# Questions & Answers of Fourier Series Representation of Continuous Periodic Signals

## Weightage of Fourier Series Representation of Continuous Periodic Signals

Total 9 Questions have been asked from Fourier Series Representation of Continuous Periodic Signals topic of Signals, Systems and Communications subject in previous GATE papers. Average marks 1.56.

Consider $g(t)=\left\{\begin{array}{lc}t-\left\lfloor t\right\rfloor,&t\geq0\\t-\left\lceil t\right\rceil,&otherwise\end{array}\right.$, where $t\in\mathbb{R}.$

Here, $\left\lfloor t\right\rfloor$ represent the largest integer less than or equal to t and $\left\lfloor t\right\rfloor$ denotes the smallest integer greater than or equal to t.  The coefficient of the second harmonic of the Fourier series represent g(t) is__________

Let $f(x)$ be a real, periodic function satisfying $f\left(-x\right)=-f\left(x\right)$. The general form of its Fourier series representation would be

The signum function is given by

The Fourier series expansion of $sgn\left(\cos\left(t\right)\right)$ has

Let $g:\left[0,\infty \right)\to :\left[0,\infty \right)$ be a function defined by $g\left(x\right)=x-\left[x\right]$, where $\left[x\right]$ represents the integer part of x. (That is, it is the largest integer which is less than or equal to x). The value of the constant term in the Fourier series expansion of $g\left(x\right)$ is _______

The fourier series expansion $\style{font-size:18px}{f\left(t\right)=a_0+\sum\limits_{n=1}^\infty a_n\cos n\omega t+b_n\sin n\omega t}$ of the periodic signal shown below will contain the following nonzero terms

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

The Fourier Series coefficient, of a periodic signal x(t), expressed as $\style{font-size:18px}{x\left(t\right)={\textstyle\sum\limits_{k=-\infty}^\infty}a_ke^{\mathrm j2\mathrm{pkt}/\mathrm T}}$ are given by a-2 = 2 - j1; a-1 = 0.5 + j0.2; a0 = j2; a1 = 0.5 + j0.2; a2 = 2 + j1; and . Which of the following is true?

A signal x(t) is given by $x\left(t\right)=\left\{\begin{array}{lc}1,& -T/4