GATE EE

Continuous Time Periodic Signal Fourier Series

Signals and Systems

(Past Years Questions)

Marks 1

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Consider $$$g\left(t\right)=\left\{\begin{array}{l}t-\left\lfloor t\right\rfloor,\\t-\left\lceil t\right\rceil,\end{arra...
GATE EE 2017 Set 1
For a periodic square wave, which one of the following statements is TRUE?
GATE EE 2014 Set 1
The fourier series expansion $$$f\left(t\right)\;=\;a_0\;+\;\sum_{n=1}^\infty a_n\cos\;n\omega t\;+\;b_n\sin\;n\omega t$...
GATE EE 2011
The second harmonic component of the periodic waveform given in the figure has an amplitude of ...
GATE EE 2010
The period of the signal $$x\left(t\right)=8\sin\left(0.8\mathrm{πt}+\frac{\mathrm\pi}4\right)$$ is
GATE EE 2010
$$x(t)$$ is a real valued function of a real variable with period $$T.$$ Its trigonometric. Fourier Series expansion con...
GATE EE 2006
The RMS value of the voltage v(t) = 3 + 4cos(3t) is
GATE EE 2005
Fourier Series for the waveform, $$f(t)$$ shown in Fig. is ...
GATE EE 2002
What is the $$rms$$ value of the voltage waveform shown in Fig? ...
GATE EE 2002
A periodic rectangular signal, $$x(t)$$ has the waveform shown in Figure. Frequency of the fifth harmonic of its spectr...
GATE EE 1996
The $$rms$$ value of the periodic waveform $$e(t),$$ shown in figure is ...
GATE EE 1995

Marks 2

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Let the signal $$$x\left(t\right)=\sum_{k=-\infty}^{+\infty}\left(-1\right)^k\delta\left(t-\frac k{2000}\right)$$$ be pa...
GATE EE 2017 Set 1
The signum function is given by $$$\mathrm{sgn}\left(\mathrm x\right)=\left\{\begin{array}{l}\frac{\mathrm x}{\left|\mat...
GATE EE 2015 Set 1
The Fourier Series coefficients, of a periodic signal $$x\left( t \right),$$ expressed as $$x\left( t \right) = \sum {_{...
GATE EE 2009
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 coeff...
GATE EE 2008
A signal $$x(t)$$ is given by $$x\left( t \right) = \left\{ {\matrix{ {1, - {\raise0.5ex\hbox{$\scriptstyle T$} \ker...
GATE EE 2007
The Fourier series for the function f(x) = sin2 x is
GATE EE 2005
For the triangular waveform shown in the figure, the $$RMS$$ value of the voltage is equal to ...
GATE EE 2005
The rms value of the resultant current in a wire which carries a dc current of 10 A and a sinusoidal alternating current...
GATE EE 2004
The $$rms$$ value of the periodic waveform given in Fig. is ...
GATE EE 2004

Marks 5

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Consider the voltage waveform $$V,$$ shown in Fig. Find. $$(a)$$$$\,\,\,\,\,\,\,\,$$ the dc component of $$V,$$ $$(b...
GATE EE 2001
Compute the amplitude of the fundamental component of the waveform given in figure. ...
GATE EE 1997

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