Question

Find the average signal power of the given signal () = 200?

Answer 1

The average signal power of the given signal
`\(s(t) = 200\)` is
`\(P_{\text{avg}} = \frac{{200^2}}{2} = 20000\)` .

Step-by-step explanation:

The average signal power
`\(P_{\text{avg}}\)` of a continuous-time signal
`\(s(t)\)` can be computed using the formula:

`\[P_{\text{avg}} = \frac{{1}}{{T}} \int_{-(T)/(2)}^{(T)/(2)} s^2(t) \, dt\]`

However, for a constant signal, we can use a simplified formula derived

from this general expression. For a constant signal
`\(s(t) = A\)` , where
`\(A\)` is the amplitude, the average power is given by:

`\[P_{\text{avg}} = \frac{{A^2}}{2}\]`

In the provided signal
`\(s(t) = 200\)` , the amplitude
`\(A\)` is also 200. Substituting this value into the formula:

`\[P_{\text{avg}} = \frac{{200^2}}{2}\]`

`\[P_{\text{avg}} = \frac{{40000}}{2}\]`

`\[P_{\text{avg}} = 20000\]`

Therefore, the average signal power of the constant signal
`\(s(t) = 200\)` is
`\(20000\)` . This calculation demonstrates that the power of a constant signal is directly related to the square of its amplitude divided by 2.

Understanding this relationship is fundamental in signal analysis, especially in fields like telecommunications and signal processing, where assessing signal strength and characteristics is essential for proper system functionality and design.