GATE EE 2009 | GATE EE Year Wise Previous Years Questions

GATE EE 2009

MCQ (Single Correct Answer)

-0.6

The Fourier Series coefficients, of a periodic signal $$x\left( t \right),$$ expressed as $$x\left( t \right) = \sum {_{k = - \infty }^\infty {a_k}{e^{j2\pi kt/T}}} $$ are given by
$${a_{ - 2}} = 2 - j1;\,\,{a_{ - 1}} = 0.5 + j0.2;\,\,{a_0} = j2;$$
$${a_1} = 0.5 - j0.2;\,\,{a_2} = 2 + j1;\,\,$$ and
$${a_k} = 0;$$ for $$|k|\,\, > 2.$$

Which of the following is true?

$$x(t)$$ has finite energy because only finitely many coefficients are non $$-$$ zero

$$x(t)$$ has zero average value because it is periodic

the imaginary part of $$x(t)$$ is constant

The real part of $$x(t)$$ is even

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