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Recent questions tagged linear-time-invariant-systems
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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 $N_{p}=5, N_{z}=2$ $N_{p}=6, N_{z}=3$ $N_{p}=7, N_{z}=4$ $N_{p}=4, N_{z}=2$
Arjun
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Continuous-time Signals
Feb 12, 2019
by
Arjun
6.0k
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146
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gate2019-ec
continuous-time-signals
signals-and-systems
linear-time-invariant-systems
0
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2
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 $y(t)$ ...
Arjun
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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
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0
answers
3
GATE ECE 2016 Set 3 | Question: 30
A signal $2 \cos(\frac{2\pi}{3}t)-\cos(\pi t)$ is the input to an LTI system with the transfer function $H(s)=e^s+e^{-s}.$ If $C_k$ denotes the $k^{th}$ coefficient in the exponential Fourier series of the output signal, then $C_3$ is equal to $0$ $1$ $2$ $3$
Milicevic3306
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Continuous-time Signals
Mar 28, 2018
by
Milicevic3306
15.8k
points
68
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gate2016-ec-3
continuous-time-signals
linear-time-invariant-systems
transfer-function
0
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0
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4
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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Continuous-time Signals
Mar 28, 2018
by
Milicevic3306
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
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5
GATE ECE 2015 Set 3 | Question: 17
The impulse response of an LTI system can be obtained by differentiating the unit ramp response differentiating the unit step response integrating the unit ramp response integrating the unit step response
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Continuous-time Signals
Mar 28, 2018
by
Milicevic3306
15.8k
points
58
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gate2015-ec-3
continuous-time-signals
impulse-response
linear-time-invariant-systems
0
votes
0
answers
6
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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Continuous-time Signals
Mar 28, 2018
by
Milicevic3306
15.8k
points
43
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gate2015-ec-3
numerical-answers
continuous-time-signals
signals-and-systems
linear-time-invariant-systems
0
votes
0
answers
7
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 $\dfrac{1}{5}e^{3t}u(-t) + \dfrac{1}{5}e^{-2t}u(-t)$ ... $-\dfrac{1}{5}e^{3t}u(-t) - \dfrac{1}{5}e^{-2t}u(t)$
Milicevic3306
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Continuous-time Signals
Mar 28, 2018
by
Milicevic3306
15.8k
points
38
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gate2015-ec-2
continuous-time-signals
signals-and-systems
linear-time-invariant-systems
0
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0
answers
8
GATE ECE 2014 Set 4 | Question: 18
A real-valued signal $x(t)$ limited to the frequency band $\mid f \mid \leq \frac{W}{2}$ is passed through a linear time invariant system whose frequency response is $H(f) = \begin{cases} e^{-j 4 \pi f}, & \mid f \mid \leq \frac{W}{2} \\ 0, & \mid f \mid > \frac{W}{2} \end{cases}.$ The output of the system is $x(t+4)$ $x(t-4)$ $x(t+2)$ $x(t-2)$
Milicevic3306
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in
Continuous-time Signals
Mar 26, 2018
by
Milicevic3306
15.8k
points
66
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gate2014-ec-4
continuous-time-signals
linear-time-invariant-systems
0
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0
answers
9
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 $s+3$ $s-2$ $s-6$ $s+1$
Milicevic3306
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Continuous-time Signals
Mar 26, 2018
by
Milicevic3306
15.8k
points
39
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gate2014-ec-4
continuous-time-signals
signals-and-systems
linear-time-invariant-systems
0
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0
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10
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 _________.
Milicevic3306
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Continuous-time Signals
Mar 26, 2018
by
Milicevic3306
15.8k
points
35
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gate2014-ec-4
numerical-answers
continuous-time-signals
signals-and-systems
linear-time-invariant-systems
0
votes
0
answers
11
GATE ECE 2014 Set 2 | Question: 44
The input-output relationship of a causal stable LTI system is given as $y[n] = \alpha \: y[n-1] + \beta \: x[n]$. If the impulse response $h[n]$ of this system satisfies the condition $\sum_{n=0}^{\infty}h[n]= 2$, the relationship between $\alpha$ and $\beta$ is $\alpha = 1-\beta /2$ $\alpha = 1+\beta /2$ $\alpha = 2\beta$ $\alpha = -2\beta$
Milicevic3306
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Communications
Mar 26, 2018
by
Milicevic3306
15.8k
points
39
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gate2014-ec-2
communications
linear-time-invariant-systems
0
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0
answers
12
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 ... $x_{1}(t)= -e^{-t}, \: x_{2}(t)= -2e^{-t}$
Milicevic3306
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Continuous-time Signals
Mar 26, 2018
by
Milicevic3306
15.8k
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62
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gate2014-ec-2
continuous-time-signals
signals-and-systems
linear-time-invariant-systems
0
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0
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13
GATE ECE 2013 | Question: 18
Which one of the following statements is NOT TRUE for a continuous time causal and stable LTI system? All the poles of the system must lie on the left side of the $j\omega$ axis Zeros of the system can lie anywhere in the $s$-plane All the poles must ... $\mid s \mid =1$ All the roots of the characteristic equation must be located on the left side of the $j\omega$ axis
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Mar 26, 2018
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60
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gate2013-ec
continuous-time-signals
linear-time-invariant-systems
0
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0
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14
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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Continuous-time Signals
Mar 25, 2018
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Milicevic3306
15.8k
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130
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gate2012-ec
continuous-time-signals
signals-and-systems
linear-time-invariant-systems
0
votes
0
answers
15
GATE ECE 2017 Set 2 | Question: 47
A second-order LTI system is described by the following state equations, $ \begin{array}{ll} \frac{d}{dt}x_1(t)-x_2(t)=0 \\ \frac{d}{dt}x_2(t)+2x_1(t)+3x_2(t)=r(t) \end{array}$ where $x_1(t)$ and $x_2(t)$ are the two state variables and $r(t)$ denotes the input. The output $c(t)=x_1(t)$. The system is undamped (oscillatory) underdamped critically damped overdamped
admin
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Control Systems
Nov 25, 2017
by
admin
32.7k
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207
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gate2017-ec-2
linear-time-invariant-systems
control-systems
0
votes
0
answers
16
GATE ECE 2017 Set 2 | Question: 34
The transfer function of a causal LTI system is $H(s)=1/s$. If the input to the system is $x(t)=[\sin(t)/\pi t] u(t)$, where $u(t)$ is a unit step function, the system output $y(t)$ as $t\to \infty$ is ____________
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Control Systems
Nov 25, 2017
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admin
32.7k
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76
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gate2017-ec-2
transfer-function
linear-time-invariant-systems
numerical-answers
control-systems
0
votes
0
answers
17
GATE ECE 2017 Set 2 | Question: 33
Consider an LTI system with magnitude response $\mid H(f) \mid=\begin{cases} 1-\frac{\mid f \mid}{20}, & \mid f \mid \leq 20 \\ 0,& \mid f \mid > 20 \end{cases}$ and phase response $\arg \{ H(f) \}= - 2f.$ If the input to the ... $y(t)$ is ____________
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Control Systems
Nov 25, 2017
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admin
32.7k
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79
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gate2017-ec-2
linear-time-invariant-systems
numerical-answers
control-systems
0
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0
answers
18
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
by
admin
32.7k
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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
19
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
by
admin
32.7k
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102
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gate2017-ec-2
linear-time-invariant-systems
continuous-time-signals
signals-and-systems
0
votes
0
answers
20
GATE ECE 2017 Set 1 | Question: 52
A continuous time signal $x(t)=4 \cos(200\pi t)+8 \cos(400\pi t)$, where $t$ is in seconds, is the input to a linear time invariant (LTI) filter with the impulse response $h(t)=\begin{cases} \frac{2 \sin (300\pi t)}{\pi t},& t\neq 0 \\ 600, & t=0. \end{cases}$ Let $y(t)$ be the output of this filter. The maximum value of $ \mid y(t) \mid $ is _________.
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Continuous-time Signals
Nov 17, 2017
by
admin
32.7k
points
84
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gate2017-ec-1
numerical-answers
continuous-time-signals
linear-time-invariant-systems
0
votes
0
answers
21
GATE ECE 2017 Set 1 | Question: 47
A linear time invariant (LTI) system with the transfer function $G(s)=\frac{K(s^{2}+2s+2)}{(s_{2}-3s+2)}$ is connected in unity feedback configuration as shown in the figure. For the closed loop system shown, the root locus for $0< K < \infty$ ... $K>1.5$ $1<K<1.5$ $0<K<1$ no positive value of $K$
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Control Systems
Nov 17, 2017
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admin
32.7k
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98
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gate2017-ec-1
linear-time-invariant-systems
transfer-function
control-systems
bode-and-root-locus-plots
0
votes
0
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22
GATE ECE 2017 Set 1 | Question: 33
Let $h[n]$ ... radians. Given that $H(\omega_{0})=0$ and $0< \omega_{0} < \pi$, the value of $\omega_{0}$ (in radians) is equal to__________.
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Continuous-time Signals
Nov 17, 2017
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65
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gate2017-ec-1
numerical-answers
continuous-time-signals
linear-time-invariant-systems
fourier-transform
0
votes
0
answers
23
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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Continuous-time Signals
Nov 17, 2017
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112
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gate2017-ec-1
linear-time-invariant-systems
continuous-time-signals
signals-and-systems
discrete-time-signals
0
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0
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24
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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Nov 17, 2017
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149
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linear-time-invariant-systems
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