1
GATE EE 2011
+1
-0.3
The fourier series expansion $$f\left(t\right)\;=\;a_0\;+\;\sum_{n=1}^\infty a_n\cos\;n\omega t\;+\;b_n\sin\;n\omega t$$\$ of the periodic signal shown below will contain the following nonzero terms
A
$$a_0\;and\;b_n\;,\;n=1,\;3,\;5,\;..............\infty$$
B
$$a_0\;and\;a_n\;,\;n=1,\;2,\;3,\;..............\infty$$
C
$$a_0\;,\;a_n\;and\;b_n\;,\;n=1,\;2,\;3,\;..............\infty$$
D
$$a_0\;and\;a_n\;,\;n=1,\;3,\;5,\;..............\infty$$
2
GATE EE 2010
+1
-0.3
The second harmonic component of the periodic waveform given in the figure has an amplitude of
A
0
B
1
C
$$2/\mathrm\pi$$
D
$$\sqrt5$$
3
GATE EE 2010
+1
-0.3
The period of the signal $$x\left(t\right)=8\sin\left(0.8\mathrm{πt}+\frac{\mathrm\pi}4\right)$$ is
A
$$0.4\;\mathrm\pi\;\mathrm s$$
B
$$0.8\;\mathrm\pi\;\mathrm s$$
C
1.25 s
D
2.5 s
4
GATE EE 2006
+1
-0.3
$$x(t)$$ is a real valued function of a real variable with period $$T.$$ Its trigonometric. Fourier Series expansion contains no terms of frequency
$$\omega = 2\pi \left( {2k} \right)/T;\,\,k = 1,2,........$$ Also, no sine terms are present. Then $$x(t)$$ satisfies the equation
A
$$x\left( t \right) = - x\left( {t - T} \right)$$
B
$$x\left( t \right) = x\left( {T - t} \right) = - x\left( { - t} \right)$$
C
$$x\left( t \right) = x\left( {T - t} \right) = - x\left( {t - T/2} \right)$$
D
$$x\left( t \right) = x\left( {t - T} \right) = - x\left( {t - T/2} \right)$$
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