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Recent questions and answers in Continuoustime Signals
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1
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1
GATE2014117
A discretetime 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
answered
Aug 12
in
Continuoustime Signals
by
phenix
(
180
points)
gate2014ec1
continuoustimesignals
discretetimesignals
0
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0
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2
GATE2020EC: 5
The output $y[n]$ of a discretetime 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 $\delta \left [ n \right ].$
asked
Feb 13
in
Continuoustime Signals
by
jothee
(
1.4k
points)
gate2020ec
continuoustimesignals
signalsandsystems
discretetimesignals
impulseresponse
0
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0
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3
GATE2020EC: 11
The polezero 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 counterclockwise direction. the origin of the $G(s)$ ... $1 + j0$ of the $G(s)$plane once in the clockwise direction.
asked
Feb 13
in
Continuoustime Signals
by
jothee
(
1.4k
points)
gate2020ec
continuoustimesignals
polesandzeros
0
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0
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4
GATE2020EC: 14
Which one of the following polezero plots corresponds to the transfer function of an $\text{LTI}$ system characterized by the inputoutput difference equation given below? $y\left [ n \right ]=\sum ^{3}_{k=0}\left ( 1 \right )^{k}x\left [ nk \right ]$
asked
Feb 13
in
Continuoustime Signals
by
jothee
(
1.4k
points)
gate2020ec
polesandzeros
continuoustimesignals
0
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0
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5
GATE2020EC: 29
A finite duration discretetime signal $x[n]$ is obtained by sampling the continuoustime 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 defined ... zero. Only $X[4]$ is nonzero. Only $X[2]$ and $X[6]$ are nonzero. Only $X[3]$ and $X[5]$ are nonzero.
asked
Feb 13
in
Continuoustime Signals
by
jothee
(
1.4k
points)
gate2020ec
continuoustimesignals
signalsandsystems
discretetimesignals
0
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0
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6
GATE2020EC: 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 ____________
asked
Feb 13
in
Continuoustime Signals
by
jothee
(
1.4k
points)
gate2020ec
numericalanswers
continuoustimesignals
signalsandsystems
fouriertransform
0
votes
0
answers
7
GATE2019 EC: 3
Let $H(z)$ be the $z$ transform of a realvalued discretetime 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?
asked
Feb 12, 2019
in
Continuoustime Signals
by
Arjun
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1.4k
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gate2019ec
continuoustimesignals
signalsandsystems
discretetimesignals
0
votes
0
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8
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
votes
0
answers
9
GATE2019 EC: 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 __________.
asked
Feb 12, 2019
in
Continuoustime Signals
by
Arjun
(
1.4k
points)
gate2019ec
numericalanswers
continuoustimesignals
tobetagged
0
votes
0
answers
10
GATE2019 EC: 22
The baseband signal $m(t)$ shown in the figure is phasemodulated 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 carrier ... the ratio of the minimum instantaneous frequency (in kHz) to the maximum instantaneous frequency (in kHz) is _________ (rounded off to $2$ decimal places).
asked
Feb 12, 2019
in
Continuoustime Signals
by
Arjun
(
1.4k
points)
gate2019ec
numericalanswers
continuoustimesignals
tobetagged
0
votes
0
answers
11
GATE2019 EC: 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.
asked
Feb 12, 2019
in
Continuoustime Signals
by
Arjun
(
1.4k
points)
gate2019ec
numericalanswers
continuoustimesignals
tobetagged
0
votes
0
answers
12
GATE2019 EC: 28
Consider a sixpoint decimationintime Fast Fourier Transform $(FFT)$ algorithm, for which the signalflow 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 $a_{1},a_{2},a_{3}$ in terms ... $a_{1}=1,a_{2}=W_{6},a_{3}=W_{6}^{2}$ $a_{1}=1,a_{2}=W_{6}^{2},a_{3}=W_{6}$
asked
Feb 12, 2019
in
Continuoustime Signals
by
Arjun
(
1.4k
points)
gate2019ec
continuoustimesignals
signalsandsystems
fouriertransform
0
votes
0
answers
13
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
14
GATE2019 EC: 44
Let $h[n]$ be a length  $7$ discretetime 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 $n\geq4.$ ... $g[n],$ respectively. For the filter that minimizes $E(h,g),$ the value of $10g[1]+g[1],$ rounded off to $2$ decimal places, is __________.
asked
Feb 12, 2019
in
Continuoustime Signals
by
Arjun
(
1.4k
points)
gate2019ec
numericalanswers
continuoustimesignals
impulseresponse
0
votes
0
answers
15
GATE201638
A discretetime signal $x[n] = \delta[n – 3] + 2 \delta[n – 5]$ has $z$transform $X(z)$. If $Y(z) = X(z)$ is the $z$transform of another signal $y[n]$, then $y[n] = x[n]$ $y[n] = x[n]$ $y[n] = x[n]$ $y[n] = x[n]$
asked
Mar 28, 2018
in
Continuoustime Signals
by
Milicevic3306
(
15.8k
points)
gate2016ec3
continuoustimesignals
signalsandsystems
discretetimesignals
0
votes
0
answers
16
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 $0$ $1$ $2$ $3$
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Mar 28, 2018
in
Continuoustime Signals
by
Milicevic3306
(
15.8k
points)
gate2016ec3
continuoustimesignals
lineartimeinvariantsystems
transferfunction
0
votes
0
answers
17
GATE2016335
A continuoustime 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$2$ decimationinfrequency FFT ... multiplications by $1$ and $1$) and the time required for addition/subtraction is negligible, then the maximum value of $N$ is _________
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Mar 28, 2018
in
Continuoustime Signals
by
Milicevic3306
(
15.8k
points)
gate2016ec3
numericalanswers
continuoustimesignals
discretefouriertransform
0
votes
0
answers
18
GATE2016336
The direct form structure of an FIR (finite impulse response) filter is shown in the figure. The filter can be used to approximate a lowpass filter highpass filter bandpass filter bandstop filter
asked
Mar 28, 2018
in
Continuoustime Signals
by
Milicevic3306
(
15.8k
points)
gate2016ec3
continuoustimesignals
impulseresponse
0
votes
0
answers
19
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 $2R_X(\tau)+R_X(\tauT_0)+R_X(\tau+T_0)$ $2R_X(\tau)R_X(\tauT_0)R_X(\tau+T_0)$ $2R_X(\tau)+2R_X(\tau 2T_0)$ $2R_X(\tau)2R_X(\tau 2T_0)$
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Mar 28, 2018
in
Continuoustime Signals
by
Milicevic3306
(
15.8k
points)
gate2016ec3
continuoustimesignals
signalsandsystems
lineartimeinvariantsystems
0
votes
0
answers
20
GATE2016210
The energy of the signal $x(t)= \frac{\sin(4\pi t)}{4\pi t}$ is ________
asked
Mar 28, 2018
in
Continuoustime Signals
by
Milicevic3306
(
15.8k
points)
gate2016ec2
numericalanswers
continuoustimesignals
tobetagged
0
votes
0
answers
21
GATE2016233
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 _________
asked
Mar 28, 2018
in
Continuoustime Signals
by
Milicevic3306
(
15.8k
points)
gate2016ec2
numericalanswers
continuoustimesignals
discretefouriertransform
0
votes
0
answers
22
GATE201617
A continuoustime 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
asked
Mar 28, 2018
in
Continuoustime Signals
by
Milicevic3306
(
15.8k
points)
gate2016ec1
continuoustimesignals
samplingtheorem
0
votes
0
answers
23
GATE2016110
A continuoustime 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 lowpass filter with a cutoff frequency of $23Hz$. The fundamental frequency (in $Hz$) of the output is _______
asked
Mar 28, 2018
in
Continuoustime Signals
by
Milicevic3306
(
15.8k
points)
gate2016ec1
numericalanswers
continuoustimesignals
tobetagged
0
votes
0
answers
24
GATE2016132
A firstorder lowpass filter of time constant $T$ is excited with different input signals (with zero initial conditions up to $t = 0$). Match the excitation signals $X, Y, Z$ with the corresponding time responses for $t \geq 0 $: $\begin{array}{ll}\text{X:Impulse}&\text{P: $ ... $X \to R, \: Y\to P, \: Z \to Q$ $X \to P, \: Y\to R, \: Z \to Q$
asked
Mar 28, 2018
in
Continuoustime Signals
by
Milicevic3306
(
15.8k
points)
gate2016ec1
signalsandsystems
lowpassfilters
continuoustimesignals
0
votes
0
answers
25
GATE2016135
Consider the signal $x[n] = 6 \delta[n + 2] + 3 \delta[n + 1] + 8 \delta[n] + 7 \delta[n  1] + 4 \delta[n  2]$ If $X(e^{jw})$ is the discretetime Fourier transform of $x[n]$, then $\frac{1}{\pi} \int\limits_{\pi}^{\pi} X(e^{jw}) \sin^2(2\omega) d\omega$ is equal to _______
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Mar 28, 2018
in
Continuoustime Signals
by
Milicevic3306
(
15.8k
points)
gate2016ec1
numericalanswers
continuoustimesignals
signalsandsystems
fouriertransform
0
votes
0
answers
26
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
27
GATE2015320
The phase margin (in degrees) of the system $G(s) = \dfrac{10}{s(s+10)}$ is _______.
asked
Mar 28, 2018
in
Continuoustime Signals
by
Milicevic3306
(
15.8k
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gate2015ec3
numericalanswers
continuoustimesignals
phasedelay
0
votes
0
answers
28
GATE2015323
A message signal $m(t) = A_{m} \sin(2πf_{m}t)$ is used to modulate the phase of a carrier $A_{c} \cos(2πf_{c}t)$ to get the modulated signal $y(t) = A_{c} \cos(2πf_{c}t + m(t)).$ The bandwidth of $y(t)$ depends on $A_{m}$ but not on $f_{m}$ depends on $f_{m}$ but not on $A_{m}$ depends on both $A_{m}$ and $f_{m}$ does not depend on $A_{m}$ or $f_{m}$
asked
Mar 28, 2018
in
Continuoustime Signals
by
Milicevic3306
(
15.8k
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gate2015ec3
communications
calculationofbandwidth
0
votes
0
answers
29
GATE2015342
Suppose $x[n]$ is an absolutely summable discretetime 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 noncausal signal It is a periodic signal.
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Mar 28, 2018
in
Continuoustime Signals
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Milicevic3306
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15.8k
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gate2015ec3
continuoustimesignals
signalsandsystems
fouriertransform
0
votes
0
answers
30
GATE2015343
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 $4\left(\dfrac{1}{3}\right)^{n}\:u[n]5\left(\dfrac{2}{3}\right)^{n}\:u[n]$ ... $5\left(\dfrac{2}{3}\right)^{n}\:u[n]5\left(\dfrac{1}{3}\right)^{n}\:u[n]$
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Mar 28, 2018
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Continuoustime Signals
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Milicevic3306
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15.8k
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gate2015ec3
continuoustimesignals
discretetimesignals
0
votes
0
answers
31
GATE2015344
Let $\widetilde{x}[n] = 1 + \cos\left(\dfrac{\pi n}{8}\right)$ be a periodic signal with period $16.$ Its DFS coefficients are defined by $a_{k} = \displaystyle{}\dfrac{1}{16}\sum_{n=0}^{15}\widetilde{x}[n] \text{exp}\big(j\dfrac{\pi}{8} kn\big)$ for all $k .$ The value of the coefficient ܽ$a_{31}$ is _______.
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Mar 28, 2018
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Continuoustime Signals
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Milicevic3306
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15.8k
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gate2015ec3
numericalanswers
continuoustimesignals
signalsandsystems
fouriertransform
periodicsignals
0
votes
0
answers
32
GATE2015345
Consider a continuoustime signal defined as $x(t)=\left(\dfrac{\sin(\pi t/2)}{(\pi t /2)}\right)\ast \sum _{n=\infty}^{\infty}\delta(t10n)$ where $’\ast’$ denotes the convolution operation and $t$ is in seconds. The Nyquist sampling rate $\text{(in samples/sec)}$ for $x(t)$ is _______.
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Mar 28, 2018
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Continuoustime Signals
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Milicevic3306
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15.8k
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gate2015ec3
numericalanswers
continuoustimesignals
convolution
nyquist
0
votes
0
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33
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 _________.
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Mar 28, 2018
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Continuoustime Signals
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15.8k
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gate2015ec3
numericalanswers
continuoustimesignals
signalsandsystems
lineartimeinvariantsystems
0
votes
0
answers
34
GATE201525
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 real numbers, and ... $x(t)\in P$ $x(t)\in (CR)$ the information given is not sufficient to draw any conclusion about $x(t)$
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Mar 28, 2018
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Continuoustime Signals
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15.8k
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gate2015ec2
continuoustimesignals
signalsandsystems
fouriertransform
0
votes
0
answers
35
GATE2015218
Two causal discretetime signals $x[n]$ and $y[n]$ are related as $y[n] = \displaystyle{}\sum _{m=0}^{n} x[m]$. If the $z$transform of $y[n]$ is $\dfrac{2}{z(z1)^{2}},$ the value of $x[2]$ is _______.
asked
Mar 28, 2018
in
Continuoustime Signals
by
Milicevic3306
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15.8k
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gate2015ec2
numericalanswers
continuoustimesignals
discretetimesignals
0
votes
0
answers
36
GATE2015223
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 response $\left(\dfrac{\sin (\pi t)}{\pi t}\right)\cos\left(40\pi t  \dfrac{\pi}{2}\right)$ The filter ... $\dfrac{15}{2}\left(\dfrac{\sin (\pi t)}{\pi t}\right)\cos\left(40\pi t  \dfrac{\pi}{2}\right)$
asked
Mar 28, 2018
in
Continuoustime Signals
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Milicevic3306
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15.8k
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gate2015ec2
continuoustimesignals
samplingtheorem
0
votes
0
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37
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 $\dfrac{1}{5}e^{3t}u(t) + \dfrac{1}{5}e^{2t}u(t)$ ... $\dfrac{1}{5}e^{3t}u(t)  \dfrac{1}{5}e^{2t}u(t)$
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Mar 28, 2018
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Continuoustime Signals
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15.8k
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gate2015ec2
continuoustimesignals
signalsandsystems
lineartimeinvariantsystems
0
votes
0
answers
38
GATE2015244
Consider two real sequences with timeorigin 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 sequence $x_{3}[n]$ is derived by taking $4$point inverse DFT of $X_{3}(k) = X_{1}(k)X_{2}(k).$ The value of $x_{3}[2]$ is ________.
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Continuoustime Signals
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15.8k
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gate2015ec2
numericalanswers
continuoustimesignals
discretefouriertransform
0
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0
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39
GATE2015117
The result of the convolution $x(t) * \delta (tt_0)$ is $x(t+t_0)$ $x(tt_0)$ $x(t+t_0)$ $x(t – t_0)$
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Mar 28, 2018
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gate2015ec1
continuoustimesignals
signalsandsystem
convolution
0
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0
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40
GATE2015118
The waveform of a periodic signal $x(t)$ is shown in the figure. A signal $g(t)$ is defined by $g(t) = x \big( \frac{t1}{2} \big)$. The average power of $g(t)$ is ________
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gate2015ec1
numericalanswers
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