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Signal and systems miscellaneous

Signals and Systems

  1. The power of the signal x(n) = e
    j2πn
    will be—
    4
    1. 18 watts
    2. 36 watts
    3. 72 watts
    4. None of these
Correct Option: B

Given, x(n) = 6e
j2πn
4

or x(n) = 6lim
s → 0
cos
2πn
+ j sin
2πn
44

The signal is periodic with period
N =
m = 4
4


with m = 1
x(0) = 6cos
· 0 + j sin
· 0= 6[1 + 0] = 6
44

x(1) = 6cos
· 1 + j sin
· 1
44

= 6cos
π
+ j sin
π
= j6
22

x(2) = 6cos
· 2 + j sin
· 1
44

= 6 [cos π + j sin π] = 6 [– 1 + j·0] = – 6
x(3) = 6cos
· 3 + j sin
· 3
44

= 6cos
+ j sin
= 6[– j] = – j6.
22

Now, the power of the signal x(n)
N - 1
P = 1/N| x(n)|2
n = 0

4 - 1
= 1/4|x(n)|2
n = 0

=
1
[|x(0)|2 + |x(1)|2 + |x(2)|2 + |x(3)|2]
4

=
1
[|6|2 + |j6|2 + |6|2+ |– 6|2]
4

=
1
[36 + 36 + 36 + 36]
4

= 36 watt
Hence, alternative (B) is the correct choice.



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