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Signal and systems miscellaneous

Signals and Systems

  1. For signal x(n) = 6 cos
    2πn
    the signal power is—
    4
    1. 36 watts
    2. 18 watts
    3. 72 watts
    4. 54 watts
Correct Option: B

Given that, x(n) = 6 cos
2πn
4

Here, N =
· m =
· 1 = 4
Ω
4

at n = 0
⇒ x(0) = 6 cos
· 0= 6
4

at n = 1
⇒ x(0) = 6 cos
· 1= 6 x 0 = 0
4

at n = 2
⇒ x(0) = 6 cos
· 2= - 6
4

at n = 3
⇒ x(0) = 6 cos
· 3= 6 x 0 = 0
4

As we know that power of discrete time periodic signal is given by the relation
N - 1
P = 1/N|x(n)|2
n = 0

3
= 1/4|x(n)|2
n = 0

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

=
1
[(6)2 + (0)2 + (– 6)2 + (0)2 ]
4

=
1
[36 + 0 + 36 + 0]
4

= 72 4 = 18 watts.
Hence, alternative (B) is the correct choice.



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