1
GATE EE 2009
MCQ (Single Correct Answer)
+2
-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?

A
$$x(t)$$ has finite energy because only finitely many coefficients are non $$-$$ zero
B
$$x(t)$$ has zero average value because it is periodic
C
the imaginary part of $$x(t)$$ is constant
D
The real part of $$x(t)$$ is even
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