GATE 2025 EE – Question 30
A continuous time periodic signal $x(t)$ is
$$x(t)=1+2\cos2\pi t+2\cos4\pi t+2\cos6\pi t.$$
If $T$ is the period of $x(t)$, then $\dfrac1T\int_0^T|x(t)|^2dt=$ __________ (round off to the nearest integer).
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Correct answer: 7
Explanation
By Parseval's theorem, the average power is the sum of the powers of the components: the DC term contributes $1^2=1$, and each cosine of amplitude 2 contributes $2^2/2=2$. Total $=1+3\times2=7$.