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Recent questions tagged signals-and-systems
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1
GATE ECE 2020 | Question: 5
The output $y[n]$ of a discrete-time system for an input $x[n]$ is $y\left [ n \right ]=\underset{-\infty \leq k\leq n}{\text{max}} \mid x\left [ k \right ] \mid$ The unit impulse response of the system is $0$ for all $n$. $1$ for all $n$. unit step signal $u\left [ n \right ].$ unit impulse signal $\delta \left [ n \right ].$
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gate2020-ec
continuous-time-signals
signals-and-systems
discrete-time-signals
impulse-response
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2
GATE ECE 2020 | Question: 29
A finite duration discrete-time signal $x[n]$ is obtained by sampling the continuous-time signal $x\left ( t \right )=\cos\left ( 200\pi t \right )$ at sampling instants $t=n/400, n=0, 1, \dots ,7.$ The $8$-point discrete Fourier transform $\text{(DFT)}$ of $x[n]$ is ... Only $X[4]$ is non-zero. Only $X[2]$ and $X[6]$ are non-zero. Only $X[3]$ and $X[5]$ are non-zero.
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Continuous-time Signals
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gate2020-ec
continuous-time-signals
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discrete-time-signals
0
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0
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3
GATE ECE 2020 | Question: 52
$X\left ( \omega \right )$ is the Fourier transform of $x(t)$ shown below. The value of $\int_{-\infty }^{\infty }\mid X \left ( \omega \right ) \mid ^{2}d \omega$ (rounded off to two decimal places) is ____________
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Continuous-time Signals
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52
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gate2020-ec
numerical-answers
continuous-time-signals
signals-and-systems
fourier-transform
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4
GATE ECE 2019 | Question: 3
Let $H(z)$ be the $z-$ transform of a real-valued discrete-time signal $h[n].$ If $P(z) = H(z) H(\frac{1}{z})$ has a zero at $z= \frac{1}{2}+\frac{1}{2}j,$ and $P(z)$ has a total of four zeros, which one of the following plots represents all the zeros correctly?
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Continuous-time Signals
Feb 12, 2019
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Arjun
6.0k
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115
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gate2019-ec
continuous-time-signals
signals-and-systems
discrete-time-signals
0
votes
0
answers
5
GATE ECE 2019 | Question: 5
Let $Y(s)$ be the unit-step response of a causal system having a transfer function $G(s)= \dfrac{3-s}{(s+1)(s+3)}$ that is ,$Y(s)=\dfrac{G(s)}{s}.$ The forced response of the system is $u(t)-2e^{-t}u(t)+e^{-3t}u(t)$ $2u(t)-2e^{-t}u(t)+e^{-3t}u(t)$ $2u(t)$ $u(t)$
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Network Solution Methods
Feb 12, 2019
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6.0k
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224
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gate2019-ec
network-solution-methods
signals-and-systems
transfer-function
0
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0
answers
6
GATE ECE 2019 | Question: 6
For an LTI system, the Bode plot for its gain is as illustrated in the figure shown. The number of system poles $N_{p}$ and the number of system zeros $N_{z}$ in the frequency range $1\: Hz \leq f \leq \:10^{7} Hz $ is $N_{p}=5, N_{z}=2$ $N_{p}=6, N_{z}=3$ $N_{p}=7, N_{z}=4$ $N_{p}=4, N_{z}=2$
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Continuous-time Signals
Feb 12, 2019
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Arjun
6.0k
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145
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gate2019-ec
continuous-time-signals
signals-and-systems
linear-time-invariant-systems
0
votes
0
answers
7
GATE ECE 2019 | Question: 28
Consider a six-point decimation-in-time Fast Fourier Transform $(FFT)$ algorithm, for which the signal-flow graph corresponding to $X[1]$ is shown in the figure. Let $W_{6}=exp\left(-\:\dfrac{j2\pi}{6}\right).$ In the figure, what should be the values of the coefficients $a_{1},a_{2},a_{3}$ ... $a_{1}=1,a_{2}=W_{6},a_{3}=W_{6}^{2}$ $a_{1}=-1,a_{2}=W_{6}^{2},a_{3}=W_{6}$
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Continuous-time Signals
Feb 12, 2019
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6.0k
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357
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gate2019-ec
continuous-time-signals
signals-and-systems
fourier-transform
0
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0
answers
8
GATE ECE 2019 | Question: 33
Let the state-space representation of an LTI system be $x(t)=A x(t)+B u(t), y(t)=Cx(t)+du(t)$ where $A,B,C$ are matrices, $d$ is a scalar, $u(t)$ is the input to the system, and $y(t)$ ...
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Continuous-time Signals
Feb 12, 2019
by
Arjun
6.0k
points
116
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gate2019-ec
continuous-time-signals
signals-and-systems
linear-time-invariant-systems
0
votes
0
answers
9
GATE ECE 2016 Set 3 | Question: 7
If the signal $x(t) = \large \frac{\sin(t)}{\pi t}$*$\large \frac{\sin(t)}{\pi t}$ with $*$ denoting the convolution operation, then $x(t)$ is equal to $\large\frac{\sin(t)}{\pi t}$ $\large\frac{\sin(2t)}{2\pi t}$ $\large\frac{2\sin(t)}{\pi t}$ $\bigg(\frac{\sin(t)}{\pi t}\bigg)^2$
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Network Solution Methods
Mar 28, 2018
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15.8k
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71
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gate2016-ec-3
signals-and-systems
0
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0
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10
GATE ECE 2016 Set 3 | Question: 8
A discrete-time signal $x[n] = \delta[n – 3] + 2 \delta[n – 5]$ has $z$-transform $X(z)$. If $Y(z) = X(-z)$ is the $z$-transform of another signal $y[n]$, then $y[n] = x[n]$ $y[n] = x[-n]$ $y[n] = -x[n]$ $y[n] = -x[-n]$
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Mar 28, 2018
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15.8k
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60
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gate2016-ec-3
continuous-time-signals
signals-and-systems
discrete-time-signals
0
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0
answers
11
GATE ECE 2016 Set 3 | Question: 49
A wide sense stationary random process $X(t)$ passes through the LTI system shown in the figure. If the autocorrelation function of $X(t)$ is $R_X(\tau)$, then the autocorrelation function $R_Y(\tau)$ of the output $Y(t)$ ... $2R_X(\tau)-R_X(\tau-T_0)-R_X(\tau+T_0)$ $2R_X(\tau)+2R_X(\tau- 2T_0)$ $2R_X(\tau)-2R_X(\tau- 2T_0)$
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Mar 28, 2018
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15.8k
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65
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gate2016-ec-3
continuous-time-signals
signals-and-systems
linear-time-invariant-systems
0
votes
0
answers
12
GATE ECE 2016 Set 1 | Question: 32
A first-order low-pass filter of time constant $T$ is excited with different input signals (with zero initial conditions up to $t = 0$). Match the excitation signals $X, Y, Z$ with the corresponding time responses for $t \geq 0 $ ... $X \to R, \: Y\to P, \: Z \to Q$ $X \to P, \: Y\to R, \: Z \to Q$
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Mar 28, 2018
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34
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gate2016-ec-1
signals-and-systems
low-pass-filters
continuous-time-signals
0
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0
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13
GATE ECE 2016 Set 1 | Question: 35
Consider the signal $x[n] = 6 \delta[n + 2] + 3 \delta[n + 1] + 8 \delta[n] + 7 \delta[n - 1] + 4 \delta[n - 2]$ If $X(e^{jw})$ is the discrete-time Fourier transform of $x[n]$, then $\frac{1}{\pi} \int\limits_{-\pi}^{\pi} X(e^{jw}) \sin^2(2\omega) d\omega$ is equal to _______
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Mar 28, 2018
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45
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gate2016-ec-1
numerical-answers
continuous-time-signals
signals-and-systems
fourier-transform
0
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0
answers
14
GATE ECE 2015 Set 3 | Question: 42
Suppose $x[n]$ is an absolutely summable discrete-time signal. Its $z$-transform is a rational function with two poles and two zeroes. The poles are at $z = \pm 2j.$ Which one of the following statements is TRUE for the signal $x[n]$? It is a finite duration signal It is a causal signal It is a non-causal signal It is a periodic signal.
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Mar 28, 2018
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84
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gate2015-ec-3
continuous-time-signals
signals-and-systems
fourier-transform
0
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0
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15
GATE ECE 2015 Set 3 | Question: 44
Let $\widetilde{x}[n] = 1 + \cos\left(\dfrac{\pi n}{8}\right)$ be a periodic signal with period $16.$ Its DFS coefficients are defined by $a_{k} = \displaystyle{}\dfrac{1}{16}\sum_{n=0}^{15}\widetilde{x}[n] \text{exp}\big(-j\dfrac{\pi}{8} kn\big)$ for all $k .$ The value of the coefficient ܽ$a_{31}$ is _______.
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32
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gate2015-ec-3
numerical-answers
continuous-time-signals
signals-and-systems
fourier-transform
periodic-signals
0
votes
0
answers
16
GATE ECE 2015 Set 3 | Question: 48
The characteristic equation of an LTI system is given by $F(s) = s^{5} + 2s^{4} + 3s^{3} + 6s^{2} – 4s – 8 = 0.$ The number of roots that lie strictly in the left half $s$-plane is _________.
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43
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gate2015-ec-3
numerical-answers
continuous-time-signals
signals-and-systems
linear-time-invariant-systems
0
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0
answers
17
GATE ECE 2015 Set 2 | Question: 5
The magnitude and phase of the complex Fourier series coefficients ܽ$a_{k}$ of a periodic signal $x(t)$ are shown in the figure. Choose the correct statement from the four choices given. Notation: $C$ is the set of complex numbers, ܴ$R$ is the set of purely ... $x(t)\in P$ $x(t)\in (C-R)$ the information given is not sufficient to draw any conclusion about $x(t)$
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58
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gate2015-ec-2
continuous-time-signals
signals-and-systems
fourier-transform
0
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0
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18
GATE ECE 2015 Set 2 | Question: 43
Input $x(t)$ and output $y(t)$ of an LTI system are related by the differential equation $y''(t) - y'(t) - 6y(t) = x(t).$ If the system is neither causal nor stable, the impulse response $h(t)$ of the system is $\dfrac{1}{5}e^{3t}u(-t) + \dfrac{1}{5}e^{-2t}u(-t)$ ... $-\dfrac{1}{5}e^{3t}u(-t) - \dfrac{1}{5}e^{-2t}u(t)$
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Continuous-time Signals
Mar 28, 2018
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38
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gate2015-ec-2
continuous-time-signals
signals-and-systems
linear-time-invariant-systems
0
votes
0
answers
19
GATE ECE 2015 Set 1 | Question: 51
In the system shown in Figure (a), $m(t)$ is a low-pass signal with bandwidth $W$ Hz. The frequency response of the band-pass filter $H(f)$ is shown in Figure (b). If it is desired that the output signal $z(t)=10x(t)$, the maximum value of $W$ (in Hz) should be strictly less than _____________.
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gate2015-ec-1
numerical-answers
signals-and-systems
continuous-time-signals
0
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20
GATE ECE 2014 Set 4 | Question: 17
A Fourier transform pair is given by $\left ( \frac{2}{3} \right ) \: u[n+3] \overset{FT}{\Leftrightarrow} \frac{Ae^{-j6 \pi f}}{1- (\frac{2}{3} ) e^{-j2 \pi f}}$ where $u[n]$ denotes the unit step sequence. The values of $A$ is ____________
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Mar 26, 2018
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42
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gate2014-ec-4
numerical-answers
continuous-time-signals
signals-and-systems
fourier-transform
0
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0
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21
GATE ECE 2014 Set 4 | Question: 43
A stable linear time variant (LTI) system has a transfer function $H(s) = \frac{1}{s^2+s-6}$. To make this system casual it needs to be cascaded with another LTI system having a transfer function $H_1(s)$. A correct choice for $H_1(s)$ among the following options is $s+3$ $s-2$ $s-6$ $s+1$
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gate2014-ec-4
continuous-time-signals
signals-and-systems
linear-time-invariant-systems
0
votes
0
answers
22
GATE ECE 2014 Set 4 | Question: 44
A casual LTI system has zero initial conditions and impulse response $h(t)$. Its input $x(t)$ and output $y(t)$ are related through the linear constant-coefficient differential equation $\frac{d^2y(t)}{dt^2} + a \frac{dy(t)}{dt}+a^2y(t)=x(t).$ Let another ... $G(s)$ is the Laplace transform of $g(t)$, then the number of poles of $G(s)$ is _________.
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33
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gate2014-ec-4
numerical-answers
continuous-time-signals
signals-and-systems
linear-time-invariant-systems
0
votes
0
answers
23
GATE ECE 2014 Set 3 | Question: 48
In the root locus plot shown in the figure, the pole/zero marks and the arrows have been removed. Which one of the following transfer functions has this root locus? $\frac{s+1}{(s+2)(s+4)(s+7)} \\$ $\frac{s+4}{(s+1)(s+2)(s+7)} \\$ $\frac{s+7}{(s+1)(s+2)(s+4)} \\$ $\frac{(s+1)(s+2)}{(s+7)(s+4)}$
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52
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gate2014-ec-3
continuous-time-signals
signals-and-systems
poles-and-zeros
0
votes
0
answers
24
GATE ECE 2014 Set 2 | Question: 46
An unforced linear time invariant (LTI) system is represented by $\begin{bmatrix} x_1 \\ x_2 \end{bmatrix} = \begin{bmatrix} -1 & 0 \\ 0& -2 \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \end{bmatrix}$ If the initial conditions are $x_1(0)= 1$ and $x_2(0)= -1$, the solution of the ... $x_{1}(t)= -e^{-t}, \: x_{2}(t)= -2e^{-t}$
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62
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gate2014-ec-2
continuous-time-signals
signals-and-systems
linear-time-invariant-systems
0
votes
0
answers
25
GATE ECE 2013 | Question: 14
For a periodic signal $v(t) = 30\sin100\:t + 10\cos300\:t + 6\sin(500\:t+\pi/4),$ the fundamental frequency in $rad/s$ is $100$ $300$ $500$ $1500$
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Continuous-time Signals
Mar 26, 2018
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59
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gate2013-ec
signals-and-systems
continuous-time-signals
0
votes
0
answers
26
GATE ECE 2013 | Question: 3
Two systems with impulse responses $h_{1}(t)$ and $h_{2}(t)$ are connected in cascade. Then the overall impulse response of the cascaded system is given by product of $h_{1}(t)$ and $h_{2}(t)$ sum of $h_{1}(t)$ and $h_{2}(t)$ convolution of $h_{1}(t)$ and $h_{2}(t)$ subtraction of $h_{2}(t)$ from $h_{1}(t)$
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36
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gate2013-ec
signals-and-systems
continuous-time-signals
impulse-response
0
votes
0
answers
27
GATE ECE 2012 | Question: 42
Let $y[n]$ denote the convolution of $h[n]$ and $g[n]$, where $h[n]=(\frac{1}{2})^nu[n]$ and $g[n]$ is a casual sequence. If $y[0]=1$ and $y[1]=\frac{1}{2}$, then $g[1]$ equals $0$ $\frac{1}{2}$ $1$ $\frac{3}{2}$
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Continuous-time Signals
Mar 25, 2018
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15.8k
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44
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gate2012-ec
continuous-time-signals
signals-and-systems
convolution
0
votes
0
answers
28
GATE ECE 2012 | Question: 32
The state variable description of an LTI system is given by ... $a_1\neq 0,a_2=0,a_3\neq 0$ $a_1=0,a_2\neq0,a_3\neq 0$ $a_1=0,a_2\neq0,a_3=0$ $a_1\neq 0,a_2\neq0,a_3=0$
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Mar 25, 2018
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121
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gate2012-ec
continuous-time-signals
signals-and-systems
linear-time-invariant-systems
0
votes
0
answers
29
GATE ECE 2012 | Question: 31
The Fourier transform of a signal $h(t)$ is $H(j\omega)=(2\cos\omega)(\sin2\omega)/\omega$. The value of $h(0)$ is $\frac{1}{4}$ $\frac{1}{2}$ $1$ $2$
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Mar 25, 2018
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15.8k
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65
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gate2012-ec
continuous-time-signals
signals-and-systems
fourier-transform
0
votes
0
answers
30
GATE ECE 2018 | Question: 54
A band limited low-pass signal $x(t)$ of bandwidth $5\:kHz$ is sampled at a sampling rate $f_{s}$.The signal $x(t)$ is reconstructed using the reconstruction filter $H(f)$ whose magnitude response is shown below: The minimum sampling rate $f_{s}(\text{in}\: kHz)$ for perfect reconstruction of $x(t)$ is ________.
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Continuous-time Signals
Feb 19, 2018
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42
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gate2018-ec
numerical-answers
continuous-time-signals
signals-and-systems
sampling-theorem
0
votes
0
answers
31
GATE ECE 2018 | Question: 14
Let $\text{x(t)}$ be a periodic function with period $\text{T = 10}$.The Fourier series coefficients for this series are denoted by $a_{k},$ that is $x\left ( t \right )=\sum ^{\infty }_{k=-\infty }a_{k}e^{jk\:\frac{2\pi }{T}t}$ The same function $x(t)$ can also ... $\sum _{k=-\infty}^{\infty } \mid b_{k} \mid$ is equal to $256$ $64$ $16$ $4$
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gate2018-ec
continuous-time-signals
signals-and-systems
fourier-transform
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0
answers
32
GATE ECE 2017 Set 2 | Question: 35
Consider the parallel combination of two LTI systems shown in the figure. The impulse responses of the systems are $ \begin{array} {} h_1(t)=2\delta (t+2)-3\delta (t+1) \\ h_2(t)=\delta (t-2). \end{array}$ If the input $x(t)$ is a unit step signal, then the energy of $y(t)$ is ____________
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Continuous-time Signals
Nov 25, 2017
by
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21.7k
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85
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gate2017-ec-2
impulse-response
numerical-answers
continuous-time-signals
signals-and-systems
0
votes
0
answers
33
GATE ECE 2017 Set 2 | Question: 19
Consider the state space realization $\begin{bmatrix} \dot{x_1}(t)\\ \dot{x_2}(t) \end{bmatrix}=\begin{bmatrix} 0 &0 \\ 0&-9 \end{bmatrix}\begin{bmatrix} x_1(t)\\ x_2(t) \end{bmatrix}+\begin{bmatrix} 0\\ 45 \end{bmatrix} u(t)$ , with ... function. The value of $\underset{t\rightarrow \infty }{\lim}\left | \sqrt{x_1^2(t)+x_2^2(t)} \right |$ is __________.
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Continuous-time Signals
Nov 23, 2017
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62
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gate2017-ec-2
discrete-time-signals
numerical-answers
continuous-time-signals
signals-and-systems
0
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0
answers
34
GATE ECE 2017 Set 2 | Question: 8
The input $x(t)$ and the output $y(t)$ of a continuous –time system are related as $y(t)=\int_{t-T}^{t}x(u) du.$ The system is linear and time-variant linear and time-invariant non-linear and time-variant non-linear and time-invariant
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Continuous-time Signals
Nov 23, 2017
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21.7k
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84
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gate2017-ec-2
linear-time-invariant-systems
continuous-time-signals
signals-and-systems
0
votes
0
answers
35
GATE ECE 2017 Set 2 | Question: 7
An LTI system with unit sample response $h[n]=5\delta [n]-7\delta [n-1]+7\delta [n-3]-5\delta [n-4]$ is a low-pass filter high-pass filter band-pass filter band-stop filter
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Continuous-time Signals
Nov 23, 2017
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21.7k
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101
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gate2017-ec-2
linear-time-invariant-systems
continuous-time-signals
signals-and-systems
0
votes
0
answers
36
GATE ECE 2017 Set 1 | Question: 31
Let $x(t)$ be a continuous time periodic signal with fundamental period $T=1$ seconds.Let ${a_{k} }$ be the complex Fourier series coefficients of $x(t)$, where $k$ is integer valued. Consider the following statements about $x(3t)$: The complex ... one of the following is correct? Only II and III are true Only I and III are true Only III is true Only I is true
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Continuous-time Signals
Nov 17, 2017
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21.7k
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77
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gate2017-ec-1
fourier-transform
continuous-time-signals
signals-and-systems
0
votes
0
answers
37
GATE ECE 2017 Set 1 | Question: 32
Two discrete-time signals $x[n]$ and $h[n]$ are both non-zero only for $n=0,1,2$, and are zero otherwise .It is given that $x[0]=1, \: x[1]=2, \: x[2]=1, \: h[0]=1$ Let $y[n]$ be the linear convolution of $x[n]$ and $h[n]$. Given that $y[1]=3$ and $y[2]=4$, the value of the expression $(10y[3]+y[4])$ is__________.
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Nov 17, 2017
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90
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gate2017-ec-1
numerical-answers
continuous-time-signals
discrete-time-signals
signals-and-systems
0
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0
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38
GATE ECE 2017 Set 1 | Question: 8
A periodic signal $x(t)$ has a trigonometric Fourier series expansion $x( t )= a_{0}+\sum_{n=1}^{ \infty } ( a_{n} \cos n\omega _{0}t+b_{n}\sin n\omega _{0}t )$ If $x(t)= -x(-t)=-x(t-\frac{\pi }{\omega _{0}})$, we can conclude that $a_n$ ... $n$ odd $a_n$ are zero for $n$ even and $b_n$ are zero for $n$ odd $a_n$ are zero for $n$ odd and $b_n$ are zero for $n$ even
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39
GATE ECE 2017 Set 1 | Question: 6
Consider a single input single output discrete-time system with $x[ n ]$ as input and $y [ n ]$ ... statements is true about the system? It is causal and stable It is causal but not stable It is not causal but stable It is neither causal nor stable
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40
GATE ECE 2017 Set 1 | Question: 5
Consider the following statements for continuous-time linear time invariant (LTI) systems. There is no bounded input bounded output (BIBO) stable system with a pole in the right half of the complex plane. There is no causal and BIBO stable with a pole in the ... following is correct? Both I and II are true Both I and II are not true Only I is true Only II is true
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