1
GATE EE 2009
+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
2
GATE EE 2008
+2
-0.6
Let x(t) be a periodic signal with time period T. Let y(t) = x(t - t0) + x(t + t0) for some t0. The Fourier Series coefficient of y(t) are denoted by bk. If bk=0 for all odd k, then t0 can be equal to
A
T/8
B
T/4
C
T/2
D
2T
3
GATE EE 2007
+2
-0.6
A signal $$x(t)$$ is given by
$$x\left( t \right) = \left\{ {\matrix{ {1, - {\raise0.5ex\hbox{T} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{4}} < t \le {\raise0.5ex\hbox{{3T}} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{4}}} \cr { - 1,{\raise0.5ex\hbox{{3T}} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{4}} < t \le {\raise0.5ex\hbox{{7T}} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{4}},\,\,\,} \cr { - x\left( {t + T} \right)} \cr } } \right.$$ Which among the following gives the fundamental Fourier term of $$x(t)$$?
A
$${4 \over \pi }\cos \left( {{{\pi T} \over T} - {\pi \over 4}} \right)$$
B
$${\pi \over 4}\cos \left( {{{\pi t} \over {2T}} + {\pi \over 4}} \right)$$
C
$${4 \over \pi }sin\left( {{{\pi t} \over T} - {\pi \over 4}} \right)$$
D
$${\pi \over 4}sin\left( {{{\pi t} \over {2T}} + {\pi \over 4}} \right)$$
4
GATE EE 2005
+2
-0.6
The Fourier series for the function f(x) = sin2 x is
A
sinx + sin2x
B
1 - cos2x
C
sin2x + cos2x
D
0.5 - 0.5cos2x
GATE EE Subjects
Electric Circuits
Electromagnetic Fields
Signals and Systems
Electrical Machines
Engineering Mathematics
General Aptitude
Power System Analysis
Electrical and Electronics Measurement
Analog Electronics
Control Systems
Power Electronics
Digital Electronics
EXAM MAP
Joint Entrance Examination