1
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
2
GATE EE 2007
+2
-0.6
A signal $$x(t)$$ is given by
$$x\left( t \right) = \left\{ {\matrix{ {1, - {\raise0.5ex\hbox{\scriptstyle T} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle 4}} < t \le {\raise0.5ex\hbox{\scriptstyle {3T}} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle 4}}} \cr { - 1,{\raise0.5ex\hbox{\scriptstyle {3T}} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle 4}} < t \le {\raise0.5ex\hbox{\scriptstyle {7T}} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle 4}},\,\,\,} \cr { - x\left( {t + T} \right)} \cr } } \right.$$ 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
$${\pi \over 4}sin\left( {{{\pi t} \over {2T}} + {\pi \over 4}} \right)$$
3
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
4
GATE EE 2005
+2
-0.6
For the triangular waveform shown in the figure, the $$RMS$$ value of the voltage is equal to
A
$$\sqrt {{1 \over 6}}$$
B
$$\sqrt {{1 \over 3}}$$
C
$${1 \over 3}$$
D
$$\sqrt {{2 \over 3}}$$
EXAM MAP
Medical
NEET