GATE EE 2006 | Continuous Time Periodic Signal Fourier Series Question 12 | Signals and Systems

GATE EE 2006

MCQ (Single Correct Answer)

-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

$$x\left( t \right) = - x\left( {t - T} \right)$$

$$x\left( t \right) = x\left( {T - t} \right) = - x\left( { - t} \right)$$

$$x\left( t \right) = x\left( {T - t} \right) = - x\left( {t - T/2} \right)$$

$$x\left( t \right) = x\left( {t - T} \right) = - x\left( {t - T/2} \right)$$

GATE EE 2005

MCQ (Single Correct Answer)

-0.3

The RMS value of the voltage v(t) = 3 + 4cos(3t) is

$$\sqrt{17}\;V$$

5 V

7 V

$$\left(3\;+\;2\sqrt2\right)\;\mathrm V$$

GATE EE 2002

MCQ (Single Correct Answer)

-0.3

Fourier Series for the waveform, $$f(t)$$ shown in Fig. is GATE EE 2002 Signals and Systems - Continuous Time Periodic Signal Fourier Series Question 11 English

GATE EE 2002 Signals and Systems - Continuous Time Periodic Signal Fourier Series Question 11 English

$${8 \over {{\pi ^2}}}\left[ {\sin \left( {\pi t} \right) + {1 \over 9}\sin \left( {3\,\pi t} \right) + {1 \over {25}}\sin \left( {5\,\pi t} \right) + ........} \right]$$

$${8 \over {{\pi ^2}}}\left[ {\sin \left( {\pi t} \right) - {1 \over 9}\cos \left( {3\,\pi t} \right) + {1 \over {25}}\sin \left( {5\,\pi t} \right) + ........} \right]$$

$${8 \over {{\pi ^2}}}\left[ {\cos \left( {\pi t} \right) + {1 \over 9}\cos \left( {3\,\pi t} \right) + {1 \over {25}}\cos \left( {5\,\pi t} \right) + ........} \right]$$

$${8 \over {{\pi ^2}}}\left[ {\cos \left( {\pi t} \right) - {1 \over 9}\sin \left( {3\,\pi t} \right) + {1 \over {25}}\sin \left( {5\,\pi t} \right) + ........} \right]$$

GATE EE 2002

MCQ (Single Correct Answer)

-0.3

What is the $$rms$$ value of the voltage waveform shown in Fig? GATE EE 2002 Signals and Systems - Continuous Time Periodic Signal Fourier Series Question 10 English