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

Start Practice## 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.
...