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For signal x(n) = 6 cos 2πn the signal power is— 4
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- 36 watts
- 18 watts
- 72 watts
- 54 watts
Correct Option: B
Given that, x(n) = 6 cos | ![]() | ![]() | ||
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 |
= | [x(0)|2 + |x(1)|2 + |x(2)|2 + |x(3)|2 ] | 4 |
= | [(6)2 + (0)2 + (– 6)2 + (0)2 ] | 4 |
= | [36 + 0 + 36 + 0] | 4 |
= 72 4 = 18 watts.
Hence, alternative (B) is the correct choice.