Discussion
What is the average power of the given signal?
Answer: B
The signal is a square wave that takes only the values +1 and −1 (it is never zero). The average power of a signal is the mean of its squared value over a period.
\[ \begin{aligned} P = \frac{1}{T}\int_0^T x^2(t)\,dt \\ &= \frac{1}{T}\int_0^T (\pm 1)^2\,dt = 1 \end{aligned} \]
Because \((+1)^2 = (-1)^2 = 1\) at every instant, the mean square is 1, whichever the proportion of time spent at each level. The mean value (the dc component) may be zero, but the power is not: a power of 0 would need a zero signal. Powers of 2 and 4 would need amplitudes of about 1.41 and 2. The answer is 1, option B.
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