Hot questions in Signals and Systems

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1

Gate 2000 signals and systems

120 points

Hanuma asked Mar 16, 2021

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2

GATE Electrical 2020 | Question: 10
Consider a linear time-invariant system whose input $\text{r(t)}$ and output $\text{y(t)}$ are related by the following differential equation: $\frac{d^{2}y\left ( t \right )}{dt^{2}}+4y\left ( t \right )=6r\left ( t \right )$ The poles of this system are at $+2j,-2j$ $+2,-2$ $+4,-4$ $+4j,-4j$

Consider a linear time-invariant system whose input $\text{r(t)}$ and output $\text{y(t)}$ are related by the following differential equation:$$\frac{d^{2}y\left ( t \rig...

1.9k points

go_editor asked Feb 28, 2020

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Gate EE-2014
For a peridic square wave ,which one of the following statements is TRUE? 1). The fourieF series coefficients do not exist 2).The Fourier series coefficients exist but the reconstruction converges at most point. I know the correct answer is 2). But I need some explanation.

For a peridic square wave ,which one of the following statements is TRUE?1). The fourieF series coefficients do not exist2).The Fourier series coefficients exist but the ...

130 points

Shaurya khare asked Jul 8, 2018

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4

GATE Electrical 2014 Set 1 | Question: 10
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 ... the reconstruction converges at most points. The Fourier series coefficients exist and the reconstruction converges at every point.

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 recon...

9.4k points

makhdoom ghaya asked Feb 11, 2017

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5

GATE Electrical 2014 Set 1 | Question: 33
The function shown in the figure can be represented as $u(t)-u(t-T)+\dfrac{(t-T)}{T}u(t-T)-\frac{(t-2T)}{T}u(t-2T) \\$ $u(t)+\dfrac{t}{T}u(t-T)-\dfrac{t}{T}u(t-2T) \\$ $u(t)-u(t-T)+\dfrac{(t-T)}{T}u(t)-\dfrac{(t-2T)}{T}u(t) \\$ $u(t)+\dfrac{(t-T)}{T}u(t-T)-2\dfrac{(t-2T)}{T}u(t-2T)$

The function shown in the figure can be represented as$u(t)-u(t-T)+\dfrac{(t-T)}{T}u(t-T)-\frac{(t-2T)}{T}u(t-2T) \\$$u(t)+\dfrac{t}{T}u(t-T)-\dfrac{t}{T}u(t-2T) \\$$u(t)...

9.4k points

makhdoom ghaya asked Feb 11, 2017

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6

GATE Electrical 2015 Set 2 | Question: 34
For linear time invariant systems, that are Bounded Input Bounded Output stable, which one of the following statements is TRUE? The impulse response will be integrable, but may not be absolutely integrable. The unit impulse response will have finite support. The unit step response will be absolutely integrable. The unit step response will be bounded

For linear time invariant systems, that are Bounded Input Bounded Output stable, which one of the following statements is TRUE?The impulse response will be integrable, bu...

9.4k points

makhdoom ghaya asked Feb 11, 2017

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7

GATE Electrical 2014 Set 3 | Question: 34
A sinusoid $x(t)$ of unknown frequency is sampled by an impulse train of period $20$ $ms$. The resulting sample train is next applied to an ideal lowpass filter with a cutoff at $25$ $Hz$. The filter output is seen to be a sinusoid of frequency $20$ $Hz$. This means that $x(t)$ has a frequency of $10$ $Hz$ $60$ $Hz$ $30$ $Hz$ $90$ $Hz$

A sinusoid $x(t)$ of unknown frequency is sampled by an impulse train of period $20$ $ms$. The resulting sample train is next applied to an ideal lowpass filter with a cu...

9.4k points

makhdoom ghaya asked Feb 11, 2017

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8

GATE Electrical 2014 Set 1 | Question: 4
Let $X(s)=\dfrac{3s+5}{s^2+10s+21}$ be the Laplace Transform of a signal $x(t)$. Then, $x(0^+) $is $0$ $3$ $5$ $21$

Let $X(s)=\dfrac{3s+5}{s^2+10s+21}$ be the Laplace Transform of a signal $x(t)$. Then, $x(0^+) $is$0$$3$$5$$21$

9.4k points

makhdoom ghaya asked Feb 11, 2017

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9

GATE Electrical 2015 Set 1 | Question: 9
A moving average function is given by $y(t) = \dfrac{1}{T} \displaystyle \int_{t-T}^{t} u(\tau ) d \tau$. If the input $u$ is a sinusoidal signal of frequency $\dfrac{1}{2T}Hz$ then in steady state, the output $y$ will lag $u$ (in degree) by __________ .

A moving average function is given by $y(t) = \dfrac{1}{T} \displaystyle \int_{t-T}^{t} u(\tau ) d \tau$. If the input $u$ is a sinusoidal signal of frequency $\dfrac{1}{...

9.4k points

makhdoom ghaya asked Feb 11, 2017

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10

GATE Electrical 2013 | Question: 41
The impulse response of a continuous time system is given by $h(t)=\delta (t-1)+\delta (t-3).$ The value of the step response at $t=2$ is $0$ $1$ $2$ $3$

The impulse response of a continuous time system is given by $h(t)=\delta (t-1)+\delta (t-3).$ The value of the step response at $t=2$ is$0$$1$$2$$3$

1.6k points

piyag476 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...

9.4k points

makhdoom ghaya asked Feb 11, 2017

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12

GATE Electrical 2015 Set 1 | Question: 28
The signum function is given by $sgn(x)= \begin{cases} \dfrac{x}{ \mid x \mid }; x \neq 0& \\ 0;x=0& \end{cases}$ The Fourier series expansion of $sgn (\cos (t) )$ has Only sine terms with all harmonics. Only cosine terms with all harmonics. Only sine terms with even numbered harmonics. Only cosine terms with odd numbered harmonics.

The signum function is given by $sgn(x)= \begin{cases} \dfrac{x}{ \mid x \mid }; x \neq 0& \\ 0;x=0& \end{cases}$ The Fourier series expansion of $sgn (\cos (t) )$ hasO...

9.4k points

makhdoom ghaya asked Feb 11, 2017

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13

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) \\$$...

1.6k points

piyag476 asked Feb 11, 2017

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14

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...

9.4k points

makhdoom ghaya asked Feb 11, 2017

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15

GATE Electrical 2014 Set 3 | Question: 20
The two signals $S1$ and $S2$, shown in figure, are applied to $Y$ and $X$ deflection plates of an oscilloscope. The waveform displayed on the screen is

The two signals $S1$ and $S2$, shown in figure, are applied to $Y$ and $X$ deflection plates of an oscilloscope.The waveform displayed on the screen is

9.4k points

makhdoom ghaya asked Feb 11, 2017

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16

GATE Electrical 2014 Set 2 | Question: 10
Consider an $LTI$ system with impulse response $h(t)=e^{-5t}u(t)$ . If the output of the system is $y(t)=e^{-3t}u(t)-e^{-5t}u(t)$ then the input, $x(t)$, is given by $e^{-3t}u(t)$ $2e^{-3t}u(t)$ $e^{-5t}u(t)$ $2e^{-5t}u(t)$

Consider an $LTI$ system with impulse response $h(t)=e^{-5t}u(t)$ . If the output of the system is $y(t)=e^{-3t}u(t)-e^{-5t}u(t)$ then the input, $x(t)$, is given by$e^{...

9.4k points

makhdoom ghaya asked Feb 11, 2017

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17

GATE Electrical 2014 Set 2 | Question: 34
An input signal $x(t)=2+5 \sin(100\pi t)$ is sampled with a sampling frequency of $400$ $Hz$ ... where, $N$ represents the number of samples per cycle. The output $y(n)$ of the system under steady state is $0$ $1$ $2$ $5$

An input signal $x(t)=2+5 \sin(100\pi t)$ is sampled with a sampling frequency of $400$ $Hz$ and applied to the system whose transfer function is represented by $$\dfrac...

9.4k points

makhdoom ghaya asked Feb 11, 2017

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18

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...

9.4k points

makhdoom ghaya asked Feb 11, 2017

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19

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)...

9.4k points

makhdoom ghaya asked Feb 11, 2017

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20

GATE Electrical 2014 Set 1 | Question: 9
$x(t)$ is nonzero only for $T_x<t<{T}'x$ , and similarly, $y(t)$ is non zero only for $T_y<t<{T}'y$. Let $z(t)$ be convolution of $x(t)$ and $y(t).$ Which one of the following statements is TRUE? $z(t)$ can be nonzero ... $T_x+T_y<t<{T}'_x+{T}'_y$ $z(t)$ is nonzero for $t>{T}'_x+{T}'_y$

$x(t)$ is nonzero only for $T_x<t<{T}'x$ , and similarly, $y(t)$ is non zero only for $T_y<t<{T}'y$. Let $z(t)$ be convolution of $x(t)$ and $y(t).$ Which one of the fol...

9.4k points

makhdoom ghaya asked Feb 11, 2017

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