Recent questions tagged fourier-transform / GO Electrical

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GATE Electrical 2021 | Question: 32
Let $f(t)$ be an even function, i.e. $f(-t)=f(t)$ for all $t$. Let the Fourier transform of $f(t)$ be defined as $F\left ( \omega \right )=\int\limits_{-\infty }^{\infty }\:f\left ( t \right )e^{-j\omega t}dt$ ... $f\left ( 0 \right )< 1$ $f\left ( 0 \right )> 1$ $f\left ( 0 \right )= 1$ $f\left ( 0 \right )= 0$

Let $f(t)$ be an even function, i.e. $f(-t)=f(t)$ for all $t$. Let the Fourier transform of $f(t)$ be defined as $F\left ( \omega \right )=\int\limits_{-\infty }^{\infty ...

Arjun

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Arjun asked Feb 19, 2021

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Arjun

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Arjun asked Feb 19, 2021

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GATE Electrical 2012 | Question: 42
The Fourier transform of a signal $h(t)$ is $H(j \omega) = (2 \cos \omega) (\sin 2 \omega )/ \omega$. The value of $h(0)$ is $1/4$ $1/2$ $1$ $2$

The Fourier transform of a signal $h(t)$ is $H(j \omega) = (2 \cos \omega) (\sin 2 \omega )/ \omega$. The value of $h(0)$ is$1/4$$1/2$$1$$2$

Andrijana3306

1.4k points

Andrijana3306 asked Mar 23, 2018

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GATE Electrical 2018 | Question: 40
The Fourier transform of a continuous-time signal $x(t)$ is given by $X(\omega) = \frac{1}{(10+j \omega)^2}, – \infty < \omega < \infty$, where $j = \sqrt{-1}$ and $\omega$ denoes frequency. Then the value of $\mid \text{ln } x(t) \mid$ at $t=1$ is _________ (up to $1$ decimal place). ($\text{ln}$ denotes the logarithm base $e$)

The Fourier transform of a continuous-time signal $x(t)$ is given by $X(\omega) = \frac{1}{(10+j \omega)^2}, – \infty < \omega < \infty$, where $j = \sqrt{-1}$ and $\om...

Arjun

15.9k points

Arjun asked Feb 19, 2018

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5

GATE Electrical 2013 | Question: 4
The impulse response a the system is $h(t)=t\:u(t).$ For an input $u(t-1)$, the output is $\dfrac{t^2}{2}u(t) \\$ $\dfrac{t(t-1)}{2}u(t-1) \\$ $\dfrac{(t-1)^2}{2}u(t-1) \\$ $\dfrac{t^2-1}{2}u(t-1)$

The impulse response a the system is $h(t)=t\:u(t).$ For an input $u(t-1)$, the output is$\dfrac{t^2}{2}u(t) \\$$\dfrac{t(t-1)}{2}u(t-1) \\$$\dfrac{(t-1)^2}{2}u(t-1) \\$$...

piyag476

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piyag476 asked Feb 11, 2017

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GATE Electrical 2014 Set 3 | Question: 35
A differentiable non constant even function $x(t)$ has a derivative $y(t)$, and their respective Fourier Transforms are $X(\omega)$ and $Y(\omega)$. Which of the following statements is TRUE? $X(\omega)$ and $Y(\omega)$ ... imaginary. $X(\omega)$ and $Y(\omega)$ are both imaginary. $X(\omega)$ is imaginary and $Y(\omega)$ is real.

A differentiable non constant even function $x(t)$ has a derivative $y(t)$, and their respective Fourier Transforms are $X(\omega)$ and $Y(\omega)$. Which of the followin...

makhdoom ghaya

9.4k points

makhdoom ghaya asked Feb 11, 2017

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7

GATE Electrical 2014 Set 3 | Question: 5
A function $f(t)$ is shown in the figure. The Fourier transform $F(\omega)$ of $f(t)$ is real and even function of $\omega$ real and odd function of $\omega$ imaginary and odd function of $\omega$ imaginary and even function of $\omega$

A function $f(t)$ is shown in the figure.The Fourier transform $F(\omega)$ of $f(t)$ isreal and even function of $\omega$real and odd function of $\omega$imaginary and od...

makhdoom ghaya

9.4k points

makhdoom ghaya asked Feb 11, 2017

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8

GATE Electrical 2014 Set 3 | Question: 9
A signal is represented by $x(t)=\begin{cases} 1 & \mid t \mid<1 \\ 0 & \mid t \mid >1 \end{cases}$ The Fourier transform of the convolved signal $y(t)$= $x(2t)*x(t/2)$ ... $\dfrac{4}{\omega ^2} \sin(2\omega ) \\$ $\dfrac{4}{\omega ^2} \sin^2\omega $

A signal is represented by $$x(t)=\begin{cases} 1 & \mid t \mid<1 \\ 0 & \mid t \mid >1 \end{cases}$$ The Fourier transform of the convolved signal $y(t)$= $x(2t)*x(t/2)...

makhdoom ghaya

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makhdoom ghaya asked Feb 11, 2017

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9

GATE Electrical 2014 Set 1 | Question: 55
The figure shows one period of the output voltage of an inverter.$\alpha$ should be chosen such that $60^{\circ}<\alpha <90^{\circ}$. If $rms$ value of the fundamental component is $50V$, then $\alpha$ in degree is__________

The figure shows one period of the output voltage of an inverter.$\alpha$ should be chosen such that $60^{\circ}<\alpha <90^{\circ}$. If $rms$ value of the fundamental c...

makhdoom ghaya

9.4k points

makhdoom ghaya asked Feb 11, 2017

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10

GATE Electrical 2014 Set 1 | Question: 35
Let $f(t)$ be continuous time signal and let $F(w)$be its Fourier Transform defined by $F(\omega )=\displaystyle{}\int_{-\infty }^{\infty }f(t)e^{-j\omega t} dt$ define $g(t)$ ... $f(t)$ only if $f(t)$ is a sinusoidal function. $g(t)$ would never be proportional to $f(t)$.

Let $f(t)$ be continuous time signal and let $F(w)$be its Fourier Transform defined by $F(\omega )=\displaystyle{}\int_{-\infty }^{\infty }f(t...

makhdoom ghaya

9.4k points

makhdoom ghaya asked Feb 11, 2017

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11

GATE Electrical 2014 Set 1 | Question: 26
Let $g:[0,\infty )\rightarrow [0,\infty )$ be a function defined by $g(x)=x-[x]$, where $[x]$ 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 $g(x)$ is _______

Let $g:[0,\infty )\rightarrow [0,\infty )$ be a function defined by $g(x)=x-[x]$, where $[x]$ represents the integer part of $x.($That is, it is the largest integer whic...

makhdoom ghaya

9.4k points

makhdoom ghaya asked Feb 11, 2017

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12

GATE Electrical 2016 Set 1 | Question: 27
Let $S=\sum_{n=0}^{\infty} n\alpha^{n}$ where $\mid \alpha \mid < 1$. The value of $\alpha$ in the range $0 < \alpha < 1$, such that $S=2 \alpha$ is _________.

Let $S=\sum_{n=0}^{\infty} n\alpha^{n}$ where $\mid \alpha \mid < 1$. The value of $\alpha$ in the range $0 < \alpha < 1$, such that $S=2 \alpha$ is _________.

makhdoom ghaya

9.4k points

makhdoom ghaya asked Jan 29, 2017

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13

GATE Electrical 2016 Set 1 | Question: 3
The Laplace Transform of $f(t)=e^{2t} \sin (5t)(ut)$ is $\dfrac{5}{s^{2}-4s+29} \\ $ $\dfrac{5}{s^{2}+5} \\ $ $\dfrac{s-2}{s^{2}-4s+29} \\$ $\dfrac{5}{s +5}$

The Laplace Transform of $f(t)=e^{2t} \sin (5t)(ut)$ is $\dfrac{5}{s^{2}-4s+29} \\ $$\dfrac{5}{s^{2}+5} \\ $$\dfrac{s-2}{s^{2}-4s+29} \\$$\dfrac{5}{s +5}$

makhdoom ghaya

9.4k points

makhdoom ghaya asked Jan 29, 2017