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Arsk= A
Tacaaken
vows, eltege oy Jaliphone wows ,Wedac
ote’
System Jes on | enion
b> wane onde
Fie Communiaskion System.
4 CQossificodion Spo Ds
A Coianius aha We Mine pes boasts Bigeye
Y Peviodia awd Abovodlo: Signoly
es Bitar own ldnde Sig no ©
Jive ard oom —Unwr sigrods
Be ne. can k signal,
GB Even ad add signals 4
H Eeey dk power sigrnds
S Consimmars ond Dsorda Tra Signds
+A signal ubsich Ja dafinad for uO y veoos of
Bima, Je cg) comdivnars ines signe -
zewept .
Becdic oA Abate 655.0
oh
pee SPR 8
ae rebansR no-
at = Tie 7 Ste
ata, 4
B Fdometo® Sjod—Lina(T,T2)
Be 9 Wo Daan ds peiolic & lun, prialic-
Qe Beis hohe She cig) & puicdic Be none
Bttmine: ~ he Banddnw ck)
bid Se Wa als)
Qe; !
non-
Gee
>x
GilsGi) xb) Sein Trey (4)
TT. 80
Be ud &
poinkio
@
Compare?
peat a oa
E ee rai sto ule)
\ Ka =H — tb Wega
=, nas
ie a Benatsio + Nene reo ee
2
ax; Examine Siena he signa Ss periodic om
nen LU paniedia daanine dhe Frrdanaded posed
(i) cost + sin
cost + sin 3%
ale) =cos 2%
cast 9
Combobing Th a
WH oo
Teas -E
|
|
|
=, mat
Ls xls) 5
Gi) sin(ios +1) — 2c os (s4- ie
> xls) = sin (lov t >
Sin
wi =\2
Vi anon peotedic. op
podaga -
Mera oh Nik N,oles) =)"
al) 4
ala) = acl-*)
Exon
ona (derieyrnndeice®)
> R cosines Bore signal 0) 8
x(s) eon xs) fo. oft oe
adi 3}
> Exoluokion
xy (4) =) Xe 0) + Ko (*)
nes) = R[x aal \
mol) =H[xts) oh Jl
Ps ate get oS eee aaa:
() x()= e** (oyu bos)
> a=e3* Sahjerbso)>_— ae
| ton x4) =(-&) eS Kone
EE Nov exon a
a
w(a) euls*2)
ead) =-alos
Nex odd
awis sgn Js kn evan or abl:
Not exon:
| aa-s@) <3)
| ee Z- aaa
Nok ott
WS 5
Fs, SE eae(ce) aba
S x)= 2444
xl») = CA)? 4 (4%
Add Comporads aff KoBowing signdle
1)
elt) = 4 fu) + a(-s] co a (ert .¢ |
= costt
tole) = 2 fer. = jcnoe
a2.
5) (a +4? +42) cos? 10%
i (4) = (2447 449) C087 1o%
as) (a4 ete ca)?) Usa vei)
= as 28) (ea? 04)
e =45] = a J (4+ 2) c0s? 108 +
welt) = 3 faid+a(-vi) =a] egos
Eealck) =4,|7 Ca 4a Jeos7V04}
molt) = 2. ele) = oc(-4)]
= ALY (a0? 24%) costios — (a +4? - £2)cos2\0%|
eVe= [2 (49) cost ox]
| To check the amewsr je connec?
wet) = te (d+ x0 (4)
SN combywisys Kma signal ts Me
xG)=0 fe 820°) oormlee vow comnld
_ ule) — corsa
‘wn Gh) —
i eu aCausa
ou le—1)
ae
dow ao
e eae wo uncardaindyy oh Da eegrtihe
Q ef ee rin SA tees af Sew LSiece
parvrinais signed eee eon
+ mabasmskicad 40>
i na) = sired a
Lae signa ehorwedeniaal bey ae vince dordy asod Ds
peevewnan Se Ramdorn Signal:
2 Gharnaharie ner
OC Enogy (Non~ Zoo) 5 Pees
i powers (Non orp) -D Rod
ores Banc fh cid
Sin Fe flatts wafiod ccpenctil igh
ATA Rowan off fWlondings signal ete
=z
oul)
E [awa elevaga
Sf in ae
ens =
e-{* as ot
p= am ale a
4. fe Gee
qo ot
se
(6) Olea cos (ut +9) a
DSeE= Sf x(a) &
et Se cos? (ud +0) 4%
: -*4 an codunsol| ae
“Ties Reed)
a (4) do
es eA a(t)
_[atcost (ure
joeFE Bingatoos Funckions ere EStmortooyy Signods
2) A” Stalp Funcdhion
ok flow ondy peailive
Sais Ben hon umtlp s magniude “shen 3k ix calla)
+
2 oe ans Jpg
wl)
Bi ule)
coiuans 7% As 23 4 ooo
UG)=S4 fou 420 ota ota ae oak
© feuvteo © for neo
Dk Ramp Fuckon [>(+)]
s Tronmess Uraady Uh shine :
2 (4) ane oe samp function hei +o wha
sdope A hea
= Agen samp “furedion hai +
Penge eee
E— 50g,2=4
alm)
b
aWl=S% fer +20 Bee Sige,
© ferrzo w fev n> 0
se
a
w@
\ as
3)
ee 8 th ca oes.)
Hig -
xt) =A for -xoeteco x
+ Baorte dma TC sign — A
aln) =A fev -coen ico
ln)
AA AA
F306 signal ave
+ Gorlwacts ima DO signal) —> J cnctat SrA ind
*ie
AAG b—
STS
aliene™
0) Signum Finckion:
: Sign () re fon oe
a fer dy
a) ReckamgeGar, Pubs? y/redal®)
k | ale ® oe
| sacks 9% je
. Vo. ates
Sn on) aS >
j swclt) = Sint few zoe to
| y sin,
pollo
ee arleSs) @
cys ule)
ay
Af Hayes h onl)
G0) Ueck SR - ard daar
a uls) = S(v)
Sle) =als)
Wi Rams rn 2D
slo) =fSas (sar
a ov (%) = S(8)
|
ay
| 4 CQassification
Speom
| > Linean ond eae
pumedion as
dee orolysria Sytom- Tk ia p
ody ok %=0 sw)
Soa 4 ee
© aehouien eee
G) Whe UGdo of pulse Ss tro ° f
+ Rakion ble stb, Bamlp ord dalle
() Wek cap sed Unk Ramp
+ TE She System Fo Mows, She Sulpow Pesthion Trewern,
hon ina system Js sci to ba Lincs Suslem,
La
aay Oa] 3
[a0 |
ee ey Oa!
yo
sed
= ayy}
[aasge)e
50 ase]
(asa are sol er = :
= Bae
& syeem os 600d -de3 bay
Septem J a Bee oS EASES
Ses in a Leovasporyg “tine sd
ata) win) be) wn)
goo oi 40 pay
LJ a) ayn
ate io) ale) na polos)
Norieak
ae
FE Linco Time Tpvoriank ond Lincoss Vimo
+ tp 3 Sydem Une “6S ina, — sriond
Mran ho Syston eee
2
20 + wl
fg | :
Be) : Temaxty wiadhin Aremso hs
, systems Daberdy on pawaandy post
coven, Syste defends of
ark da natcay leet heey ets | sep
Diskerted
(S40 e
SS Sto snd Unsinbte
Syke
STB the system produes BIBGO(Bordad Td to
Borda oop)
stron Hee stam Jy seid +0 be Shable Sucve
Be Funcda. ds
ais een bigs. ta: eM Bi pay
MH _RHP( Rips HaMP Plone) Hon tre Sysbem &
protalate -
Tips Bl) Cah ele
AwpSehde ; ao
Unk Stop Tn = a
Time ig
+
Stabe
apie
AN
Unbounded olp
Vistable sate
ivan Hem Prom dhe Seuslim| oie
Iel¥ dePalos with, Pole, wih +e
repent oo ||| ee
suxQues, «So, Are
§ wen my Vewdohile
sec ||
wiclean- Soe
on va a o) )
: +(e) = ce) ol)
ee as od6)
eN[s) moots gives Too
cand Ds) socks ges
Pode ~3 kas Now = Witintass Sagadeen
Que 4s Check whdhow dng Gin sutton Vn Dinan
eu nek, yl) er. ;
Sols TB Tpke gle) + Th Tepe & ale)
ress inte) eee? dG: yorl)=eP 4)
Liws = aiynls)+ angy 2}
(Zaire
S Tapa Je ayarr(r)+ ar9l +)
LHS =e RH.S
So, systim Se non/Uncan cyacdom-
uss 22 ylt)= a2)
Soler cae Ea Sx otal 4)/ + TE Thpd & seals)
Boge wi(H)=aPs) _ Baephees yol= 22 (4)
LS = auynlt) Hanya (+)
Baie oct (+)
ST Tpd Se acxi(s) + ar000(4)
RLS = Cara (4) + ara (a)?
eS == RH-S 2
: Soy syetore eet ion —Uincorn suctm-
Pe pln) = atv) n(n a) ee
! aro Bo ou(n i + TH In eau
} poy Yo) = oln)+noalnea) ooCHyrln) =
! LS ary (n)saryrln) Seale) sw aualm)
i =a, (a(n) sno (wat) 4 42 (al) +n aalan))
i > Th Dpd Sy ay au(n) +arx2 Cn)
| RAS = ardaln) +02 d2.(m) + a2 (ws) + na2dcalna)
LHS SRHS
So,system os | incwr, Sistem.
Quem
Sole
e
ge
g el
——.lei eae x) —3y)
sn plan’) = Sy) Coie
Menon System -
A) So, Fa system Ths
24) | eee yr) 2 aln— ol
¥ ‘sade yt) = acl») alm)
loa) = 007 Hy alnre<9)
Se Ae) Mes Hw -9)
yey)
eee ps ne evarion’ System:
(a) -29
on
(move) —2 (=)
abn scl Qn
aly) P| 1) %)
5 Te orionk Sipstowm
fos) | ff LTV gators
ie fabs nen agsten UTE ond
) | a on Be ple Sul:
Sale Linea Oe
va) Ss >)
| ct, Se a) ;
- ap aut > xalv
cages yoln) =asl)
Ls Zaye Jaan yl)
Sanden) + and ‘n)Tabada ti(w) + ancl,
RAS = nay calla (w
SLAs SRS
So, System
=> Tr Wo
System -
wln Cn-¥) c(t)
wile) =n oel(n-¥)
pln-k) eayln
Sor Syetem cima Norimece System -
> Ponce » System Jy LTV
Quad? y(n) = xln)+ an—4)
Sel: Linsantby Gheole
ange gale) = calys eel)
+ Th Taped & x2ln)
(gay
yon) =2x02(m) + %2
Luis = agile) saryely)
Hai (abe) +anlv-") ap (abe) se2(n-u!)
+ TH Tvpt & Gc abe ax oeln)
RS =a, ily) + aader(n)+ ar2i(n—-a)Faraalv4)
Peers GMs.
So; System 8 Ohare Syston -
=> Tine Nenioner Qrecile
— yl) = aleyex(w 4)
ylo® Been yi a (ne.
win, %) =x(n-¥) + aly - 2)
Je wln-¥) = y(n)
Systm Sy Hine Tyvortane?
> Hewes ) Susdim Sa, bak eutaty
ea eo Copsc® Syectinn bus AIR Cones Ge
© AR Non —Cousnd fo. + A
Be iat Noe rs bt AB
Aen NOHO) SLaption of SIp[olp, von systom boaGe ®
one
(n)
vance Ave
@® ye =e (wo), ol
maedwe tp a
Vows eo
wo hed» = ay > tena,
pol & nel Fred
poet tp gee
(oc ee pivett ingadem cel ateee
(w) vin = x20)
=x ole Re a
ares = ele Je op tht A depend om
Honet wa yor len ton
w yo =
oy Caused B Noa Comrade
ae Owe” weno Bea given systems 028 Gane ov
») Now — Coven
G) yo) = eal rectn2)
lve) = desk TIP %
I Sytem Se Cone System
(i) gare 2 SOs xox),
ae edn SP
Fy non Gow
fej ue - BE aly 3) ales)
| pum IP gosh a eae IP
| nee ren Se Som Je non Gorse -
| tw) exeirason > optiad to aypisvs ob Simo
| So sabe ers 2p 28 ET:
lejos Ar aaeee PO
ri yim
“So, Sypenn
tv) yi) = ‘x(-)
3 90, ol? yl») a on por SIP: Pi Nor-Cal Syalen
020, 0P wplin), Aaberds om pidwe Sl fe”alga 2