GATE EE 2017 Set 1 | Continuous Time Periodic Signal Fourier Series Question 3 | Signals and Systems

GATE EE 2017 Set 1

Numerical

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Consider $$$g\left(t\right)=\left\{\begin{array}{l}t-\left\lfloor t\right\rfloor,\\t-\left\lceil t\right\rceil,\end{array}\right.\left.\begin{array}{r}t\geq0\\otherwise\end{array}\right\}$$$ where $$t\;\in\;R$$
Here, $$\left\lfloor t\right\rfloor$$ represents the largest integer less than or equal to t and $$\left\lceil t\right\rceil$$ denotes the smallest integer greater than or equal to t. The coefficient of the second harmonic component of the Fourier series representing g(t) is _________.

Your input ____

GATE EE 2014 Set 1

MCQ (Single Correct Answer)

-0.3

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

The Fourier series coefficients do not exist

The Fourier series coefficients exist but the reconstruction converges at no point

The Fourier series coefficients exist and the reconstruction converges at most points.

The Fourier series coefficients exist and the reconstruction converges at every point

GATE EE 2011

MCQ (Single Correct Answer)

-0.3

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 shown below will contain the following nonzero terms GATE EE 2011 Signals and Systems - Continuous Time Periodic Signal Fourier Series Question 22 English

GATE EE 2011 Signals and Systems - Continuous Time Periodic Signal Fourier Series Question 22 English

$$a_0\;and\;b_n\;,\;n=1,\;3,\;5,\;..............\infty$$

$$a_0\;and\;a_n\;,\;n=1,\;2,\;3,\;..............\infty$$

$$a_0\;,\;a_n\;and\;b_n\;,\;n=1,\;2,\;3,\;..............\infty$$

$$a_0\;and\;a_n\;,\;n=1,\;3,\;5,\;..............\infty$$

GATE EE 2010

MCQ (Single Correct Answer)

-0.3

The second harmonic component of the periodic waveform given in the figure has an amplitude of GATE EE 2010 Signals and Systems - Continuous Time Periodic Signal Fourier Series Question 21 English