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Byju's Answer
Standard XII
Physics
Kinetic Energy Formulae
Consider the ...
Question
Consider the discrete time signal,
x
(
n
)
=
(
1
3
)
n
u
[
n
]
where
u
[
n
]
=
{
1
n
≥
0
0
n
<
0
y
[
n
]
=
x
[
−
n
]
,
−
∞
<
x
[
−
n
]
<
∞
Then,
∑
∞
n
=
−
∞
y
(
n
)
=
___.
1.5
Open in App
Solution
The correct option is
A
1.5
x
[
n
]
=
(
1
3
)
n
u
[
n
]
y
[
n
]
=
x
[
−
n
]
=
(
1
3
)
−
n
u
[
−
n
]
∑
∞
n
=
−
∞
y
(
n
)
=
∑
∞
n
=
−
∞
(
1
3
)
−
n
u
[
−
n
]
u
[
−
n
]
=
{
1
,
n
≤
0
0
,
n
>
0
So,
∑
∞
n
=
−
∞
y
[
n
]
=
∑
0
n
=
−
∞
(
1
3
)
−
n
Let n = -m, then we get,
∑
∞
n
=
−
∞
y
[
n
]
=
∑
∞
m
=
0
(
1
3
)
m
=
1
+
1
3
+
(
1
3
)
2
+
.
.
.
=
1
1
−
1
3
=
3
2
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4
Similar questions
Q.
Consider the discrete time signal
x
(
n
)
=
(
1
3
)
n
u
(
n
)
,
w
h
e
r
e
u
(
n
)
=
{
1
,
n
≥
0
0
,
n
<
0
and
y
(
n
)
=
x
(
−
n
)
,
−
∞
<
n
<
∞
Then
∞
∑
n
=
−
∞
y
(
n
)
is______.
Q.
If
a
=
∑
∞
n
=
0
x
n
,
b
=
∑
∞
n
=
0
y
n
,
c
=
∑
∞
n
=
0
(
x
y
)
n
where
|
x
|
,
|
y
|
<
1
; then
Q.
Consider a discrete-time periodic signal
x
[
n
]
=
{
1
,
0
≤
n
≤
7
0
,
8
≤
n
≤
9
with period of N = 10.
A function y[n] is defined as y[n] =x[n]-x[n-1] then y[n] is periodic with period________
Q.
Consider a discrete time signal as shown in the figure below:
If
y
[
n
]
=
n
x
[
2
n
+
1
]
, then the value of
∞
∑
n
=
−
∞
y
[
n
]
will be _________.
Q.
Consider a discrete time signal x[n] whose discrete time Fourier transform is
X
(
e
j
ω
)
where
X
(
e
j
ω
)
=
1
1
−
e
−
j
ω
⎛
⎜ ⎜
⎝
s
i
n
3
2
ω
s
i
n
ω
2
⎞
⎟ ⎟
⎠
+
5
π
δ
(
ω
)
;
−
π
≤
ω
≤
π
Then the value of x[n] at n=3 is
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