
2 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$'r
rtu .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 4
r ' l , -Al z| | i ' e
to r -(r+A)/,1
4frn4 1=> r+A >0
- t < 4 < l
o!.Hr' t=ff i
A
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 = W
t (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 ; ^arz 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"
, - R
R cs'r t
frCs+l
7 -
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
J vu
: # n
R, 4 - R,z.t
J'tt frrutok, /*e%b
4 '=+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
&8t
F,
4 W-F- #,
- 3 ? -
WZ ab S-tra*/ha 6 (?,rtt 7<?.4
Ytlt - 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 - ' ) ' = I
n=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 ? o
Z 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'/4
y41 = 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' Ulil
Yrt)
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"nd
tlo 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 , 8
I 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,) = O
t - 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 - r
arrtil,*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 n^at 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
//. /3
1t2 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)=fu
0t144 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 z
4 t 4 , s 2 / 1 " 2
i + l
q-,( f: b*l= fiot h | ++1,(')n'Lrn(t )o
t 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-Trtu4
e 
t 
fr? o)t/ ^ n^o{ 
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!'t
d .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& o
o,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