GATE EE

Signals and Systems

Continuous Time Periodic Signal Fourier Series

Previous Years Questions

## Marks 1

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...

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...

For a periodic square wave, which one of the following statements is TRUE?

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...

The period of the signal $$x\left(t\right)=8\sin\left(0.8\mathrm{πt}+\frac{\mathrm\pi}4\right)$$ is

The second harmonic component of the periodic waveform given in the figure has
an amplitude of
...

$$x(t)$$ is a real valued function of a real variable with period $$T.$$ Its trigonometric. Fourier Series expansion contains no terms of frequency
$...

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

Fourier Series for the waveform, $$f(t)$$ shown in Fig. is
...

What is the $$rms$$ value of the voltage waveform shown in Fig?
...

A periodic rectangular signal, $$x(t)$$ has the waveform shown in Figure. Frequency of the fifth harmonic of its spectrum is
...

The $$rms$$ value of the periodic waveform $$e(t),$$ shown in figure is
...

## Marks 2

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...

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...

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...

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 ...

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...

The Fourier series for the function f(x) = sin2 x is

For the triangular waveform shown in the figure, the $$RMS$$ value of the voltage is equal to
...

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

The $$rms$$ value of the periodic waveform given in Fig. is
...

## Marks 5

Consider the voltage waveform $$V,$$ shown in Fig. Find.
$$(a)$$$$\,\,\,\,\,\,\,\,$$ the dc component of $$V,$$
$$(b)$$$$\,\,\,\,\,\,\,\,$$ the a...

Compute the amplitude of the fundamental component of the waveform given in figure.
...