aii
ftp.E
convoutionofthetwosianals
tt
mat
net
i.t
ti
sctnsasctn nXCt
xas
i
i
t
n
ii it
o
t
z
sieiiramamasen
EE
eil tbyn
atedty'Zverticany
I.si
1
2
go.se
i
txtbk29 let hit
e'tiffey
e
i
n
a
n
zntzxct 1
o
t
z
zÉÉB
determineaandB suchthat not e
affff
man
nette
EEffIo
Iii
IEEE
txtbk2.11 let t net 3 net 5 andnet e struct
i iti i
b computeget
it
now
it
at hit
fi
sa i
litinetsgets
t i
na
anti
its
ssnette
stua
txt
then
owingimpulseresponsescorresponds tostable LTIsystems
li i
thesystemisstable
e
t in
b h t e cosat N t
needto checkif h is absolutelyintegrable ornot
S h t at Slecoscanat as l cost 2sinat
0 5 2sinz o cos210
thesystemisstable
seat
cosbtat a b acosbtbsinbt
5 2 0 1 5 ca
txtbk2.15 whichof thefollowingimpulseresponsescorresponds tostableLTTsystems
a h.cn ncos En non
needtocheckif hisabsolutelysummableornot
in then l n IncosEnt a
thesystemisunstable
b ha n 3 v1 n 10
needtocheckif hisabsolutelysummableornot
3h1 a
in then
thesystemis unstable
txtbk2.17consideran LTI systemwhoseinput t andoutputyet arerelatedbythedifferential
st alsosatisfiesthecondition of initialrest
t.isiti tinta
earth
Iiitiiiiiiiiiiiiiiiiiiiiiiiiiiiii
Ii
yn needtosolve
I
7
am
yn t o andassumethat yn t Best aftersubstitution sBest 4Best o
Ee i't.be ftpigiginitialconditiontofindB yes f i b i o B f
b
at t t t with Re y t determine y t ofthe LTI system
9tsfy y 44
pite
Ée i e scosts ietsincstse.atuct
H re ecresistant
yet re felt iiE jii
yet
n
retiretoscsn ie teoscsn.ie sthitt
yt
31 e t u t
e cos3H e sin
i i
Ii lid ii
atsuct
ge
txtbk 2.18 considera causal LTI systemwhoseinput Cnsandoutputyen are relatedbythe
differenceequation
n'if
yen yen1 ns
n
n2
Lily
1
determing
n 4
y4
y
ÉY
yes
yin
4
4
4 0
vn1
yes to
y 4 64
txtbk2.28 determinewhethereachdiscretetime LTIsystemiscausalandorstable
hens ca
stable
o for no
high
a men
Ea
yes
causal
in iiIiii m
ma
b hn
oe n n 2
causal
yes
11 12
µ man
stapleslentil
a nin
2 110851 10.8 410.8s
E
cousin
5
E.at 2n1 2 2 22 20
311
n 3
i
iii
causing
ans
causal
ninski
f hn
stq.EIininiin 1czmt.EEkoint a
E von comnu i n
causan
sta
a
EaininsilnE.lt nt E.di.oisnl a
g hn
er ris
I
n
stable
erener
n 5much 1
causal
t.az
fncniiisiinc ini a
0.8
1.5625 1.25 1
d8 2.8125 a
tbh 2
ie
29291mi
a h t p oct 2
continuous
fire
eygach
Instead
causalandorstable
avg.i.IE
if at s e at
stables
t
at
e
e at at
feet
fiat zezt1 o
0 e
b h t e tu 3 t
cause
Il o e s
Ie_ ca
I3
init at s
c h t e tu
50
f le 18 at
a
cays
stabs pe
d h t e tu t t
causal
stab
ca
it
219 zest
ez e
Ele 2 03 co
txtbk2.31considerthe LTIsysteminitially atrestanddescribedbythedifferenceequation
in 2x n 2 find theresponseofthissystem totheinputdepicted in the figure
yen 2yen1
bysolvingthe differenceequation recursively
iiIii
i
iiiii
iiii.is
iiiiiiiiiiiiiiiiiiii.iei iiiiiiiiiiiiiiii.it
I
am
i
iiiiiiiiiiiiiiiiii.in
