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'<i/' x , . ? ^ d t 1 1 . JI Y ) con.5172-07.

- t\/

> tJ/\qu' ). >aJ-,t'J (REVISED URSE) CO (3 Hours)

tf lt-l'-/

*ffii",
,' \l !,{ ;\

I Tor{b{elks ; 100

N . B . ( 1 ) Q u e s t i oN o .1 t s c o m p u l s o r y . n (2) Attempt four questons of remaining questions. any out six (3) Assume suitabledataif rr:quired. I (a) Sketch shgl+sidedsnddoublo the spec8a of
f -l f )-1

"iW

,1 \-'

(20)

x ( t ) = l o c x E 2 +t+ l +3 s i r6 z t+ 1 : I t l 4l 3l L L
(b) (c) What ii Cibb's pheroDmcDoD D{)termiBe whether the following signals slr eDcrry siglrls or power signak strd evalurta thcir

normalizrd encrgysld powcr

(i', x(t) = rer4 L I


\lo ''l

r,\

(ii) r(r) = cos'z(@or) (d) (e) Detennine whichoftbe followirg signals periodic. ale

(i) ,t,(/) = sinl5tl

(ii),,(t)=sin2on

(t) (iii) -xr = irr(/) + rr (r)

Slctchthc followingsignals

= +3) {i) r(r) n(2r


(iii) r(t) = cos(202, 5z)
,2rLn

\ (iv)r(4 = r( -{.5r + 2)

ii;l16=znfr-11 4./

2 (a) O)

Showthst thc a.qunoe '

is an otdogouql i.qucrcc, periodic i! N.

(r)'
(8)

Expandthc periodic garaibction abowtrirrfig by the qxFoqEDrlrl Fouriersc.iesa'ld Dlo! thc frequency snd powcr speatnm.

(c)

3(r)

ID tte aLor'cxsmple( Q, No. 2 (b) ), what fu thc.frcct oDthc lpcctur!1 ifpcriod ? bccoacs largcr 3!d Lrger' - -l= p tc O, Determire the outpd response oftle low-pals RC Detworkdue to rtr itput x(t) convolution.
)t(t) = .!Bc

(4)

(8)

(b) (c)

sigltl f(r\=106(t "2) find s&plitudcandphs$e spectrum thetioe lhiffcd ixnputse of FiodtbeFourier Transform ofrhe sig!.I sho*trin fi8.

(6) (6)

-l

4. (a)

Obtai! i-ovcrs - balrsfomt of thc following z

x(z)
2 z z- ' 7 2+ 3

(8)

X(z) =

if rle ROc's ar

(i) lzl>3

(014.:

tit;1.P1.,
(6) (6)

btween bplsca Tralsforu atrdFouier Tralsfor[. O) D6iv thrslstionship (c) Courparc Dscrae Time FouricrTrttrforo d z ta$forDl 6 5 (a) A DSPsysts|n described thc ltreardifrotenc is by quatioD y(!) = 0.2x(!) -0.5 x(o- 2 ) +0.4x(d- 3 ) Civenthrl tbedigitsl i{put sequedcc- l, l, 0, " I } is spplid lie DSPsysteor determhe the to {

(6)
(7) (1)

(l') (c)

coaresponding digital ourputsequen(e. Provctt-at LitrearTime lo\,8rialt sFtcm is stsbleifits impulsrcspolse is absolu!9lysutlrDable,

A discretc ligorl is gvcnby time.

= _.r(z) tco{ " #J:

and O_"ITTID." period tbi scqueocd of ry

sLctcbtbc acqucrccfor lhe variablG for tlro fro&. n 6.(.) FiadLrplac.c Traosfornof f(t) = e4'u(-t) + e-&a(r) . Docothe Laplace Traofond exist?SLowthe ROC. (8) (8)

(b)

If F(.r) =

(r + 2)(s+3)

(c)

(i) Dctcnninethe 6nal valuEby spplicdioD of final vslue theorem, (ii) Verify thc resultsby findirg f(t) Li5t pmpertils oflaplace Traosforo

(4)

-d

(a)

Devclopthc block diagramstatevariablemodeloftbc systcmdsct'ibd thc diffcrcntial cquation by

(E)

d.y(t) -;ii-7F- _W!),",,,,, = u(t) r +zy\l,


whclc J/(t) is tbc outpu!and (t) r.i is tb input (8) Find tbc st tc hs.uritio! estix e/' fo. the systeE,modcledi! stot. spscr whosemotix is giveDby
A=l

-r(b)

. fo
t-o

-)

ll I
|

.A

Dcfilc ststeFallitiou mrLtrixfor a discrctcolld o tiBuous tildc systc&s.Explsi! its riSnilicr.ce.

(4)

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