Official PYQ · 2021Set 1 · Q39Continuous-time SignalsNAT2 marks

GATE EC 2021 Set 1 Q39 — Continuous-time Signals

The exponential Fourier series representation of a continuous-time periodic signal $x(t)$ is defined as

$x\left ( t \right )=\sum_{k=-\infty }^{\infty }a_{k}e^{jk\omega _{0}t}$

where $\omega _0$ is the fundamental angular frequency of $x(t)$ and the coefficients of the series are $a_{k}$ . The following information is given about $x(t)$ and $a_{k}$ .

$x(t)$ is real and even, having a fundamental period of $6$
The average value of $x(t)$ is $2$
$a_{k}=\left\{\begin{matrix} k, & 1\leq k\leq 3\\ 0,& k> 3 \end{matrix}\right.$

The average power of the signal $x(t)$ (rounded off to one decimal place) is ______________

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Answer: 31.9:32.1

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Published 10 Oct 2026

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