# Continuous Time Periodic Signal Fourier Series · Signals and Systems · GATE EE

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## Marks 1

GATE EE 2022
The discrete time Fourier series representation of a signal x[n] with period N is written as $$x[n] = \sum\nolimits_{k = 0}^{N - 1} {{a_k}{e^{j(2kn\pi... GATE EE 2017 Set 1 Consider$$$g\left(t\right)=\left\{\begin{array}{l}t-\left\lfloor t\right\rfloor,\\t-\left\lceil t\right\rceil,\end{array}\right.\left.\begin{array}{r... GATE EE 2014 Set 1 For a periodic square wave, which one of the following statements is TRUE? GATE EE 2011 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 show...
GATE EE 2010
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 2006
$$x(t)$$ is a real valued function of a real variable with period $$T.$$ Its trigonometric. Fourier Series expansion contains no terms of frequency $... GATE EE 2005 The RMS value of the voltage v(t) = 3 + 4cos(3t) is GATE EE 2002 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 1996 A periodic rectangular signal, $$x(t)$$ has the waveform shown in Figure. Frequency of the fifth harmonic of its spectrum is ... GATE EE 1995 The $$rms$$ value of the periodic waveform $$e(t),$$ shown in figure is ... ## Marks 2 GATE EE 2017 Set 1 Let the signal $$x\left(t\right)=\sum_{k=-\infty}^{+\infty}\left(-1\right)^k\delta\left(t-\frac k{2000}\right)$$$ be passed through an LTI system wit...
GATE EE 2015 Set 1
The signum function is given by $$\mathrm{sgn}\left(\mathrm x\right)=\left\{\begin{array}{l}\frac{\mathrm x}{\left|\mathrm x\right|};\;\mathrm x\neq0... GATE EE 2009 The Fourier Series coefficients, of a periodic signal$$x\left( t \right),$$expressed as$$x\left( t \right) = \sum {_{k = - \infty }^\infty {a_k}{e...
GATE EE 2008
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 ...
GATE EE 2007
A signal $$x(t)$$ is given by $$x\left( t \right) = \left\{ {\matrix{ {1, - {\raise0.5ex\hbox{\scriptstyle T} \kern-0.1em/\kern-0.15em \lower0.2... GATE EE 2005 The Fourier series for the function f(x) = sin2 x is GATE EE 2005 For the triangular waveform shown in the figure, the$$RMS$$value of the voltage is equal to ... GATE EE 2004 The rms value of the resultant current in a wire which carries a dc current of 10 A and a sinusoidal alternating current of peak value 20 A is GATE EE 2004 The$$rms$$value of the periodic waveform given in Fig. is ... ## Marks 5 GATE EE 2001 Consider the voltage waveform$$V,$$shown in Fig. Find.$$(a)\,\,\,\,\,\,\,\,$$the dc component of$$V,(b)\,\,\,\,\,\,\,\, the a...
GATE EE 1997
Compute the amplitude of the fundamental component of the waveform given in figure. ...
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