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Most viewed questions in Continuous-time Signals
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1
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
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Milicevic3306
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Mar 25, 2018
Continuous-time Signals
gate2012-ec
continuous-time-signals
signals-and-systems
linear-time-invariant-systems
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0
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0
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2
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
503
views
Arjun
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Feb 12, 2019
Continuous-time Signals
gate2019-ec
continuous-time-signals
signals-and-systems
fourier-transform
+
–
0
votes
0
answers
3
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
436
views
admin
asked
Feb 16
Continuous-time Signals
gateece-2024
fourier-transform
continuous-time-signals
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–
0
votes
2
answers
4
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
378
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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–
0
votes
0
answers
5
GATE ECE 2017 Set 2 | Question: 49
The signal $x(t)=\sin (14000\pi t)$, where $t$ is in seconds, is sampled at a rate of $9000$ samples per second. The sampled signal is the input to an ideal lowpass filter with frequency response $H(f)$ ... $= 3$, frequencies $= 2,7,11$ Number $= 2$, frequencies $= 2,7$ Number $= 2$, frequencies $= 7,11$
The signal $x(t)=\sin (14000\pi t)$, where $t$ is in seconds, is sampled at a rate of $9000$ samples per second. The sampled signal is the input to an ideal lowpass filte...
admin
46.4k
points
362
views
admin
asked
Nov 25, 2017
Continuous-time Signals
gate2017-ec-2
continuous-time-signals
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–
0
votes
0
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6
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
324
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
7
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
303
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Milicevic3306
asked
Mar 25, 2018
Continuous-time Signals
gate2012-ec
continuous-time-signals
signals-and-systems
fourier-transform
+
–
0
votes
0
answers
8
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
302
views
Arjun
asked
Feb 12, 2019
Continuous-time Signals
gate2019-ec
numerical-answers
continuous-time-signals
to-be-tagged
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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
294
views
Milicevic3306
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Mar 25, 2018
Continuous-time Signals
gate2014-ec-1
continuous-time-signals
discrete-time-signals
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–
0
votes
0
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10
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
285
views
Milicevic3306
asked
Mar 27, 2018
Continuous-time Signals
gate2015-ec-1
numerical-answers
continuous-time-signals
signals-and-system
periodic-signals
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–
0
votes
0
answers
11
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
+
–
0
votes
0
answers
12
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
13
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
240
views
go_editor
asked
Feb 13, 2020
Continuous-time Signals
gate2020-ec
continuous-time-signals
signals-and-systems
discrete-time-signals
impulse-response
+
–
0
votes
0
answers
14
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 $256$ $64$ $16$ $4$
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$$x\left ( t \right )=...
gatecse
1.6k
points
235
views
gatecse
asked
Feb 19, 2018
Continuous-time Signals
gate2018-ec
continuous-time-signals
signals-and-systems
fourier-transform
+
–
0
votes
0
answers
15
GATE ECE 2017 Set 1 | Question: 6
Consider a single input single output discrete-time system with $x[ n ]$ as input and $y [ n ]$ ... statements is true about the system? It is causal and stable It is causal but not stable It is not causal but stable It is neither causal nor stable
Consider a single input single output discrete-time system with $x[ n ]$ as input and $y [ n ]$ as output, where the two are related as$$y [ n ]= \begin{cases} n \mid x [...
admin
46.4k
points
223
views
admin
asked
Nov 17, 2017
Continuous-time Signals
gate2017-ec-1
linear-time-invariant-systems
continuous-time-signals
signals-and-systems
discrete-time-signals
+
–
0
votes
0
answers
16
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
+
–
0
votes
0
answers
17
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
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...
admin
46.4k
points
216
views
admin
asked
Nov 17, 2017
Continuous-time Signals
gate2017-ec-1
linear-time-invariant-systems
continuous-time-signals
signals-and-systems
+
–
0
votes
0
answers
18
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_...
Milicevic3306
16.0k
points
211
views
Milicevic3306
asked
Mar 26, 2018
Continuous-time Signals
gate2014-ec-2
numerical-answers
continuous-time-signals
fourier-transform
+
–
1
votes
1
answer
19
The value of the integral ∫ ∞ − ∞ 12 cos ( 2 π ) sin ( 4 π t ) 4 π t d t is
akalok808
130
points
206
views
akalok808
asked
Aug 24, 2021
0
votes
0
answers
20
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
204
views
admin
asked
Feb 16
Continuous-time Signals
gateece-2024
impulse-response
continuous-time-signals
linear-time-invariant-systems
+
–
0
votes
0
answers
21
GATE ECE 2013 | Question: 54
The state diagram of a system is shown below. A system is described by the state-variable equations $\dot{X}= AX+Bu;\:\: y = CX+Du$ ...
The state diagram of a system is shown below. A system is described by the state-variable equations$$\dot{X}= AX+Bu;\:\: y = CX+Du$$The state-variable equations of the sy...
Milicevic3306
16.0k
points
199
views
Milicevic3306
asked
Mar 25, 2018
Continuous-time Signals
gate2013-ec
continuous-time-signals
state-equations-for-networks
+
–
0
votes
0
answers
22
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
197
views
go_editor
asked
Feb 13, 2020
Continuous-time Signals
gate2020-ec
poles-and-zeros
continuous-time-signals
+
–
0
votes
0
answers
23
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
197
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
24
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
195
views
Milicevic3306
asked
Mar 27, 2018
Continuous-time Signals
gate2015-ec-2
numerical-answers
continuous-time-signals
discrete-fourier-transform
+
–
0
votes
0
answers
25
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 _________.
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...
admin
46.4k
points
192
views
admin
asked
Nov 17, 2017
Continuous-time Signals
gate2017-ec-1
numerical-answers
continuous-time-signals
linear-time-invariant-systems
+
–
0
votes
0
answers
26
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
187
views
Milicevic3306
asked
Mar 27, 2018
Continuous-time Signals
gate2016-ec-1
continuous-time-signals
sampling-theorem
+
–
0
votes
0
answers
27
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
+
–
1
votes
0
answers
28
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$$h[0]=4, \quad h =3,\quad h =2,\quad h[3]=1,$$$$\quad h[-1]=-3, \quad h[-2]=-2, \qua...
Arjun
6.6k
points
183
views
Arjun
asked
Feb 12, 2019
Continuous-time Signals
gate2019-ec
numerical-answers
continuous-time-signals
impulse-response
+
–
0
votes
0
answers
29
GATE ECE 2017 Set 2 | Question: 7
An LTI system with unit sample response $h[n]=5\delta [n]-7\delta [n-1]+7\delta [n-3]-5\delta [n-4]$ is a low-pass filter high-pass filter band-pass filter band-stop filter
An LTI system with unit sample response $h[n]=5\delta [n]-7\delta [n-1]+7\delta [n-3]-5\delta [n-4]$ is a low-pass filter high-pass filter band-pass filter band-s...
admin
46.4k
points
181
views
admin
asked
Nov 23, 2017
Continuous-time Signals
gate2017-ec-2
linear-time-invariant-systems
continuous-time-signals
signals-and-systems
+
–
0
votes
0
answers
30
GATE ECE 2017 Set 1 | Question: 33
Let $h[n]$ ... radians. Given that $H(\omega_{0})=0$ and $0< \omega_{0} < \pi$, the value of $\omega_{0}$ (in radians) is equal to__________.
Let $h[n]$ be the impulse response of a discrete-time linear time invariant(LTI) filter. The impulse response is given by $$h[0]=\frac{1}{3}; \, h =\frac{1}{3}; \, h =\fr...
admin
46.4k
points
181
views
admin
asked
Nov 17, 2017
Continuous-time Signals
gate2017-ec-1
numerical-answers
continuous-time-signals
linear-time-invariant-systems
fourier-transform
+
–
0
votes
0
answers
31
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
179
views
Milicevic3306
asked
Mar 27, 2018
Continuous-time Signals
gate2015-ec-2
continuous-time-signals
sampling-theorem
+
–
0
votes
0
answers
32
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
178
views
Milicevic3306
asked
Mar 27, 2018
Continuous-time Signals
gate2015-ec-3
continuous-time-signals
signals-and-systems
fourier-transform
+
–
0
votes
0
answers
33
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
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)=...
admin
46.4k
points
176
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admin
asked
Nov 17, 2017
Continuous-time Signals
gate2017-ec-1
fourier-transform
continuous-time-signals
signals-and-systems
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0
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0
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34
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
175
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Arjun
asked
Feb 12, 2019
Continuous-time Signals
gate2019-ec
numerical-answers
continuous-time-signals
to-be-tagged
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0
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0
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35
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
175
views
Milicevic3306
asked
Mar 27, 2018
Continuous-time Signals
gate2016-ec-2
numerical-answers
continuous-time-signals
to-be-tagged
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0
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0
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36
GATE ECE 2014 Set 3 | Question: 43
Let $H_{1}(z)= (1-pz^{-1})^{-1},H_{2}(z)= (1-qz^{-1})^{-1},H(z)=H_{1}(z)+rH_{2}(z).$ The quantities $p,$ $q$, $r$ are real numbers. Consider $p=\frac{1}{2},q=-\frac{1}{4},\mid r \mid < 1.$ If the zero of $H(z)$ lies on the unit circle, then $r$ $=$ _________
Let $H_{1}(z)= (1-pz^{-1})^{-1},H_{2}(z)= (1-qz^{-1})^{-1},H(z)=H_{1}(z)+rH_{2}(z).$ The quantities $p,$ $q$, $r$ are real numbers. Consider $p=\frac{1}{2},q=-\frac{1}{4}...
Milicevic3306
16.0k
points
170
views
Milicevic3306
asked
Mar 26, 2018
Continuous-time Signals
gate2014-ec-3
numerical-answers
continuous-time-signals
poles-and-zeros
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0
votes
0
answers
37
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 ____________
Consider the parallel combination of two LTI systems shown in the figure.The impulse responses of the systems are $$ \begin{array} {} h_1(t)=2\delta (t+2)-3\delta (t+1) \...
admin
46.4k
points
170
views
admin
asked
Nov 25, 2017
Continuous-time Signals
gate2017-ec-2
impulse-response
numerical-answers
continuous-time-signals
signals-and-systems
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–
0
votes
0
answers
38
GATE ECE 2014 Set 4 | Question: 18
A real-valued signal $x(t)$ limited to the frequency band $\mid f \mid \leq \frac{W}{2}$ is passed through a linear time invariant system whose frequency response is $H(f) = \begin{cases} e^{-j 4 \pi f}, & \mid f \mid \leq \frac{W}{2} \\ 0, & \mid f \mid > \frac{W}{2} \end{cases}.$ The output of the system is $x(t+4)$ $x(t-4)$ $x(t+2)$ $x(t-2)$
A real-valued signal $x(t)$ limited to the frequency band $\mid f \mid \leq \frac{W}{2}$ is passed through a linear time invariant system whose frequency response is $$H(...
Milicevic3306
16.0k
points
169
views
Milicevic3306
asked
Mar 26, 2018
Continuous-time Signals
gate2014-ec-4
continuous-time-signals
linear-time-invariant-systems
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0
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0
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39
GATE ECE 2018 | Question: 13
A discrete-time all-pass system has two of its poles at $0.25\angle 0^{\circ}$ and $2\angle 30^{\circ}$. Which one of the following statements about the system is TRUE? It has two more poles at $0.5\angle 30^{\circ}$ and ... response is two-sided. It has constant phase response over all frequencies. It has constant phase response over the entire $\text{z-plane}$.
A discrete-time all-pass system has two of its poles at $0.25\angle 0^{\circ}$ and $2\angle 30^{\circ}$. Which one of the following statements about the system is TRUE?It...
gatecse
1.6k
points
162
views
gatecse
asked
Feb 19, 2018
Continuous-time Signals
gate2018-ec
continuous-time-signals
impulse-response
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–
0
votes
0
answers
40
GATE ECE 2014 Set 2 | Question: 48
Consider the state space system expressed by the signal flow diagram shown in the figure. The corresponding system is always controllable always observable always stable always unstable
Consider the state space system expressed by the signal flow diagram shown in the figure. The corresponding system isalways controllablealw...
Milicevic3306
16.0k
points
158
views
Milicevic3306
asked
Mar 26, 2018
Continuous-time Signals
gate2014-ec-2
continuous-time-signals
to-be-tagged
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