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Hot questions in Continuous-time Signals
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GATE ECE 2024 | Question: 34
Consider two continuous time signals $x(t)$ and $y(t)$ as shown below If $X(f)$ denotes the Fourier transform of $x(t)$, then the Fourier transform of $y(t)$ is $\_\_\_\_\_\_$. $-4 X(4 f) e^{-j \pi f}$ $-4 X(4 f) e^{-j 4 \pi f}$ $-\frac{1}{4} X(f / 4) e^{-j \pi f}$ $-\frac{1}{4} X(f / 4) e^{-j 4 \pi f}$
Consider two continuous time signals $x(t)$ and $y(t)$ as shown below If $X(f)$ denotes the Fourier transform of $x(t)$, then the Fourier transform of $y(t)$ is $\_\_\_\_...
admin
46.4k
points
430
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admin
asked
Feb 16
Continuous-time Signals
gateece-2024
fourier-transform
continuous-time-signals
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0
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0
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2
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 with impulse response \[ h(t)=\left(\frac{\sin 2 \pi t}{\pi t}\right) \cos (38 \pi t-\pi / 2) \] ... $15 \sin (38 \pi t-\pi / 3)$ $15 \cos (38 \pi t-\pi / 6)$ $15 \cos (38 \pi t+\pi / 6)$
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 s...
admin
46.4k
points
202
views
admin
asked
Feb 16
Continuous-time Signals
gateece-2024
impulse-response
continuous-time-signals
linear-time-invariant-systems
+
–
0
votes
2
answers
3
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.
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 ...
go_editor
1.9k
points
376
views
go_editor
asked
Feb 13, 2020
Continuous-time Signals
gate2020-ec
continuous-time-signals
signals-and-systems
discrete-time-signals
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–
1
votes
1
answer
4
The value of the integral ∫ ∞ − ∞ 12 cos ( 2 π ) sin ( 4 π t ) 4 π t d t is
akalok808
130
points
198
views
akalok808
asked
Aug 24, 2021
0
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0
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5
GATE ECE 2020 | Question: 11
The pole-zero map of a rational function $G(s)$ is shown below. When the closed contour $\Gamma$ is mapped into the $G(s)$-plane, then the mapping encircles the origin of the $G(s)$-plane once in the counter-clockwise direction. the origin of the ... $-1 + j0$ of the $G(s)$-plane once in the clockwise direction.
The pole-zero map of a rational function $G(s)$ is shown below. When the closed contour $\Gamma$ is mapped into the $G(s)$-plane, then the mapping encircles ...
go_editor
1.9k
points
318
views
go_editor
asked
Feb 13, 2020
Continuous-time Signals
gate2020-ec
continuous-time-signals
poles-and-zeros
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–
0
votes
0
answers
6
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 $\delta \left [ n \right ].$
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 uni...
go_editor
1.9k
points
238
views
go_editor
asked
Feb 13, 2020
Continuous-time Signals
gate2020-ec
continuous-time-signals
signals-and-systems
discrete-time-signals
impulse-response
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–
0
votes
0
answers
7
GATE ECE 2020 | Question: 14
Which one of the following pole-zero plots corresponds to the transfer function of an $\text{LTI}$ system characterized by the input-output difference equation given below? $y\left [ n \right ]=\sum ^{3}_{k=0}\left ( -1 \right )^{k}x\left [ n-k \right ]$
Which one of the following pole-zero plots corresponds to the transfer function of an $\text{LTI}$ system characterized by the input-output difference equation given belo...
go_editor
1.9k
points
196
views
go_editor
asked
Feb 13, 2020
Continuous-time Signals
gate2020-ec
poles-and-zeros
continuous-time-signals
+
–
0
votes
0
answers
8
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 ____________
$X\left ( \omega \right )$ is the Fourier transform of $x(t)$ shown below. The value of $\int_{-\infty }^{\infty }\mid X \left ( \omega \right ) \mid ^{2}d \omega$ (round...
go_editor
1.9k
points
129
views
go_editor
asked
Feb 13, 2020
Continuous-time Signals
gate2020-ec
numerical-answers
continuous-time-signals
signals-and-systems
fourier-transform
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–
0
votes
1
answer
9
GATE ECE 2014 Set 1 | Question: 17
A discrete-time signal $x[n] = \sin(\pi^{2}n),n$ being an integer, is periodic with period $\pi$ periodic with period $\pi^{2}$ periodic with period $\pi/2$ not periodic
A discrete-time signal $x[n] = \sin(\pi^{2}n),n$ being an integer, isperiodic with period $\pi$periodic with period $\pi^{2}$periodic with period $\pi/2$not periodic
Milicevic3306
16.0k
points
290
views
Milicevic3306
asked
Mar 25, 2018
Continuous-time Signals
gate2014-ec-1
continuous-time-signals
discrete-time-signals
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–
0
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0
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10
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 $a_{1},a_{2},a_{3}$ ... $a_{1}=1,a_{2}=W_{6},a_{3}=W_{6}^{2}$ $a_{1}=-1,a_{2}=W_{6}^{2},a_{3}=W_{6}$
Consider a six-point decimation-in-time Fast Fourier Transform $(FFT)$ algorithm, for which the signal-flow graph corresponding to $X $ is shown in the figure. Let $W_{6}...
Arjun
6.6k
points
502
views
Arjun
asked
Feb 12, 2019
Continuous-time Signals
gate2019-ec
continuous-time-signals
signals-and-systems
fourier-transform
+
–
0
votes
0
answers
11
GATE ECE 2019 | Question: 25
In the circuit shown, the clock frequency, i.e., the frequency of the ClK signal, is $12\:kHz$. The frequency of the signal at $Q_{2}$ is _______ kHz.
In the circuit shown, the clock frequency, i.e., the frequency of the ClK signal, is $12\:kHz$. The frequency of the signal at $Q_{2}$ is _______ kHz.
Arjun
6.6k
points
301
views
Arjun
asked
Feb 12, 2019
Continuous-time Signals
gate2019-ec
numerical-answers
continuous-time-signals
to-be-tagged
+
–
0
votes
0
answers
12
GATE ECE 2019 | Question: 22
The baseband signal $m(t)$ shown in the figure is phase-modulated to generate the $PM$ signal $\varphi(t)=\cos(2\pi f_{c}t+ k\:\: m(t)).$ The time $t$ on the $x-$ axis in the figure is in milliseconds. If the ... ratio of the minimum instantaneous frequency (in kHz) to the maximum instantaneous frequency (in kHz) is _________ (rounded off to $2$ decimal places).
The baseband signal $m(t)$ shown in the figure is phase-modulated to generate the $PM$ signal $\varphi(t)=\cos(2\pi f_{c}t+ k\:\: m(t)).$ The time $t$ on the $x-$ axis in...
Arjun
6.6k
points
254
views
Arjun
asked
Feb 12, 2019
Continuous-time Signals
gate2019-ec
numerical-answers
continuous-time-signals
to-be-tagged
+
–
1
votes
0
answers
13
GATE ECE 2019 | Question: 44
Let $h[n]$ be a length - $7$ discrete-time finite impulse response filter, given by $h[0]=4, \quad h[1]=3,\quad h[2]=2,\quad h[3]=1,$ $\quad h[-1]=-3, \quad h[-2]=-2, \quad h[-3]=-1,$ and $h[n]$ is zero for $|n|\geq4.$ A ... and $g[n],$ respectively. For the filter that minimizes $E(h,g),$ the value of $10g[-1]+g[1],$ rounded off to $2$ decimal places, is __________.
Let $h[n]$ be a length – $7$ discrete-time finite impulse response filter, given by$$h[0]=4, \quad h =3,\quad h =2,\quad h[3]=1,$$$$\quad h[-1]=-3, \quad h[-2]=-2, \qua...
Arjun
6.6k
points
182
views
Arjun
asked
Feb 12, 2019
Continuous-time Signals
gate2019-ec
numerical-answers
continuous-time-signals
impulse-response
+
–
0
votes
0
answers
14
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$
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 fre...
Arjun
6.6k
points
221
views
Arjun
asked
Feb 12, 2019
Continuous-time Signals
gate2019-ec
continuous-time-signals
signals-and-systems
linear-time-invariant-systems
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–
0
votes
0
answers
15
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)$ ...
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 syst...
Arjun
6.6k
points
195
views
Arjun
asked
Feb 12, 2019
Continuous-time Signals
gate2019-ec
continuous-time-signals
signals-and-systems
linear-time-invariant-systems
+
–
0
votes
0
answers
16
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?
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...
Arjun
6.6k
points
184
views
Arjun
asked
Feb 12, 2019
Continuous-time Signals
gate2019-ec
continuous-time-signals
signals-and-systems
discrete-time-signals
+
–
0
votes
0
answers
17
GATE ECE 2019 | Question: 21
Consider the signal $f(t)=1+2 \cos(\pi t)+3 \sin \left(\dfrac{2\pi}{3}t\right)+4 \cos \left(\dfrac{\pi}{2}t+\dfrac{\pi}{4}\right)$, where $t$ is in seconds. Its fundamental time period, in seconds, is __________.
Consider the signal $f(t)=1+2 \cos(\pi t)+3 \sin \left(\dfrac{2\pi}{3}t\right)+4 \cos \left(\dfrac{\pi}{2}t+\dfrac{\pi}{4}\right)$, where $t$ is in seconds. Its fundament...
Arjun
6.6k
points
172
views
Arjun
asked
Feb 12, 2019
Continuous-time Signals
gate2019-ec
numerical-answers
continuous-time-signals
to-be-tagged
+
–
0
votes
0
answers
18
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$
The state variable description of an LTI system is given by$$\begin{pmatrix} \dot{x_1}\\ \dot{x_2}\\ \dot{x_3} \end{pmatrix}=\begin{pmatrix} 0 & a_1 & 0\\ 0 & 0 & a_2\\a_...
Milicevic3306
16.0k
points
515
views
Milicevic3306
asked
Mar 25, 2018
Continuous-time Signals
gate2012-ec
continuous-time-signals
signals-and-systems
linear-time-invariant-systems
+
–
0
votes
0
answers
19
GATE ECE 2015 Set 1 | Question: 18
The waveform of a periodic signal $x(t)$ is shown in the figure. A signal $g(t)$ is defined by $g(t) = x \big( \frac{t-1}{2} \big)$. The average power of $g(t)$ is ________
The waveform of a periodic signal $x(t)$ is shown in the figure.A signal $g(t)$ is defined by $g(t) = x \big( \frac{t-1}{2} \big)$. The average power of $g(t)$ is _______...
Milicevic3306
16.0k
points
281
views
Milicevic3306
asked
Mar 27, 2018
Continuous-time Signals
gate2015-ec-1
numerical-answers
continuous-time-signals
signals-and-system
periodic-signals
+
–
0
votes
0
answers
20
GATE ECE 2016 Set 3 | Question: 35
A continuous-time speech signal $x_a(t)$ is sampled at a rate of $8\:kHz$ and the samples are subsequently grouped in blocks, each of size $N$. The DFT of each block is to be computed in real time using the radix-$2$ decimation-in- ... by $1$ and $-1$) and the time required for addition/subtraction is negligible, then the maximum value of $N$ is _________
A continuous-time speech signal $x_a(t)$ is sampled at a rate of $8\:kHz$ and the samples are subsequently grouped in blocks, each of size $N$. The DFT of each block is t...
Milicevic3306
16.0k
points
253
views
Milicevic3306
asked
Mar 27, 2018
Continuous-time Signals
gate2016-ec-3
numerical-answers
continuous-time-signals
discrete-fourier-transform
+
–
0
votes
0
answers
21
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 $\frac{1}{4}$ $\frac{1}{2}$ $1$ $2$
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$$2$
Milicevic3306
16.0k
points
302
views
Milicevic3306
asked
Mar 25, 2018
Continuous-time Signals
gate2012-ec
continuous-time-signals
signals-and-systems
fourier-transform
+
–
0
votes
0
answers
22
GATE ECE 2015 Set 2 | Question: 44
Consider two real sequences with time-origin marked by the bold value, $x_{1}[n] = \{\textbf{1},2,3,0\},\:\:x_{2}[n] = \{\textbf{1},3,2,1\}$ Let ܺ$X_{1}(k)$ and ܺ$X_{2}(k)$ be $4$-point DFTs of $x_{1}[n]$ and $x_{2}[n]$, respectively. Another ... $4$-point inverse DFT of $X_{3}(k) = X_{1}(k)X_{2}(k).$ The value of $x_{3}[2]$ is ________.
Consider two real sequences with time-origin marked by the bold value, $$x_{1}[n] = \{\textbf{1},2,3,0\},\:\:x_{2}[n] = \{\textbf{1},3,2,1\}$$ Let ܺ$X_{1}(k)$ and ܺ$X_{...
Milicevic3306
16.0k
points
194
views
Milicevic3306
asked
Mar 27, 2018
Continuous-time Signals
gate2015-ec-2
numerical-answers
continuous-time-signals
discrete-fourier-transform
+
–
0
votes
0
answers
23
GATE ECE 2016 Set 1 | Question: 7
A continuous-time function $x(t)$ is periodic with period $T$. The function is sampled uniformly with a sampling period $T_s$. In which one of the following cases is the sampled signal periodic? $T =\sqrt2 \: T_s$ $T = 1.2 \: T_s$ Always Never
A continuous-time function $x(t)$ is periodic with period $T$. The function is sampled uniformly with a sampling period $T_s$. In which one of the following cases is the ...
Milicevic3306
16.0k
points
180
views
Milicevic3306
asked
Mar 27, 2018
Continuous-time Signals
gate2016-ec-1
continuous-time-signals
sampling-theorem
+
–
0
votes
0
answers
24
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.
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.$ Whic...
Milicevic3306
16.0k
points
177
views
Milicevic3306
asked
Mar 27, 2018
Continuous-time Signals
gate2015-ec-3
continuous-time-signals
signals-and-systems
fourier-transform
+
–
0
votes
0
answers
25
GATE ECE 2015 Set 2 | Question: 23
The signal $\cos \left(10\pi t + \dfrac{\pi}{4}\right)$ is ideally sampled at a sampling frequency of $15 Hz.$ ... $\dfrac{15}{2}\left(\dfrac{\sin (\pi t)}{\pi t}\right)\cos\left(40\pi t - \dfrac{\pi}{2}\right)$
The signal $\cos \left(10\pi t + \dfrac{\pi}{4}\right)$ is ideally sampled at a sampling frequency of $15 Hz.$ The sampled signal is passed through a filter with impulse ...
Milicevic3306
16.0k
points
177
views
Milicevic3306
asked
Mar 27, 2018
Continuous-time Signals
gate2015-ec-2
continuous-time-signals
sampling-theorem
+
–
0
votes
0
answers
26
GATE ECE 2016 Set 2 | Question: 10
The energy of the signal $x(t)= \frac{\sin(4\pi t)}{4\pi t}$ is ________
The energy of the signal $x(t)= \frac{\sin(4\pi t)}{4\pi t}$ is ________
Milicevic3306
16.0k
points
172
views
Milicevic3306
asked
Mar 27, 2018
Continuous-time Signals
gate2016-ec-2
numerical-answers
continuous-time-signals
to-be-tagged
+
–
0
votes
0
answers
27
GATE ECE 2016 Set 3 | Question: 36
The direct form structure of an FIR (finite impulse response) filter is shown in the figure. The filter can be used to approximate a low-pass filter high-pass filter band-pass filter band-stop filter
The direct form structure of an FIR (finite impulse response) filter is shown in the figure.The filter can be used to approximate alow-pass filterhigh-pass filterband-pas...
Milicevic3306
16.0k
points
156
views
Milicevic3306
asked
Mar 27, 2018
Continuous-time Signals
gate2016-ec-3
continuous-time-signals
impulse-response
+
–
0
votes
0
answers
28
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)$
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 fo...
Milicevic3306
16.0k
points
156
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Milicevic3306
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Mar 27, 2018
Continuous-time Signals
gate2015-ec-2
continuous-time-signals
signals-and-systems
fourier-transform
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–
0
votes
0
answers
29
GATE ECE 2015 Set 3 | Question: 45
Consider a continuous-time signal defined as $x(t)=\left(\dfrac{\sin(\pi t/2)}{(\pi t /2)}\right)\ast \sum _{n=-\infty}^{\infty}\delta(t-10n)$ where $’\ast’$ denotes the convolution operation and $t$ is in seconds. The Nyquist sampling rate $\text{(in samples/sec)}$ for $x(t)$ is _______.
Consider a continuous-time signal defined as$$x(t)=\left(\dfrac{\sin(\pi t/2)}{(\pi t /2)}\right)\ast \sum _{n=-\infty}^{\infty}\delta(t-10n)$$where $’\ast’$ denotes ...
Milicevic3306
16.0k
points
150
views
Milicevic3306
asked
Mar 27, 2018
Continuous-time Signals
gate2015-ec-3
numerical-answers
continuous-time-signals
convolution
nyquist
+
–
0
votes
0
answers
30
GATE ECE 2016 Set 2 | Question: 33
The Discrete Fourier Transform (DFT) of the $4$-point sequence $x\left [ n \right ]=\left \{ x\left [ 0 \right ],x\left [ 1 \right ], x\left [ 2 \right ], x\left [ 3 \right ] \right \}= \left \{ 3,2,3,4 \right \}$ ... $\left | \frac{X_{1}\left [ 8 \right ]}{X_{1}\left [ 11 \right ]} \right |$ is _________
The Discrete Fourier Transform (DFT) of the $4$-point sequence$x\left [ n \right ]=\left \{ x\left [ 0 \right ],x\left [ 1 \right ], x\left [ 2 \right ], x\left [ 3 \righ...
Milicevic3306
16.0k
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149
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Milicevic3306
asked
Mar 27, 2018
Continuous-time Signals
gate2016-ec-2
numerical-answers
continuous-time-signals
discrete-fourier-transform
+
–
0
votes
0
answers
31
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
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 ...
Milicevic3306
16.0k
points
148
views
Milicevic3306
asked
Mar 27, 2018
Continuous-time Signals
gate2015-ec-3
continuous-time-signals
impulse-response
linear-time-invariant-systems
+
–
0
votes
0
answers
32
GATE ECE 2015 Set 3 | Question: 20
The phase margin (in degrees) of the system $G(s) = \dfrac{10}{s(s+10)}$ is _______.
The phase margin (in degrees) of the system $G(s) = \dfrac{10}{s(s+10)}$ is _______.
Milicevic3306
16.0k
points
147
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Milicevic3306
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Mar 27, 2018
Continuous-time Signals
gate2015-ec-3
numerical-answers
continuous-time-signals
phase-delay
+
–
0
votes
0
answers
33
GATE ECE 2015 Set 3 | Question: 43
A realization of a stable discrete time system is shown in the figure. If the system is excited by a unit step sequence input $x[n ],$ the response $y[n ]$ is $4\left(-\dfrac{1}{3}\right)^{n}\:u[n]-5\left(-\dfrac{2}{3}\right)^{n}\:u[n]$ ... $5\left(\dfrac{2}{3}\right)^{n}\:u[n]-5\left(\dfrac{1}{3}\right)^{n}\:u[n]$
A realization of a stable discrete time system is shown in the figure. If the system is excited by a unit step sequence input $x[n ],$ the response $y[n ]$ is$4\left(-\df...
Milicevic3306
16.0k
points
147
views
Milicevic3306
asked
Mar 27, 2018
Continuous-time Signals
gate2015-ec-3
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GATE ECE 2015 Set 1 | Question: 31
In the circuit shown, switch SW is closed at $t=0$. Assuming zero initial conditions, the value of $v_c(t)$ (in Volts) at $t=1$ sec is _________.
In the circuit shown, switch SW is closed at $t=0$. Assuming zero initial conditions, the value of $v_c(t)$ (in Volts) at $t=1$ sec is _________.
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Continuous-time Signals
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35
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)$
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 autoco...
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Continuous-time Signals
gate2016-ec-3
continuous-time-signals
signals-and-systems
linear-time-invariant-systems
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36
GATE ECE 2015 Set 1 | Question: 23
Consider the signal $s(t)=m(t) \cos(2 \pi \: f_ct)+ \hat{m}(t) \sin(2 \pi f_c t)$ where $\hat{m}(t)$ denotes the Hilbert transform of $m(t)$ and the bandwidth of $m(t)$ is very small compared to $f_c$. The signal $s(t)$ is a high-pass signal low-pass signal band-pass signal double sideband suppressed carrier signal
Consider the signal $s(t)=m(t) \cos(2 \pi \: f_ct)+ \hat{m}(t) \sin(2 \pi f_c t)$ where $\hat{m}(t)$ denotes the Hilbert transform of $m(t)$ and the bandwidth of $m(t)$ i...
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Continuous-time Signals
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37
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$
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 th...
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Continuous-time Signals
gate2016-ec-3
continuous-time-signals
linear-time-invariant-systems
transfer-function
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38
GATE ECE 2016 Set 1 | Question: 10
A continuous-time sinusoid of frequency $33 Hz$ is multiplied with a periodic Dirac impulse train of frequency $46Hz$. The resulting signal is passed through an ideal analog low-pass filter with a cutoff frequency of $23Hz$. The fundamental frequency (in $Hz$) of the output is _______
A continuous-time sinusoid of frequency $33 Hz$ is multiplied with a periodic Dirac impulse train of frequency $46Hz$. The resulting signal is passed through an ideal ana...
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Continuous-time Signals
gate2016-ec-1
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continuous-time-signals
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39
GATE ECE 2014 Set 2 | Question: 52
In the figure, $M(f)$ is the Fourier transform of the message signal $m(t)$ where $A = 100$ Hz and $B = 40$ Hz. Given $v(t)= \cos (2\pi f_{c}t)$ and $w(t)= \cos (2\pi (f_{c}+A)t)$, where $f_{c}>A$. The cutoff frequencies of both the filters are $f_{c}$. The bandwidth of the signal at the output of the modulater (in Hz) is ______.
In the figure, $M(f)$ is the Fourier transform of the message signal $m(t)$ where $A = 100$ Hz and $B = 40$ Hz. Given $v(t)= \cos (2\pi f_{c}t)$ and $w(t)= \cos (2\pi (f_...
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Mar 26, 2018
Continuous-time Signals
gate2014-ec-2
numerical-answers
continuous-time-signals
fourier-transform
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40
GATE ECE 2015 Set 1 | Question: 45
The pole-zero diagram of a casual and stable discrete-time system is shown in the figure. The zero at the origin has multiplicity $4$. The impulse response of the system is $h[n]$. If $h[0]=1$, we can conclude $h[n]$ is real for all $n$ $h[n]$ is purely imaginary for all $n$ $h[n]$ is real for only even $n$ $h[n]$ is purely imaginary for only odd $n$
The pole-zero diagram of a casual and stable discrete-time system is shown in the figure. The zero at the origin has multiplicity $4$. The impulse response of the system ...
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Continuous-time Signals
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continuous-time-signals
poles-and-zeros
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