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. ...
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