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The power of the signal x(n) = e j2πn will be— 4
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- 18 watts
- 36 watts
- 72 watts
- None of these
Correct Option: B
Given, x(n) = 6e | 4 |
or x(n) = 6 | lim s → 0 | ![]() | cos | + j sin | ![]() | ||
4 | 4 |
The signal is periodic with period
N = | m = 4 | |
4 |
with m = 1
x(0) = 6 | ![]() | cos | · 0 + j sin | · 0 | ![]() | = 6[1 + 0] = 6 | ||
4 | 4 |
x(1) = 6 | ![]() | cos | · 1 + j sin | · 1 | ![]() | |||
4 | 4 |
= 6 | ![]() | cos | + j sin | ![]() | = j6 | |||
2 | 2 |
x(2) = 6 | ![]() | cos | · 2 + j sin | · 1 | ![]() | |||
4 | 4 |
= 6 [cos π + j sin π] = 6 [– 1 + j·0] = – 6
x(3) = 6 | ![]() | cos | · 3 + j sin | · 3 | ![]() | |||
4 | 4 |
= 6 | ![]() | cos | + j sin | ![]() | = 6[– j] = – j6. | |||
2 | 2 |
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 |
= | [|x(0)|2 + |x(1)|2 + |x(2)|2 + |x(3)|2] | 4 |
= | [|6|2 + |j6|2 + |6|2+ |– 6|2] | 4 |
= | [36 + 36 + 36 + 36] | 4 |
= 36 watt
Hence, alternative (B) is the correct choice.