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Recent questions tagged lineartimeinvariantsystems
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GATE2019 EC: 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 $N_{p}=5, N_{z}=2$ $N_{p}=6, N_{z}=3$ $N_{p}=7, N_{z}=4$ $N_{p}=4, N_{z}=2$
asked
Feb 12, 2019
in
Continuoustime Signals
by
Arjun
(
1.4k
points)
gate2019ec
continuoustimesignals
signalsandsystems
lineartimeinvariantsystems
0
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0
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2
GATE2019 EC: 33
Let the statespace 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 $y(t)$ is its output. Let $B=[0\quad0\quad1]^{T}$ ... $A=\begin{bmatrix} 0&1&0\\ 0&0&1\\3&2&1 \\\end{bmatrix} \text{and} \quad C=\begin{bmatrix} 0&0&1 \end{bmatrix}$
asked
Feb 12, 2019
in
Continuoustime Signals
by
Arjun
(
1.4k
points)
gate2019ec
continuoustimesignals
signalsandsystems
lineartimeinvariantsystems
0
votes
0
answers
3
GATE2016330
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 $0$ $1$ $2$ $3$
asked
Mar 28, 2018
in
Continuoustime Signals
by
Milicevic3306
(
15.8k
points)
gate2016ec3
continuoustimesignals
lineartimeinvariantsystems
transferfunction
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0
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4
GATE2016349
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 $Y(t)$ is equal to $2R_X(\tau)+R_X(\tauT_0)+R_X(\tau+T_0)$ $2R_X(\tau)R_X(\tauT_0)R_X(\tau+T_0)$ $2R_X(\tau)+2R_X(\tau 2T_0)$ $2R_X(\tau)2R_X(\tau 2T_0)$
asked
Mar 28, 2018
in
Continuoustime Signals
by
Milicevic3306
(
15.8k
points)
gate2016ec3
continuoustimesignals
signalsandsystems
lineartimeinvariantsystems
0
votes
0
answers
5
GATE2015317
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
asked
Mar 28, 2018
in
Continuoustime Signals
by
Milicevic3306
(
15.8k
points)
gate2015ec3
continuoustimesignals
impulseresponse
lineartimeinvariantsystems
0
votes
0
answers
6
GATE2015348
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 _________.
asked
Mar 28, 2018
in
Continuoustime Signals
by
Milicevic3306
(
15.8k
points)
gate2015ec3
numericalanswers
continuoustimesignals
signalsandsystems
lineartimeinvariantsystems
0
votes
0
answers
7
GATE2015243
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 $\dfrac{1}{5}e^{3t}u(t) + \dfrac{1}{5}e^{2t}u(t)$ ... $\dfrac{1}{5}e^{3t}u(t)  \dfrac{1}{5}e^{2t}u(t)$
asked
Mar 28, 2018
in
Continuoustime Signals
by
Milicevic3306
(
15.8k
points)
gate2015ec2
continuoustimesignals
signalsandsystems
lineartimeinvariantsystems
0
votes
0
answers
8
GATE2014418
A realvalued 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 $x(t+4)$ $x(t4)$ $x(t+2)$ $x(t2)$
asked
Mar 26, 2018
in
Continuoustime Signals
by
Milicevic3306
(
15.8k
points)
gate2014ec4
continuoustimesignals
lineartimeinvariantsystems
0
votes
0
answers
9
GATE2014443
A stable linear time variant (LTI) system has a transfer function $H(s) = \frac{1}{s^2+s6}$. 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 $s+3$ $s2$ $s6$ $s+1$
asked
Mar 26, 2018
in
Continuoustime Signals
by
Milicevic3306
(
15.8k
points)
gate2014ec4
continuoustimesignals
signalsandsystems
lineartimeinvariantsystems
0
votes
0
answers
10
GATE2014444
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 constantcoefficient differential equation $\frac{d^2y(t)}{dt^2} + a \frac{dy(t)}{dt}+a^2y(t)=x(t).$ Let another signal $g(t)$ ... $G(s)$ is the Laplace transform of $g(t)$, then the number of poles of $G(s)$ is _________.
asked
Mar 26, 2018
in
Continuoustime Signals
by
Milicevic3306
(
15.8k
points)
gate2014ec4
numericalanswers
continuoustimesignals
signalsandsystems
lineartimeinvariantsystems
0
votes
0
answers
11
GATE2014244
The inputoutput relationship of a causal stable LTI system is given as $y[n] = \alpha \: y[n1] + \beta \: x[n]$. 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 $\alpha = 1\beta /2$ $\alpha = 1+\beta /2$ $\alpha = 2\beta$ $\alpha = 2\beta$
asked
Mar 26, 2018
in
Communications
by
Milicevic3306
(
15.8k
points)
gate2014ec2
communications
lineartimeinvariantsystems
0
votes
0
answers
12
GATE2014246
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 $x_2(0)= 1$ ... $x_{1}(t)= e^{t}, \: x_{2}(t)= 2e^{t}$
asked
Mar 26, 2018
in
Continuoustime Signals
by
Milicevic3306
(
15.8k
points)
gate2014ec2
continuoustimesignals
signalsandsystems
lineartimeinvariantsystems
0
votes
0
answers
13
GATE201318
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 lie within $\mid s \mid =1$ All the roots of the characteristic equation must be located on the left side of the $j\omega$ axis
asked
Mar 26, 2018
in
Continuoustime Signals
by
Milicevic3306
(
15.8k
points)
gate2013ec
continuoustimesignals
lineartimeinvariantsystems
0
votes
0
answers
14
GATE201232
The state variable description of an LTI system is given by ... for $a_1\neq 0,a_2=0,a_3\neq 0$ $a_1=0,a_2\neq0,a_3\neq 0$ $a_1=0,a_2\neq0,a_3=0$ $a_1\neq 0,a_2\neq0,a_3=0$
asked
Mar 25, 2018
in
Continuoustime Signals
by
Milicevic3306
(
15.8k
points)
gate2012ec
continuoustimesignals
signalsandsystems
lineartimeinvariantsystems
0
votes
0
answers
15
GATE2017 EC2: 47
A secondorder 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
asked
Nov 25, 2017
in
Control Systems
by
admin
(
2.8k
points)
gate2017ec2
lineartimeinvariantsystems
controlsystems
0
votes
0
answers
16
GATE2017 EC2: 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 ____________
asked
Nov 25, 2017
in
Control Systems
by
admin
(
2.8k
points)
gate2017ec2
transferfunction
lineartimeinvariantsystems
numericalanswers
controlsystems
0
votes
0
answers
17
GATE2017 EC2: 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 $\arg \{ H(f) \}=  2f.$ ... $y(t)$ is ____________
asked
Nov 25, 2017
in
Control Systems
by
admin
(
2.8k
points)
gate2017ec2
lineartimeinvariantsystems
numericalanswers
controlsystems
0
votes
0
answers
18
GATE2017 EC2: 8
The input $x(t)$ and the output $y(t)$ of a continuous –time system are related as $y(t)=\int_{tT}^{t}x(u) du.$ The system is linear and timevariant linear and timeinvariant nonlinear and timevariant nonlinear and timeinvariant
asked
Nov 23, 2017
in
Continuoustime Signals
by
admin
(
2.8k
points)
gate2017ec2
lineartimeinvariantsystems
continuoustimesignals
signalsandsystems
0
votes
0
answers
19
GATE2017 EC2: 7
An LTI system with unit sample response $h[n]=5\delta [n]7\delta [n1]+7\delta [n3]5\delta [n4]$ is a lowpass filter highpass filter bandpass filter bandstop filter
asked
Nov 23, 2017
in
Continuoustime Signals
by
admin
(
2.8k
points)
gate2017ec2
lineartimeinvariantsystems
continuoustimesignals
signalsandsystems
0
votes
0
answers
20
GATE2017 EC1: 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 _________.
asked
Nov 17, 2017
in
Continuoustime Signals
by
admin
(
2.8k
points)
gate2017ec1
numericalanswers
continuoustimesignals
lineartimeinvariantsystems
0
votes
0
answers
21
GATE2017 EC1: 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 $0< K < \infty$ intersects the ... $K=1.5$. The closed loop system is stable for $K>1.5$ $1<K<1.5$ $0<K<1$ no positive value of $K$
asked
Nov 17, 2017
in
Control Systems
by
admin
(
2.8k
points)
gate2017ec1
lineartimeinvariantsystems
transferfunction
controlsystems
bodeandrootlocusplots
0
votes
0
answers
22
GATE2017 EC1: 33
Let $h[n]$ ... in radians. Given that $H(\omega_{0})=0$ and $0< \omega_{0} < \pi$, the value of $\omega_{0}$ (in radians) is equal to__________.
asked
Nov 17, 2017
in
Continuoustime Signals
by
admin
(
2.8k
points)
gate2017ec1
numericalanswers
continuoustimesignals
lineartimeinvariantsystems
fouriertransform
0
votes
0
answers
23
GATE2017 EC1: 5
Consider the following statements for continuoustime 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 right half of ... 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
asked
Nov 17, 2017
in
Continuoustime Signals
by
admin
(
2.8k
points)
gate2017ec1
lineartimeinvariantsystems
continuoustimesignals
signalsandsystems
0
votes
0
answers
24
GATE2017 EC1: 6
Consider a single input single output discretetime system with $x[ n ]$ as input and $y [ n ]$ ... following 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
asked
Nov 17, 2017
in
Continuoustime Signals
by
admin
(
2.8k
points)
gate2017ec1
lineartimeinvariantsystems
continuoustimesignals
signalsandsystems
discretetimesignals
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