EE8591 DSP

EE8591 DSP

1. OMT © ~
CloMitication Of Sigrak and pies |
Signal! A Sgral à dif ob 0 physi! qua, LRU |
Carries Some anforrehon ad yooues Li ome (mimere |
indeqendart vaatoiles
(a) Seca Amal, noise Signal, ECG Angra) y Power au

werd 4 aad kprahure, me. ete

pen
Er} an Ja defined os At of elements of funch oval

blocks Ustich axe Connect dogetter, and produc an output
Ke on input signal.

mE
am output

a oases

Cet) eleciital pts, medianical Apter, biologia Sten,

clechome dontcel ejem , electronic After, He
|

I Signals ove broadly dom fied ido
> mos He Signe
> pisere Hee Algal:

China ous he sil il
=
A Ala eat is specified fe every besten of Het
ÿ called à Cohnuss he Sigma? (ET) sig) 29 4 deneŒd

15
Eg PO" ey au Arber y
discret tine Alt =

Discreta fe Adres are defined only by diente
jastads of Hee. Try dans by Win], nadar iahgey
un
ex) r atade fuera 23 |
Wel. u

2. Reprerectation of emi u:
Conknuowy Hee atgmab ove Teper Ep
Y) Funchal vepremntetion

D Groped wprerctetten ali
EZ mire v |
| 0, Aria LL,
o fune) Spa

Reprmatete of OT Arab!
Discreta fine ¿iguala ove opened bg,
» nchmal vepresedetièn TH) Sepan Reprepnietion
5) Grepitet Teprenntalion W rabulox Reprecctotion.
Funchinal repr esetotion |
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| -3 fer ner à |
| » = op nad = |
| uns | eno mis |

3 fey att

fer nee

2 fern:3

Gpat vapor -
The DT Apel Ly en Derweil.

ee) mea)s-3 „ame? 7 Mose PANT | Mer
=|

|

4

Grephical won‘

3. | sequen Represedabion’ -
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¡NS Bi A hv ge BLES told dt des

> aus À 212/0102) Due meme, do atop à
Tabalos, Repterentition -

The mogritudo ef th Sigel ot da
Fa tabalen form

| Elemento Continuous Ree Signes (Rosie “ne L) e
There alementarg Anal Serve 02 bosic uilding blocks for

| cemsiruation of move Comper Aigwals

«he standard Sal o,

Quest Tmpelas Aal! cst

ns nanan ng Greate due Rates: $

pa
Saw de>! +
oe gli fr bre
Hu pe FT. I fer tt L
te:
Properties of CT unit impulse function

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le D

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æ

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lo

4. [© voit Sp amet + ui)

©

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fanion +4

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+

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at

tro

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e fe tz

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o

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|

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nips AS Fer allt,

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ut abs Ae BD terre
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6. (O) Gaumiar Function
nat?
gate et i tor ex bee

Bat.

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|
|

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Elementary Distance Time Sigma [Basic Signal)
[ED uds Tale An) CE
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seo! for nse
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Preperts Of diyurel Kore nid Topube digeel

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@ Sinusoidal Sigral! |

y-mence az À diner | en <0)
are AA 17 s = As

and AO

11h.

= Tr aby opp

Basic opFennon on StawaLs
asic opseanen asian tS

O Time Ai © Time reversa] (Dtime Aeabing

© troplitude sealing © Signal Addihon © Signal muthrlichen

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re noe df of Apel may out in Hime delay Crist)
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puter |
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a > an) > deby by 3
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i Î nine?
ren), 7 x 1
2, | | =
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ol I | 1
To aa SA “WS 24 bo 2 aM

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Biquel. GO volathg a Abel by 180 locket we ser Fe mimo

| Image gie Altra AUD, Ond clincted by AE

act)

0% aw

fey

9. #) 3) an, me

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Kee Comprtision

a Ss ato € riphed by at
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ee > hm erpartion
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ED Given A; fore the Algal Into nt and
AS gral ah) , Hons pu

| mn CHR).

ant) wu, |

al al, ser |

Time ur

a et u S & Tos le ins +
al) 5 ah“
4 Time exponded |
|
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EP For Me Given Bigrad Xen), sketch 212M) and tf).

10. Yor

Yio) = Ato) =1 |
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ED = mew
yo = ax) =
te) = a

3 JO = MA) asp

90 2402)
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412) 2 au schszel
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= YER 2 21-4)00

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|

ALL |

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3543

|® Amplitude Seabing : |

3

The Algma] wtb) oftey omplituco sel resalta à Ant)
eile à
mo Les An de only rend
| Tp A>) > te Agua) à aplica ieee Ze
Y Aer Me Mali oi a.

11. CREER

| xen) yond = 2x1)
a

| \
©
© st si o yl) = AI
CI LT *
+
2
1
O1 33 + 1 à °

lao 1joctcı
mrp 1erer
pected

ocres sine WE jecteı
peter za
sey 2 ceed

Pieter
= sta qe; acte

(98) ame ns) este, hi
| ser
| ya mes ated = foie 43, 244, 350

Le

pia, 5903
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de ;
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ae o
SEO] qu
Y
3
e NE ®
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12. 29 amo dd ma 3/23 1

Yu) = MX ADEN?
ges dz, 2e, 343, 6x2]

gen 242,259,583

Ralotionbip between impule, step, resp and Hatier

|
| que iz uy PS et E
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sto His y Sitting Feet
en were EL Core)

Y Stat = ute) Sunat =t Jeet 24% Sünde th
a

iris duen
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The fallowty Uerevch Aoulel be followed while Shaun
O Time alfa
@ Time veversal
© Time sub
O berpUrude Mali >

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| Y ut) $) uta) -U lt -10) i Sar
Y st Y) arte) vi) Arte. |

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aL)

13. PS) E
HD ame L243 rra 3,23
Yin > AAN

yA 2, 21, 383, UDG

yws12,2,5,73

: A
A A dep, snp and patate apa Ia or |
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aide nit e iS |
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“ + &
Crmnpule) Lunit step) A

E

|
CES (wir pumbotie)
MW Sstat = ete sie a x
Sswar D Jumatse jeu 2% Sundes E
HE)" Ar um du = sue
The Fallowig Mevorely aloutsl be followed while Ahaus
© Time auifRag
© Time reversal
© Time suelos
9 drpühule Mali

© Sres Bu Allowing 01 signal
y un) Y uu) 1) Sar
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ate) ute te)
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Sketch la following Alprals

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2) ree)

> 0) UL

Fe

pat) o) -uvtt) d) arte-2)
D 0-2)

uri)

ur?) ath)
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ze a à

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ante

16. O A oficio Ree signal & fil o>
AU) eb Ub) | rt
otterwise

= 0 }

Skelh a) att) DETTE] art) Y ay)

Lay qu) i
qe
sl
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%
%
Y
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nat)
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ele
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a
CETTE or A

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UE 4 UCL“)

9) wtb) Ut)

ule)

uw | E |
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i |
ute-u)

17. ©

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(90 ateo -uce-w)

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im

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y rn Ste)

5er Ste)

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an 9) atuti-t)

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à 9 aw 8lt- 9)

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se
a) At) uC) que aie MUSED
uan
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o À y € je +

ary [uy outro)
A

ace) 5 CE 3h) |

(6-4) Cute u

de

© A cr: nr. ds phown. Sketch ad label abe followieg Aigrals.

=

af |

18. DT Dial e
© Plot te following Morel if mere fy, 3,-1,24
À

arm BALA)” Y tran dy
Big Pa a apes
3 > 2
ME > 2
HT te Ih
AN PE © ae Va a TT |
rT, re ae

2 7 |
| N N
= oe A
Tr
lo 3, | ue? enn)
2
\
Pres © oan cal
A id
À get PTE ee)
* &
2 %
x [

19. @

each of He following Aigrals-

0) Mim ulm)

1b) atm) futur y

€) Am $ En)

|© n dede tine Aigral Mn) da Shaun in Age Sketch end bu) |

ag
|
x 3 |
| 9) am ati ern |
wind urn |
: \ |
ee e |
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0) MW un) -uw)
u
un?) ( , fine]
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ve | 1 |
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e Un) sn)
Hon) sn)
sas)
1
1
3 n or
| pdditionc! Prblems el

) Shen ue following Aires
a) DULAH2) -zutt-3)

9 wary Çut-tsu)]

20. © For Aigral ALO Blown dan Fig. fret Bar sigle |
un a) uta)

5 D art

© x %b-2)

d) At

y mm

a
ES
&

21. &
aes > O)
A Jo)
ya “e o
als) .
o| 2 “ 6 3 hi
a) act) at-t-2?
ale) A
2
‘ wh {
tts ==
Evaluat iu follo iegrels
eo) SE“ sie-Dar nee
Le oit#s
ate ee
- e Es
= Ce
D Jesu) Sle-O 21 ;e26
o oy tte.
= =36
= (is
3
e) J S00 ae sat dt El=1 tre
© o) t4o
[sesnt} ye, =° *

22. 4) EC a

ey

E [e Je =o

9 SLsw-ws2t cb

> Gr. Bed

= Co + AU D 204,

© ves ha Fallows Aummaltonsin
a) 2 sn

©

Lo) ©

Y À Sm-twsin

2 (Cases © ee

) msm

= fs su
a Zsume
RS A al

e £smma
+

= BUN.

‘8

9 Se! ste) sue) !

Sam tin,
Sins

23. gen m ®

Pto oe
Continues Hme_ond Distrets ième signals are closi fico! os,
O Deseminbre ond Banden Arab
© Pwodte and Aperiodte Syrah
© Energy and Power signals
© camel and Non- camal Aiqrals
© Even and odd signals +
© velevmiatsrie and Random 5i grabs

r en nn
= Detaminaht Sie) Random Signal.

© A Hal extibihe no haïgrel chorecteniged by |

uncertainty of IIS mognibuelo ond luncertainity about IS occurante
Prose at ony Given time Tested % called à Panclom signal |
% Called petamaèhe Aral, |
Has regular potter | Ho Ireguloa pattern
© Ms omplinde & plox wate TS amplibude plex Cannot be |
| Predictid in odvente- Predided à advante
o Can be repr by Cannot be pra oy
| a) ayustion wrottamatial {ua on
In sad Aire, Mt A) Voie Aire)
weve Agra), iaguler wore uy
Alpral. 4 |
a moe Most
| à +
| So.

| ‘To fete |

ON

24. © Pulodic and Apuicdic Sigral

Paiadie signal fpantodie Sigel
O Bañera) uRick has a left 5 A Agral usbich doelat have
Lal late mbit rm nae O Pattern ond ui dessnof repeal
Into af mei called Pertodic y

od ats .
pas [et egos intervals
O4 ct Apt periode A t
Hz ACERT for alle. a
“a E AAA ay

FER] women fray,
Fa ee nn)
A DT Agra) ds peradic , Hf O Frdomental period tanret

ANUN), for all n’ R
, te Pound Spirale At pea),
NS pundematal Period $ 7

mods Small tänteger ©
© 4 n= mueva data io | (62004 win), Use
+= Lem(T,,Ta,72) ‘

Ko Adin, ten,

| (amorr w30t) em.
A Wend E ALF AIHA En) |

NE Len (m2, 03) la que
Wat, shot, cat, | lam.
EA

sur, it et

ARTA, Anata , torn, ere
> A comporte Mal Y parce
Y Ua ho Turn 6)
Nia Ns Oe amie ef Iategers.

“PAT

25. ey

ol Eno Miel Power signal
O Te Aigra) utd has fire | Signal uch hos “pute
ond zu avuag pair | soga perte and fiat ener
© Preertockic gra ore Chample | Pemioslic Aiguab are arar |
of Ener) Aigrals \ Of Po digna:
O Enero ae a y pair dea er Aigeal Y
[e 5 ‘Set AL Souls Pe ae = 5 Vato dt |
|
For dr ie
I ml
an
| RE ae YA Per Pons Age)

[exe | 62

|
NEES Energy one Power Aigrels ove hall erclunse

> Energy Aigral must Le of Rte amplitucle ancl Anita diva fio,
amd ad prie and negative Infinity dime He gral amplia
proud be gero -

® Casal Agra) [ Nen-caseed Anal.
O Act Agral ds old tebe
cause If AO | fr Eo

A gral 4 paid Lo Le non-tausa/

@ animal if atthe ¡to
©) 1m=0/t>o

PP Fev DT gral any = 0 pase.

D D non- casita) Agra) dono |

A |
PRD der Positive Hoe Later Val. |

© For DT Mgnel amro neo

À A tamal Máral Asamet 225+
| for negative Time tata vel
fe) un, euh,

EX) Un), nt), E ue
Ar wt UC, ui), au, N y da

author. |

26. ®

“Bren Stay odd Hip

© Aer Ayal wy 3 sald te be DA are m À ada to
an even (Aymmebic) Agra) y ¡EF be ax odd CanBAgmmahic) Aral,

Botner Bu editen WW sabio BL conciben ,
ALO = ALE) ET
For DT Al, For DT Aal,
Am = an) An) = Un)

1© Te: gras ore Symmete)
obeut ta Vertaal ati
KA) Ces verve

D The Wgrals ore aa agmmee |
about tu vesical at
| QD Scr weve

Taste tt |

Byampies om Peadte € eeweckic Sippel >
O Prove teat A Batwot +4) Jy Pemodie, |
2 Amer RA [woe td)

Mest) = 4 48 [wo lean +47
= Asa L wot + wor #7
= AA 5

Loot + oon 563

= A A0 [ot $) 9)

= dt dde

Am (25 46,

27. 2) prove Hat myc et Y Pewodic
a ME
| 2 à mtme get hum, |
| = pet Pie
alter) = gt

NA = AMIT Menu ee given gral à Period

| — —— ade
(3) Fromine bettie tha Folleto, Wired are penioctic ne)
| pewiodic oltermine the fordanmadtal Period.

y ur att)

| a) suınt D 40tu dy e

IN EA D Ain rent + caro |

Date) mans Ya Haan

Y) ¿eta start)
LR +80 1) unir m) 24 Conroe
ES |
| ETS Ñ : |
Cox ant y Aho) cer jsut jane

TH ven Aipals pagode Panic), |
Te 3E 226 en Waves |
> “e

Parodie Lit EA

BA og
mw.) Ce 0 pw |
un fe |

SAGE à probe wile Pee) 7220 2D 2 24e. |
Bra UID RGB Only been Eno deze
pea du Pedud dp Periode Aj) (And od urn à

no) 0 periodic mal:

|
|
Le) nz nt um
|
|
|

28. ey

ue :
ul = fa arpanankte| Agrel dones

a) aw
À pet (hava it à parodie 4igral
Y .

Se mee

ees

S quer ah ii

3 me fe Fe
= Da =

anti:

qu du geen pala opened =
3 fin Doo Dt + k ces ioot

ati toll MH = Fan vee TE
ait a y testeo €

y toot

D nwo
oro AE HED ES
pa En ; Math = rent
22m +28 -
12th = A da 219% y dun 8 36

y penvodic

ported) Tis Len CT)

| rat > mI)

29. æ

Wo me Ado (lo EH) -2 Gos (54-2)

ge vie MU) = Ande au)
re e ne N
PA :
so y, Crane 9 Wego) Venu perdeabic

—— Moca)

Teeny We Vet.

TARA Tete hr
Tm

» au ee
ao: FLEET HE) em ie Wy,
4 a
ER A 1
mip > Jcosbt - Amb ne whe Le
20 le \ Posay)

pira Parodie Aral
m à
purdonetal uted TA + 2 + D 1-0 GOT

ar “BTA Jéce ty Ba Render! ema.
u =

But +2 492€

lt a nal A
TL AAC

° x
She uty y fen odo ©

and 24H24 à ende ob

Both exe addition E Agra with diftered
Venn Ha voie) A zum Binet u apartes,

D wes

Lu), |

35 (net rete
¿ss y Et

Y) ary de
«a = be Ve

30. RS ault-s

att)
==
u; a À
o © =

E
ae)

+30)

TRES AUD Algae] AD dea pad, ee
gan Miral à opened . + —

m My s2¢ ws20t
2- a tite de Apel from ES oo

à Fa >=. ..o
cos nt à a cn ee Der

| = Mutts 2 sont
À

p Debamina “He Perediätg fr the ET Aïe à
La) nity wirt) D) nu = Sees UD E+ 74 SGT
e) az cortos a) MOT KOOP (IE) + e)

1) 2209 € + 4 ces Yi

Ade Ay) Gen - ao [

31. ale 13)

Ye

e) AE tes 24 Hin Ys

Cre ar
228 27 er
I 22 Crane tags
| au. wit genen
;
15 Vena periodic
Tatort, @ TT,
ys
1=100 Teion

Pudomata) pened [T= 10M 46e
d) ays 4 ce Wer) +23 um)
> à
The Mos Y O gym)

32. ———
e) nie 3to4 + 005 ta

112 2s 20 220

)
la
$)

[sa
E

9

=

D Tzat, @) Ten
72200) Tun
Tun

wu delewing Diswebi dime 4igrels are
Astnminz Yu Sordomentel period . |

© darumine wheter
| peñodie ay not ? M Penodic

sinteormm) ME) c) coin

EL) +) 2

jones jenna
e

33% (044)

u 5 |
7 A ña n
0) ams Jn Coon wr oot
220) = 20 cm)
nn st
N = wotm) U mar Tu sioo) arintager

the given Aigral Y peñodie Qi Aralar) Period

[R= 20) 40rpor

An) = ASTIN _ 2H em) = 2 tm)
NE Rte = on ES |

wo
E 2 2155 2 (o >

a mes ma 219 Con integer ha
2. The given atgnal Y perienbe Wile Tals 2 Jot fret

|

Min) Goan A AA

33. a) ME tn, )- 40 (ne) +3 ces (9, +03)

Wem A Mg, Sem,
nem = as) = &tm)\ wre 2B (m) > ER Cm)
za = oo De
ae res) fee
Re tn ee a em =
5

The watts Di = (vanos) Tree)
se BR

Mi 2 M qe q ives?
n3 z 5
ba. Ep raie a
“a +

= D penedic

NN 403)

IS
eLo li 16, 2) : ous

Ts
Lema ura a Ib ES ten

QUES) à tu hs Po, a?

3305 Cn ath)

[3 iin min) = € Jun 177
tamper aly ee à be foo = 295 D
> 20 m = 2m) = 19, Um)
Nz Lo 015

| 2 [Neto ) ro men

++; en re wit Febr REN we)

De i UE ¿dama um

au) À Ñ

PT = Noe us =
ane te as 40/4

34. AN ant vote q Enagers, luna Peredtic era.
= fof pre ni = Lente, No Wa)

Lem ( 13,47 227

IN)

INTE Power Sigrals!
© Find forte tae given Slava à Ent (ov) Panty age) Flo |
| Hee Pens value -
0) ab = fain (wot +®) |
Y m6 = cos (net)

J moe acer

Ss 9) nb = 4 2 (met + 8) gun — 7
6 & et Jon at MDE Adin (mot Hdd bo |
wer peniodic sigral Mena Hy
si eee dx \ Aro we, I)

= te 5 Pr Di tes tt) al

mn) en
| +
sue m a Partio
ae Loe — Jens wer)

2 te, ODA mg einen shee
7 Full Gye Ly Zave
= lé, Berard se |

Ange ponts Pe = +3 EE
e ten
e ie E =
Average Power [p= AY, wots) Rms vale JE = À
=

35. D reer = Coot) |

E Inco! at
Energy Ee te) Sim

>
2 2, Y a ur ar

N y res] at
+ E SL de (a srnct) at

” ee Fa not ott

qee Y
= EE 13 5 ic ruranret (ara ]

te A me]

>.
As ¥ lar x a pel

al +o rol ondes
etal Be
are? it zus |
me Y

we en + E)

Lf State at]

meg roer pat
Re Ponte PF a Beh oF

a
e

"
B

(Since powers Rue 8

wi ay Argel
Vence 4 4 en Power Ba Le il
Arteta) E 7
ns 2 Ti Steet #4) 2
x Swot
Edt Le a Pot
er tt Shun 2, a

tae 2

PEL > CS

A

36. e REO, = Fam cw

me
| average Power, pe Le
ES ru at
A
y E = ——
PE es after = a PA? vo

(© persan wheter Ue following signals axe PR igre (or)

Power Aie : calculate the Energy (or) Power
a) alts vect (Er) b) Am 8unut coset

We) amu dE tutty e) AID = un

IS ere uy

a) alt = vet He) po
SH gor »
| Es $ vos dt 1,

4) azumzuteg),

MN prat A th
“Ye M
° >» ll de = ath Bt

a finito valine

Te

5,
Powe p= LE Y tarde
nr

ee de ur

me 27
<>

LA LE

Frs

me ren Syal de Enero sim!

D abe Fre Cos bt
Ge 9 tor B = CoBCAHE)+ costa- ED
= Bf aC uesor) + costat 6010) 2

Peas valve = [RR A

37. @

= aus ut AH rt

wei ASG wk andAtesut om Parodie and hence power

Argrals ule Power p= AY

x Pe = lores
igrel .
BETETE | .
mes BE jist de >
me
te T T
En yo ss”. fes

"Rise El

Power P= LE = 3 nude

15»
si & ‘ed ch
ne 2 pareada :
a) acy = tu)
) E nat tuts =f ty tz
N ve me) Ls
Y Es oyt<s
aie Tide ai
2 LC Te
satire
13° al energy rev
pe LE or at al
12. +

1414] e

py MBE Gun
ES tt Fura

38. SE

2% apy=ere% aw 3k aru

nung En = 4, prb dt >

a “ces sol ee
= © CT J cove Pa +)

A

m. v Te

« Ble Ja +5, Eur à wpetae ]
sl

2, lv! en Er)

5 ate

ee

te) ls

tk curd +4 44 ( %)
ae ENS 4, (%

a
ez te à Sat
or ot +
Lear ++]
sur

y bi
mw aster Sel ese

67

39. Y nb: aw SU rer
e Tauorda ’
= i var | 5 à à
ae
ete [ts y E= 4 Jouly
ve
á
2 LE Lf rmndt
Pe se mal
oe i ee 8

The given Aipral ds 20197 Aigral.

|) Detayodnr wheter num 61) Power Kiyo! GV) neiker ne
9) nu = (¿um Y) aw = eE Mm) Sail

Jam = Anl) Adam = num) e) HERD = UM) uta-6)

4) Any = sin) -Vin-4)

So) am = E) ur
Energy ES Lt, a mar

2166 ges y

nar Zo

“(ob Soules ]

3
fe À 2 No

now Sah soy

= 1.063 Soule

sE An 0-25)"
ETS E

40. Y am = Em" +087
2 2
Energy Es Lt $ uml

BOR asm mn ma) ve
a 7 dran

5 Le '
EA LL

a
„uw 5%

Pow pate É
poe Bar) n°

Lu DUD 2 rent
DELL can)

a nt

e nz

ET
Bret 62 be E

Sum 6 dos q sine ovir ome
Full Wee à 2070

Pours pr Le 1 7 2
A

= E y cano)
5 Laos Gus

Ya

(area

un - alma)

41. a) nn) = num) n a
Jaw!
En a 2
e ES on a
= a
& ae num) = LE mM” =
= aes Foe ke 2°
" u E)
poy pe D. ee aia
138 Grid aed m
= ES Ji A

22? ana OF?

nina dan)
2
| sos) | "an el J

Min ETES]

e) A2 un -Un) \
Energy E> 2 ar“

mae Sita eA

Z
re a mor só sed.

cee wee
,
i à
pours pa tt 1 Sm)
NDS GH) AD n
ace 1 LS tlums LE, ere
non Gest) rn noe Gay ne

$ am Ye) —vin-4)
2 tmnt

Se en

Tu, bey zer)

¿tra 2.
> a

42. u Litro) ez) "a

a Zen

us À [3e+ w (us)

ill

oa ar <
vo. STR aG SbTSGA
A 2 (30+ len -
si tas De vun win)

A (tw 343

Castel & ne PET
fa mu gi a pra ene cael ed mer cul Fire

a) x 5 Stu) awe ULEAD e) amo sc

IN O athe eos2t
Juro uma

4) ats AMAR ULO

9) An) = ucng yy ulm) NDE

Y awma=zuth) D mm Farry

DO) nus Sue

RE F2
|

D min = E uti
iy a we Dee fe te Mae nen tessa! Si jrel,

ae
e) Ay =233nert Sine co
| Sine Algal aan fey Exo alto ASIS,

Herre non corel ed

$) an = Ute a) ute

ge Hes PA,

43. 0) mye wsrt

que Agral BAD Foy ext <oo
Here non Coal Sigma)

9 ad AR 2tUley

spa i
Since iy y mag lid LE un), of an gral marta irk

uty Aw Ay)

Gente AUD = Sin 24 UE Ua ante] Signal
D wee) = (RAH) Un)

meo
wor) a

A res us |

Anas À

r Rast
FIDEL

Te Agel lia from n= bi

D a = yum -

Tie Given nel eu

peru non canal Sal.

iY anew

for neo, aio. Here noncamsel Ait

anse 77 —
[y my 2 nk à

Tu Ayrel eur der bo

ac,

Werte noncausal Agrel —
y ams ue a
| Tee pal ents ov rr m |
| Bene it nnd Ale LE |
| Even and ad Aie 5

B |

a) Rd uber tht Given Al gmals are event )edel gr) nel.
|
a) no = EF -St HO D) ary = the uth +6 |
9 ays Orze dame 2) mys me

$) aw > à 44.

44. 5) a) wie Est he
aros ELPHSEO I = {ste
mu FILO :

aie sets

= en Ei
Daye ETE Les ee en

RUD ao)

9 wales Part =

are = CDPHE À nie fet?

0-9

(cos base] bene 1 ban edd signal
Jet = — a
a) muse 2
) 2 ot a FEO os
aro: e
ot am Joe
ao e

bene rein even nor ode age.

e) mt = cert
antes =
me ty = mtb = Cort
au 4x6
ao = tat + 2

oe lea gran ¡lied cor Brel

Haie Ant
us a. À ARR
aro = -2bt atic wie

45. [© wa a even ou add Corpo of the pat =
ame yr (meta)

©) am ABIL AA tc diet) nina EH EOL?

| $2) xe ap mue et
Tue above Aal à

Venen Even componer gj ta Amel de,
yu

pajar, avin nor oda,

Creo
SAR = MA ai
ne
pt nb Fe
nahe BSED
~ En
ES Re
IA = cost e LD 2 cosa
le.
| En
pr. ote jae
wots age ee
=
Lod Fi
wee are es geet !
Ÿ Vode

Even

D atty = tes(wot 41/3)

AH = Cod (Wot +0) = ee
Even cont Ib) = slots 113)
Melty = MDAC Y] tlwet + le
> eit tot 9 ERES E 0)

wet a

ere: Cast AR) 4021-8) |
+ un D ww tes Ty =
Nol = ALY = Alt)

=

= Cos( wot +W)y)- Glan!
=

Fade =

46. E) AUDE dark A stnrt corre 4 core
The given Algal U combinohon of even and add Sigel. Hana ity
ame avin ner odd Aire! .
Bin Dodd Aigral coat > even Algal.
Aint GAZ’ = eddy even = odd signe!

a Rey eat | fae = shat cart aid) 5 Ke

odd pn

A) ams ara BUT
Mess even nor ode 4
A A id

Da 0)

Even cemporet ALE AD eae)

30-44)

= tartes ue Kara
2

aeee? _ eset

TZ

ANA ;
AS

=
= ka quel rare ati)

cad temporet Motte

mein = 24348

3) Find even (or) odd Aigral (01) nella, even nor odd. 14 30 fol th
even and old comporents . .
y mad a as

) mine cud d am 2j3,1,2, 9,2
is a2}

a

mu)

sa 2) ao 1130 10733
The given Signal y Aymmehic

about vertical

47. A o

nen EL Bete 11 39
en and
on even get

pene V4

3

ES ee

BER TEE)
)

wens [al

=

an = A hd 3
um um | ad fru tach J

Here Sa odd Atgral >

e) mms mat 13
aw =f 13053 nel

AD ERED) arg WD EME
alter even nor odd’ sigral

nd

Vena
Even tomperert edd torpersst
heen) = rien Mn) mole) = An) AC
ee
= Su qa rt 2055 Ss bass
— al
2 2
= Tat, tye Bee! PER:
Me os rn

3

Me — pe
St Es 5,2005,1.053] aus Les ns 2,020"
T +1

pe
AE
T
Ba

48. N zen u
ee an [2,42 133
di +

porcs) ond pren

enue neitter even ner add

an

Peer Zaun

Even comporet dd corp ors
ney AD olny = Au ut?
2

= tr 2 0/2J 4200030103) aaa]
ba bl A ——————or

2 = passes 25)

sie zu, 253)

512-570 172812 sj

A a

4) gear te even and odd components ay a Aig e
pee an Sosa
EA AS | |

eo 3% 3% a ie |

are te)

mc

shetty = LAO
+.

Bet

a DE

49. al

UN,

un = Allrad

ES

Ra

aso eur

RO WIAA à

{es

18,2, 8,2,15,1,05]
+

Odd, ot, 043, 044,595, Wo, 396, 10,14.

Acto)
s

ses

50. |
3 [mov 00,64), €87,0-9,0-9,0-9,

pe
BETEN 3

Holey 7 ADAC) >

lama of systerns : ,
Sites ane Alam fad OF + Go CTA ond DT Fremd,
D Lin and ron Liner Systems |
E qien variant enel time Envortent systems CNE Voriant [tavertont)

Stare (mamenjum) and dynamic (memory) ystems

Counsel and von tana] Spies

Steble and urstable 2957:

Trvertible and non Lave Sgt >

Recursive and Non Recursive Systems (Fad tn [non (erdeetle >

ur soeur
Me ETS Orton

sin = Ten) Tp

rá 5 are
DT
output
ae |

O Une and Wenn Unser Sites
i ayas et dr Bios (POOR hau
wich Asset ever D Non-Linear system

806688

fresa Ape and
a [ruvsmto) = Thaw) + 100)
Cat rat) = TERM] + Tan)

© Were Vertont and Time Tnsarant Systems:
A ten LU Anid te be Ame void (SHEL Veron!) if ib

51. GO if a Ame SEH in teinpet ets Ina Credit Kime Shaft
in Bu output as shown ah the fey. |

"m |

away 15 Pre)
a
In werin,

T

= |
xy 39
ater) > 9) : |

Lint vonlane Gn be feed by Following Ares:
O delay a put Aigrel Ad gives aE 1)
YU 7) = ALE)
D Delay Bu output Gey Ylt-T)= Y)
| Th SETI = YET), HA syste U gine Tavertant
| TE DUT) ut), Me Aire iy Time Vondant

Sinèlext, fr DT
Delay inpud OD YEOH) =
wn)
LT © Delay out A AU geek) = ION]

tn)

| 4 San) Yin], Ha agite Mine Invoniont
© Hehe ad dent systems:
| Y dard ds Le dive Erro), 1f “thee: wur
2 A Agen u vo td
que Arten oleada oot on lu pre lapa
PYLE ND y Je QF)
>) Asykm bi Bad ko be dynamic (mener), if He output
dame! decis oan Sion: BE hal! tae Ta

À tess.

52. on Py
Ang Cr avi dmevibed by differenkal quaten cm) ony DT
Apron deswibed by difference epuation Ly ade a dynamic tyson
Example 4 She Syphon
Resyter
eq dynamic Ste
capacitar, Tachuchey ,

O cama god zur quel Sates ©

jummer (6) accumalater

GE a oid ko los Causa) (non-ankeipative) , IF,

Ada output 6 We Appin dapends open the pres, soit

votues of inpud ‚not on Ot future vedas 9

Lo cea) get s WDE RUE? 7
ne

yu + anim)

ÓN

mon Caral System!
A aitu dy Baldo he be nom tar) Conkeipative), if the output

Ua Agen depends on tha future valles Of input

A WG carpe AAD

|
Yims arm HrMin+3) |
‚© Strole and vegiable Sara i |

Sipe Sms À AY In Y old ko he Bourclact= Input |
— |
Bounded ouput stable CBigo stable) , 14 every boundas int)
preduws à bounded output H

| Gt) [nw] Mn 4 For all be abewetadiput,
| |
| ak if luto l z my Soo UN YH ale bola, Jen

Br age iy Bie Stube Ma, My Poßhverudnunbers.

Y SALI an be found fom the Impuls Yeporic of the Ayszm

53. : , Br — ED
The tonolifion fer stability 4 7
T wren ute ht Tmputie response

Of oe Sem

For DT Sen:
Pa NOUS
For DT oyster A Condition for Amb lit 4 {

Zik 2e | hey tap tuner g
= DA system.
Lahaie System:

Bh any bounded input Produces comprada output, fe

Ayton y soil to le Unable Ayn à
0 y
Sante | |
Siren a
° E 7
Bounded input

E, er

Bourdad y ©
er Ursula dapat

© Anvers acd Non ever Agir

À system Sold to Le Event, $ distinct Iepuls Preta
Arret eutputs- Therefore for an inventible Atem antavese git exista

A Aion da Aold ho be hon mame if duinct Inpun produces |
GO ony input Produces Zero Curput « Therefore Inverse

dome octet
| ef Bu again Cannot Le datermanad-
Las For nte Sem ex denon saut Syst
A yell Gen? BED um) BO FW”

guns my aa
2092 AAA RTE)

yun am) Dawa Jen) Se ol FTE.
Men) Corned be

yey Aa 2 AZ | yy stw- 50-0 fa

54. waive quon = Rteuraive +
© Recursive ond. quen Recuraive Botes»

I The dystem à ut the output ad any Hee depends
om te ord output, Pod lapul and Présent input, is tabled

Rega Ager. C Feedback Agen) de
+ O AO = ao

22) aed” yin 40,97 900 + -
GO ange Er
ead nigra be tor oot be y FBO abate
de Et Su in

D Te Ay by wrt the Cult dapan only ov Hee present
and part input y called a nenfesdback Aer. a ren Besar
| ax gure be ao A nO ai

| Y) = + ain De + AAA

EST
[D cheek whither ths following Dilo age Lines, Tet Snvoriont
Broke ond mel @hrek:

I = 1:35 +4 en A)
t

3) FP Line) non Lines

WENO) AA, 2 dt yn FUDD 43%, OS +)
hara Te ae 26

Fa

| riput is dun pg d AS UN
ae CE at >38

| The Mes tebrehn of De-4® 9
BD 4 HY gar d'au a apis Ay, An

| m ay ae” J+ aE iF En

| 43 [tn Co = ACEH Am COND |

55. [€

E ay a eer: [$ at lau een |
|
|

ar
DOS |

aes Lane Je tee Combined Anpub

Atty > MALO Sl MR M

|
|
|
E A (te rt? meena
F304 MH) = ace, mio |
DAD Werte Syston y mon Linear |
aime verte + ©) Tnverant: |
Since HAL Combficionh Gf tha Aifferankel Rua hiena ave Lens jet,
co) vs + Agu a du à 2 ee meer
Me given wyatt u Time Ita : |
Start | dy rermie .
grue tu Ber Atem D Governed ty difpere te
equation , wid darge Wilh Kee Nu à Aynamıc Syste,
IPP
I Tr opt depa on thy dure value put
dey atte), hau Se U anon - wa) Syrm.

Merce Be Lie BER ir MEA Tie Invariant , non tassel y
prends

{
|
|

> AI 490 don Sad ann.
ES ott
Fox input MD > ox, pls lime
| Fo put à
8 > En a PUD adele + aqu = Be
a

56. = AA | — A —

Unzer wnoinchn 4 O ed

at (tos Maca) “a LOGE
ae Je
an (er) > RS RARE

|

anh stp de Ts
“ai ei

>

|
| utp du Be conti np
| al qye rar) +a Bros) pd
Je pS
silo) =

ADAMO.

=>0 |

tS eek a Oe dic. frs or

qa given Ay u MONT inte
m Verte fanventent
| A tee cofre q fF
ee PA
Venee tine vasta Ask: :

differonbel aqueños ox net
an aes term GE su)

Cased [mon mot
The a u“ cor o PA
| pense Ha à Game AR

Static | orense : Ñ

| a ea ar dee MIRE Sp ies

| gene en pa = |
4 ° 7

e yw- Sande |

Lines [on y
anat Aus J aiwelt

* +
MIDI UD = J that vf mindt

57. ———{"

Combined Inputs and ar op.
Fob rete J = 3 bueno] dt, De.
© =D Venu wu Fron Aysem b Liason,
Time voient | rentar
Dela Ata Input LIN ou à
94, = uns

pay eu cupo 4
ye 90 le D yu-n. REDE: j

The Sen apio y: Tire eta -

teen anal [ Srehic € dynamic
©

Saro dt 9 PA

at end post votes. Hate |

caval
316

Depend) only on PY
comal & dynamic Sim |

d) Eye (am).
2 sed e LT = 4 Cu raced

Linea : 5 |
s À + ALO |
yu. À Ca |
outputs due te MB RO
—— pe ws cd Ean MOOD
ger "5
(4 Mr |

bahut = À [ menu + MO
+ RO],
-o

pa. BOO

Liang Combination Y Y

A obove ape à :

outpet du À tres quelo
O) |

58. time voriant | Invertant !
sine Crane)
SANO Delay Heu it & olor one:

ye, Ds A [en 4764-79) >O

Delay we Given rt QU YO) ET EI

a [ren aan(-le-m)]
Tee a

PR)
y=)
get) = 4 Cate

come) [non tera) g Spiel der
ym=x (abr)

& Time varient Sr

| gens à LAC + Ruin pures input
gui ek ba 4.03) port input
LT input
Stare + dps ow furore volar Vu pun und An
| oo
y dynonte Systm

| Abo MS

2) A
) ID APA) o € ntt-u)
Lo limas:

Oily apro r bt A LE)
Malo ast arc bt mtr)

BOO Tt = oft dam] À LE Cac am
coined App fe Se Bs eal Fr;

Y CY Ut) = ar Lt mc) tbe ao |
on WER
bea 4b Lim Systems y 0:0 . 3

59. Te etant EXE

tetas
na ott ary + bt alt- uw) |
Yan = art nate +bErli-4)

JU-D = aC b-t)t att) PEN E-T-4)

yt + 9 4-1): Henee ere Vanier) Syst
canned [wenconrel $ Stable [dyrooie

Y = otra 4 RENE 4)
N gene art) rs) mr
|
|
|

=
ay ques dh
SS
a = à mul FERED?
a

| Ga sims Hann
=

Au Bar re Gord pus Den“ Counsel Salem
pile it dopants e pout input rene dana Syston

a ba?

4) y taco
Se Lineas [am Unas
yan = be AIO) 20

e Lancer, PCHRD
Oval por, es

output due Lo vocal dun yet
(ww) = [nen + men) |
[pos en txED + im t0 | on

Tine variant | Teme shvertent
Bun: man] 0
yen GY aun)

Tren = =) a (- 4)

ati ain at ae
De Tr Given Ant & nach |
|

60. r

Y) vis dx
at

Causal Nontattsa) & Static [Dynamic = e
Since er olepanola on Purine

y: teo :
depa y MU given system |

gis ao A

restes) and drama
YA) ara eue and core

Linesa] en - Linear System

Sue Ad LAVE
at oe
overall HK, yaa = AML 4 AML O
~ ae dt

A AS pets
[urna] = Sy Cartes

Bete s das + dit >0
siterip = JA Le

0-0 lee Ler system -

OS EA :
The cortfint 9) Hu dire
Ama Inyaniont AS »

cause) fuen coma) G StaXe] Byranis

gay da
“alt

Laja Da costas Term: Mince

O Ananda pon Se Port valu; han + 4

does ond casal SANS *

y

90 ADA
Linear] en Liceos se
Y= AAD AO ins ateD Ane

MIS) Hare) ERE \ 30,

61. Time Vowtont | Invariant

YO: Aa) 4 O

DUNE Ea a
YU-T) = ACES + Ge en |>®

BOT) FILET). pente Time variant System.

compel er como) & Static /DYromic
YO) = ALD 13m The output ola penota on ti Poot
veus oy bie input -

Bente i+ dy cams) and dlynense
gays ned E sem

91) = 103) 43

2) Wach Fey Linasaing , comtabitty, Time variance , Skane for tu
Given Distreli Kme system
8) YO) = Log tne]
Linear] mon—Liseas
Seta = Leg men | Mama Reg [ait]
Wr Ll à SoG Laren! > O
migas den oh Eta
YA de] ama O
D4O Hente Non-Linesh System .
Time voxioat | avatar

Jtn,e) = 203 | X ta) .
ve YUE) SGAE): bene
Yn-k) = dog, | xun-k)| de a
camsd]ajer comel & Syrah] Oyromic
JU = Lede! M291 CIP Depancls upon only pres
4) = Lega | 200! yn, bine Sres Y
Mens tee lated url spi

62. Yo = AA Mate) 2 mid

An)
ke
pes

mained)
y

32 0
Ma at)

SM) FY = WMD A ta

| welgetd tum of input & 0)P

YI ra + — ad
: Aa tata

=(O ne non limas Shen

9% Netvertan | Favoriser

Yun) = renee 4 — aps 0 dela ad bey”
Anke)
| E FLL A
An)

Heme TAL ad yen, Catan) = TES

| Gael /Nengunel 4 Stabe | Byram'e

que > arm 4

REN Pett pur
y

e) Sin it Dulput claret upe,
Sere noes DE Um poutre pk tape it
=

E E

9) Sn = an) EOD
es

Yan AI ERA) ann) Imagen)

Ad mn Amann] an Cano art) 0
Bar alpin Feige bar Dre

Dios pee Drum] ta En ind in int] O
Uuce Au given syn u Mazar

©

63. — o @
7

Tio vola | votan y

A Uy verter n CM) (notes) |
Ya Ager Will be Time Variant |
Yeni) = nena) Me delayed

| Yin) = ta Ir Ge) ACHR a ep delayed (n=n-k)

= \
por ee) lente Time variant Syarm

causa) [menus 2 Stmhe] Byrands :
2 01) + Haan
DE Pene nontawal & |

a) ces ds Tepe
= aie dyremic System,

Y Oda cubatas Ma Agen yo Linear | pème PAPE, Saale aw

| mann.

La) Ys) B Yin) = acom

SL à) genre rer)
31d)

| hy
Be nz Alene

Aad 310093 Yala) = ACME AT. O |

op des Bo veia tom gré

HOO? = fm mA

y O FD Werte Nom Lines System,
Mex varient | avaient
| Gente) o atente) O inpetelelayed 69
Yn-k)2 Rn) y um lega (y
gen) = Yin-k): Hana Time Invanlantiysum

nek

causal animal & Stabe] Drame
YO) = Rem) MCD AOL olaperels only m
PURA Tapas Vence Austen de

ge) = nto)

64. A verpere hin 2 700)
ha mtm 2 5): |

mo Shee

For\t) 4 0+ 04

HR System D Bie 2tebte
| Trennen mie

90) = Wen) |
rate + [vn |

|
pere Sign of Min) @nnet he Preckictey

Vente won Bavertiote Ayn

| LT ls o
| b) yu) = noo
| E 5 Mimerend 7 |
Aad Ind dan) WEI tod. ID |
cie due do al Bun oh coran .
O Head 3 Aa O
Fa es Base,
PS a venant
Sta) = An)
ine) = CHK = ay cen te |
Yuan) F Ya). Wena rime Vota Sim |
TESTA |
yous ten Since 34 dep pon faire 2 pres
aon inputs 14 D non Cao) ond atte

| Mini AD a oe

65. hn) cr Ute Cord Ren fer sta

| hace hen D Au Tepubcrmaponte g tht Due à

27 ge treo BEE
> iv
pa = eis»
eZ hu +0 4e Hence 29m 4 pmo
Favertibte [man Sete >
yn-acm Slam!

un Mn EYE)
Pena ABA averse for He en >

Vene the agar a Syvertible

4) Check balla Au Gwen Aysens ove Anke
Yous = das 1) gee taco Hi) Y act

e 4 |
Y yu. shi) Y WH = Spear. YU MED

se)
2 Ur yiyahty A ale Std
Condition fey Aine tity à

J Ineoiat << |
ES

Ciegagevos 2 Aifferenhiehien)

Ñ
> A dí =.

> [rages ose Samia
E Sib=i peso

fF hen ak +1 +
de
Here a Ain Y B1Be MÈRE

yay = EAE

| whan any Apr MO AO
| gurpul eros unboundad. Heng Mu system y unstable ,

)

PARTS ORT À? te

66. DETTES :

2 : am à sw
O MBFEWT SHLD 2
YY Ara Criterion

5 ES

“ows at <2
ea
Fist lat

2”
eli
a OS
Hess: Syston y SBIBO Sable

W ste costar)
dot for any velar of o

= fobias vals eon
for any value 0 AD / cosCato) delo vols fromm fol.

ex ougpet Zub) y boundel
ne m an Stee -

Y yw Sade

D ur yoy ho Da E Se)

ae
Ror arg Y Mt e 2
>

a Tias [ede =

Gon at

The Sgen 15 ala
Vi) yacen a o
| ) aA be 2 mee = Ste)
| = hugs Sem a ” u
ued
_ fisce-oiat =
Llene Site À Sula

Tinmlat = 22

67. o ®
mej Un Sala NS hey impul Te ore
op
gra Lalo cil
AS IS ¿uv

a) ki? €
ay buys Ee lutte) Re = Etc sy hey = + )ary
| u
ls y tm. y hiss eut
poros, LA $ intra

En

lente Staite System
oe Sade sys

e) hs gt Fatty 4 hs tete
= Tliuwtat = [leat e) kit Festal)
= ia 5) When ED ml pl cuit
je «petty > ae f
), EJ. + ay Algal, À} be corm

Es [osdamanes . Han

PRE Mile buys tuto q At Leo Fur)
[ane Unstable Syste.

45 hits = (ar Yun 2 2. E
. A Safar a 3/4 at
Spebkitg tondihen Y e g

[irolar <>

22

©
ES J Jose utwlat
ES

= Just
= Therefore system 4 Unable

68. 6) wi m = — =
) edo whekier Ce Given DT Asien y State er) not

1

m

| 0) yen = ane
) 5 mib Y Yin €) em + à X En#1) FEA A“ |

La] yon una za Da UND

Sa) ym zanntb
mm, EN su)
pl
“eee
Spuiity condition 2 nl <=
ath y len |

> ese! F6 hen ate

| = apt eter emote e: |
|

pes, hance Stern dy arsinbls

The series never Conv!

CARTE ge
à tn) 7 8)

y ym: ATID aba)

ber win 90 een gy ELU]

La yo sama dar
| testers ce apa AE ¡AY Sir)

69. | Spel pase 2 Stat net ef gin)!
| a Flute Mtg race.

Bera the System Y Stable CBI BO ars)
1) Gece the Stability fer the Distrah Ame stem.
DANS] bat Ey ue) 5) hin) = a%uca) N) htm = Wend
W) hes Sut coon vy) hemp = Puto) W) Woo = ura)

VA) 900 = do Inu!

D i) hm "um y) hi z Ruten)
Elbo! = ¿Erie Els ¿ue
ee ne re)
ee s2<e
e er
Ben Stable System
DA Kin) = 2° un)
hm) = E laut
2) a El vi) him = putain)
ee -e E Varna]

Hence Unstable Apte

wa) Rey = uen

N) hus Sim + sat

o > fl Prince state yate
mile Breen
ge 2M vi) You = Leg Laem

alba lender | boos Lits
pos: E tho) E \ deptscotl
nme E

Loge 40) + lego À
= Mw 14 25.004 loue © +

20
bete uote, ‘stem