2
.
1)
x[n]
S[n] +28 [n-17-s[n-3]
=
.
h[n]
9) Y (n]
=
,
.
26 [n
=
+
13
+
2 S(n-13
x2n] xh[n]
*[n]
9
h[n]
p
,
=
x[n]
(S[n]
(28(n
=>
=>
I
h[n]
<
+
(26[n
=>
28 2n -1]
+
13
+
1)
+
-
f<n
28 (n+]
+
·
2
A
B
y,(n]
2
11
.
+
48[n]
3])(262n + 13 28(n-1])
+
-
45[n] +48(n-2)-28 [n-23-75[n-43)
+
28 [n -13
+
25 [n 23
-
-
28(n-43)
plot
y [n]
I
"II
N
y [n]
2
si
he
Ez
x[n +2] xh[n]
=
LT1 system Shift
2 to
the
left
y [n]
=
2
I
<3
4p
+
2
+
!345
2
2
Y(n]
.
=
x[n]
*
h[n]
x[n]
y()x2k]h(n- k] =
k
-
=
D
sum
formula :
"
an
=
=
(E) u[n]
,
h[n]
=
UCn-2]
---
CR]
·
nSn-ck-S
Shaier at
for
<z
,
urnaz
no
overlap
, it
n
11
↑ ↑y
·
23
/
site's cus
x<n]
-
1
2n-2
-
e
L
h(k z]
-
!
-
2 22
.
+
a)
x(t)
.
h(t)
y(t)
=
3)
2-
=
-
x(t)
f uct)
!
+
-
=
e
Gx(i)h(t
-
T)d+
= eateft-
-
) d4
act -
-
<O
x(t)h(t 4)
-
=
y(t)
0
↑
-R
=
->0
:
/
when
a
=
H
-y(t)
&
-
=
e
Y
Je
=
yct)
yet 9 +d4
y(t)
act
=xtfI
2I
di
2
e-
Pt
.
efT
di
et /
=
hY
e
.
ef d4
0
-
whe
*
-
↓
f
=
I
·
f(t Y)
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g
f
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=
2
f+
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0
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A
=
2
=
4
-
↓
A
e
a
f
=est; ttethe
-
2
+
↑
b)
x(t)
·
zuct -2)
U(t)
=
x
#
u(t -5)
+
-
-
-
h(t)
ei +u(l- t)
=
T
usI-t)
+2/2
2Ct
I
+34
-
O
=
I(e2t
=
14t
-
->
3
e2st-
-
C
L
dT
n(t
i
22(t
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+
t
2(t 2)
-
2
-
1
-
2
2e2t-)
↓
e
<
5)
2
2+
-
>
t-
6
3
->
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>
-
1
5))
< 32
, ct-4d4-Je2Ct-i) &T
2
2
2
2(t 2)
-
2
=
-
-
2
-
2
-
32 +
5)
+
t
E
(e
=
-
2e2t
e2-5)
+
6
=
25 2
5
-fezt y
e
-
=
t 1
-
=
-
(2
e2(t
-
5) z(e2t 522)
-
-
=
-
t 26
overlap
NO
,
y(t)
zero
y(t)
x(t)
=
y(t)
I
I(e2tze2-)+e2Ct=(e
-
zet
= (e2t-5)
-
0
-2)
+
e2t-5))
e)
t 21
12t 23
S(t)
i(t)
=
*
-
-I
h(t)
US5)
·
-
t 1
-
(2)
-
=
+
n(t
5))xh(t)
-
S(t-5)
d5
-
+
fe2t T)d4
-
+
e2Ct-5 u(1 -(t 4)
+ - 10
=
32 t d
6t
h(t)
2n(t -2)
-
S(t) -2S(t-2)
->
5)
*
[u(t)
=
-
18
,
2
-
4)d4
=
=
et
2
h(t)
s
h(t)
2 23
.
I
x(t)
k
=
I
-
<
-
I
I
-
S
⑧
y(t)
y(t)
x(t)
=
#
h(t)
*
E
8t
=
h(t)
-
kT)x h(t)
8(t-to)
x
y(t)
-h(t
-
=
h(t-to)
=
kT)
y(t
-
+
T)
=
25t
-
(k- T
~
T =2
y(t)
8h(t
=
-
<
R- D
y(t
+
T)
k
2029
=
4
h(t)
12
i
4
D
2R
-
unt
Fits
-
2)
-
>
I
D
↓
I
+
-
e
=
I
-
2h(t
=
,
/↳
2)
=
.
c
-
,
&
a)
g(t-kT)
=
<
-
-
for
·
·
h(t)
+ >O
nct)
=
a)
0
sal
A
.
(hct/dt
=
table
.
.
&e-4
+
dt
te
C)
.
for
h
-
e
=
+CO
=tu(t
FO
,
Shldt
=
-
fe
50
+
50)
NOn-Causal
E
i
.
+
+
=
e
we
f) h(t)
=
.
+et ult)
frtr0gh-net
=
=>
lable
2
30)
,
y <n]
·
+
y <n]
Assume
y [n]
y [0]
y 20]
·
y
[1]
y[z]
y[3]
=
0
2y[n+1]
=
x2n]
=
,
x[n]
=
=
-
xC0]
x[1]
=
e
D
impy be resson se
2y<n-1]
[n]
X
=
S[n]
!
x[0]
=
-
x[n]
=
(0-0) -
x[z]
x(3]
=
-
-
n
zy[ 1]
-
yC03
-
·
0
2y[0]
2y[1]
2y[23
(-2)"u<n]
I->
=
1
=
2
-
=
=
4
8
-
<0