McqMate
| Q. |
Determine the power of the signal: x(t) = cos(t). |
| A. | 1/2 |
| B. | 1 |
| C. | 3/2 |
| D. | 2 |
| Answer» A. 1/2 | |
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Explanation: To determine the power of the given signal x(t) = cos(t), we need to calculate the average power over time. The power of a continuous-time signal x(t) can be calculated using the formula: P = (1/T) * ∫[T] |x(t)|^2 dt Where T is the period of the signal. In this case, the signal x(t) = cos(t) is a periodic signal with a period of 2π. So we need to evaluate the integral over one period, from 0 to 2π. P = (1/(2π)) * ∫[0 to 2π] |cos(t)|^2 dt Using the trigonometric identity cos^2(t) = (1 + cos(2t))/2, we can simplify the integral: P = (1/(2π)) * ∫[0 to 2π] (1 + cos(2t))/2 dt P = (1/(2π)) * [t/2 + (sin(2t))/4] evaluated from 0 to 2π P = (1/(2π)) * [(2π/2 + (sin(4π))/4) - (0/2 + (sin(0))/4)] P = (1/(2π)) * (π + 0 - 0) = 1/2 Therefore, the power of the signal x(t) = cos(t) is 1/2. The correct answer is A. 1/2. |
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