Register

Recent questions tagged impulse-response

0 0 votes
1 1 answer
359
359 views
GATE ECE 2026 | Question: 13
The relation between the input current ( $I$ ) and the output voltage ( $V$ ) of a circuit is governed by the equation: $C \dfrac{d V}{d t}=I(t)-m(t)$. The circuit is exc...
0 0 votes
0 0 answers
106
106 views
GATE ECE 2026 | Question: 37
Consider the discrete time system (S) with input $x[n]$ and output $y[n]$ as shown in the Figure. The two sub-systems represented by their impulse responses $h_{1}[n]$ an...
0 0 votes
1 1 answer
704
704 views
GATE ECE 2025 | Question: 7
Consider the discrete-time system below with input $x[n]$ and output $y[n]$. In the figure, $h_{1}[n]$ and $h_{2}[n]$ denote the impulse responses of LTI Subsystems $1$ a...
User Avatar
2 2 votes
1 1 answer
1.8k
1.8k views
GATE ECE 2024 | Question: 11
​​​​A causal and stable $\text{LTI}$ system with impulse response $h(t)$ produces an output $y(t)$ for an input signal $x(t)$. A signal $x(0.5 t)$ is applied to another c...
2 2 votes
1 1 answer
888
888 views
GATE ECE 2024 | Question: 38
​​​​A continuous time signal $x(t)=2 \cos (8 \pi t+\pi / 3)$ is sampled at a rate of $15 \mathrm{~Hz}$. The sampled signal $x_{s}(t)$ when passed through an LTI system wi...
1 1 vote
0 0 answers
813
813 views
GATE ECE 2023 | Question: 39
Let $x(t)=10 \cos (10.5 W t)$ be passed through an LTI system having impulse response $h(t)=\pi\left(\frac{\sin W t}{\pi t}\right)^{2} \cos 10 Wt$. The output of the sys...
0 0 votes
0 0 answers
497
497 views
GATE ECE 2023 | Question: 49
Let $X(t)$ be a white Gaussian noise with power spectral density $\frac{1}{2} \mathrm{~W} / \mathrm{Hz}$. If $X(t)$ is input to an LTI system with impulse response $e^{-t...
1 1 vote
0 0 answers
435
435 views
TIFR ECE 2015 | Question: 1
For a time-invariant system, the impulse response completely describes the system if the system iscausal and non-linearnon-causal and non-linearcausal and linearAll of th...
1 1 vote
0 0 answers
322
322 views
TIFR ECE 2022 | Question: 3
Consider two linear time invariant $\text{(LTI)}$ systems $T_{1}$ and $T_{2}$ with impulse responses $h_{1}(n)$ and $h_{2}(n)$, respectively. Let there be two cascades $C...
0 0 votes
0 0 answers
219
219 views
GATE ECE 1997 | Question 5.1
In the case of a linear time invariant system(1) Poles in the right half plane implies Exponential decay of output(2) Impulse response zero for $t \leq 0$ impliesSystem i...
0 0 votes
0 0 answers
296
296 views
GATE ECE 1997 | Question 6
The figure is shows the block diagram representation of control system. The system in block A has an impulse response $h_{A}(t)=e^{-t} u (t)$. The system in block $B$ has...
0 0 votes
0 0 answers
373
373 views
GATE ECE 2000 | Question 2.4
A linear time invariant system has an impulse response $e^{2 t}, t>0$. If the initial conditions are zero and the input is $e^{3 t}$, then output for $t>0$ is$e^{3 t}-e^{...
0 0 votes
0 0 answers
217
217 views
GATE ECE 2000 | Question 6
The network $\mathrm{N}$ in given figure consists only of two elements: a resistor of $1 \; \Omega$ and an inductor of $\text{L}$ Henry. A $5 \mathrm{~V}$ source is conne...
0 0 votes
0 0 answers
304
304 views
GATE ECE 2001 | Question: 1.3
The transfer function of a system is given by $H(s)=\frac{1}{s^{2}(s-2)}$. The impulse response of the system is$\left(t^{2 *} e^{-2 t}\right) \mathrm{U}(t)$ (* denotes c...
0 0 votes
0 0 answers
204
204 views
GATE ECE 2002 | Question: 2.4
If the impulse response of a discrete-time system is $h[n]=-5^{n} u[-n-1]$, then the system function $\mathrm{H}(z)$ is equal to$\frac{-z}{z-5}$ and the system is stable$...
0 0 votes
0 0 answers
296
296 views
GATE ECE 1998 | Question 1.9
The unit impulse response of a linear time-invariant system is the unit step function $u(t)$. For $t>0$, the response of the system to an excitation $e^{-a t} u(t), a>0$ ...
0 0 votes
0 0 answers
304
304 views
GATE ECE 2004 | Question: 19
The impulse response $h[n]$ of a linear time-invariant system is given by\[h[n]=u[n+3]+u[n-2]-2 u[n-7]\]where $u[n]$ is the unit step sequence. The above system isstable ...
0 0 votes
0 0 answers
278
278 views
GATE ECE 2004 | Question: 65
The impulse response $h|n|$ of a linear time invariant system is given as\[h[n]=\left\{\begin{array}{cc}-2 \sqrt{2} & n=1,-1 \\4 \sqrt{2} & n=2,-2 \\0, & \text { otherwis...
0 0 votes
0 0 answers
248
248 views
GATE ECE 2004 | Question: 74
Consider the signal $x(t)$ shown in the figure. Let $h(t)$ denote the impulse response of the filter matched to $x(t)$, with $h(t)$ being non-zero only in the interval 0 ...
0 0 votes
0 0 answers
326
326 views
GATE ECE 2005 | Question: 20
Which of the following can be impulse response of a casual system?
0 0 votes
0 0 answers
242
242 views
GATE ECE 1995 | Question 1.16
Let $h(t)$ be the impulse response of a linear time invariant system. Then the response of the system for any input $u(t)$ is$\int_{0}^{t} h(\tau) u(t-\tau) d \tau$$\frac...
0 0 votes
0 0 answers
247
247 views
GATE ECE 2006 | Question: 57
The unit impulse response of a system is\[h(t)=e^{-t}, t \geq 0\]For this system, the steady-state value of the output for unit step input is equal to$-1$$0$$1$$\infty$
0 0 votes
0 0 answers
332
332 views
GATE ECE 2006 | Question: 74
Common Data for Questions 74, 75:Let $g(t)=p(t)^{*} p(t)$, where * denotes convolution and $p(t)=u(t)-u(t-1)$ with $u(t)$ being the unit step functionThe impulse response...
0 0 votes
0 0 answers
185
185 views
GATE ECE 2006 | Question: 83
Statement for Linked Answer Questions 82 and 83Consider a unity-gain feedback control system whose open-loop transfer function is\[G(s)=\frac{as+1}{s^{2}}\]With the value...
1 1 vote
0 0 answers
276
276 views
GATE ECE 2008 | Question: 10
The impulse response $h(t)$ of a linear time-invariant continuous time system is described by $h(t)=\exp (\alpha t) u(t)+\exp (\beta t) u(-t)$, where $u(t)$ denotes the u...
1 1 vote
0 0 answers
276
276 views
GATE ECE 2008 | Question: 31
A linear, time-invariant, causal continuous time system has a rational transfer function with simple poles at $s=-2$ and $s=-4$, and one simple zero at $s=-1$. A unit ste...
1 1 vote
0 0 answers
318
318 views
GATE ECE 2008 | Question: 33
A discrete time linear shift-invariant system has an impulse response $h[n]$ with $h[0]=1, h =-1$, $h =2$, and zero otherwise. The system is given an input sequence $x[n]...
1 1 vote
0 0 answers
353
353 views
GATE ECE 2008 | Question: 74
The following series $\text{RLC}$ circuit with zero initial conditions is excited by a unit impulse function $\delta(t)$.For $t>0$, the output voltage $V_{c}(t)$ is$\frac...
1 1 vote
0 0 answers
420
420 views
GATE ECE 2008 | Question: 75
The following series $\text{RLC}$ circuit with zero initial conditions is excited by a unit impulse function $\delta(t)$. For $t>0$, the voltage across the resistor is$\f...
1 1 vote
0 0 answers
213
213 views
GATE ECE 2008 | Question: 84
The impulse response $h(t)$ of a linear time-invariant continuous time system is given by $h(t)=\exp (-2 t) u(t)$, where $u(t)$ denotes the unit step function.The frequen...
Page: