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Recent questions in Continuous-time Signals
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1
The value of the integral ∫ ∞ − ∞ 12 cos ( 2 π ) sin ( 4 π t ) 4 π t d t is
akalok808
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Continuous-time Signals
Aug 24, 2021
by
akalok808
130
points
117
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0
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0
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2
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 $\delta \left [ n \right ].$
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127
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gate2020-ec
continuous-time-signals
signals-and-systems
discrete-time-signals
impulse-response
0
votes
0
answers
3
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.
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146
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gate2020-ec
continuous-time-signals
poles-and-zeros
0
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0
answers
4
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? $y\left [ n \right ]=\sum ^{3}_{k=0}\left ( -1 \right )^{k}x\left [ n-k \right ]$
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poles-and-zeros
continuous-time-signals
0
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0
answers
5
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.
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gate2020-ec
continuous-time-signals
signals-and-systems
discrete-time-signals
0
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0
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6
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 ____________
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gate2020-ec
numerical-answers
continuous-time-signals
signals-and-systems
fourier-transform
0
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0
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7
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?
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continuous-time-signals
signals-and-systems
discrete-time-signals
0
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0
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8
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 $N_{p}=5, N_{z}=2$ $N_{p}=6, N_{z}=3$ $N_{p}=7, N_{z}=4$ $N_{p}=4, N_{z}=2$
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linear-time-invariant-systems
0
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9
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 __________.
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Feb 12, 2019
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101
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gate2019-ec
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continuous-time-signals
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0
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10
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).
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0
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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.
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158
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continuous-time-signals
to-be-tagged
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0
answers
12
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 $a_{1},a_{2},a_{3}$ ... $a_{1}=1,a_{2}=W_{6},a_{3}=W_{6}^{2}$ $a_{1}=-1,a_{2}=W_{6}^{2},a_{3}=W_{6}$
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357
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continuous-time-signals
signals-and-systems
fourier-transform
0
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0
answers
13
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 $y(t)$ ...
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signals-and-systems
linear-time-invariant-systems
1
vote
0
answers
14
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 __________.
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gate2019-ec
numerical-answers
continuous-time-signals
impulse-response
0
votes
0
answers
15
GATE ECE 2016 Set 3 | Question: 8
A discrete-time 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 $y[n] = x[n]$ $y[n] = x[-n]$ $y[n] = -x[n]$ $y[n] = -x[-n]$
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gate2016-ec-3
continuous-time-signals
signals-and-systems
discrete-time-signals
0
votes
0
answers
16
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 $0$ $1$ $2$ $3$
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transfer-function
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17
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 _________
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continuous-time-signals
discrete-fourier-transform
0
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0
answers
18
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
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impulse-response
0
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0
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19
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 $Y(t)$ ... $2R_X(\tau)-R_X(\tau-T_0)-R_X(\tau+T_0)$ $2R_X(\tau)+2R_X(\tau- 2T_0)$ $2R_X(\tau)-2R_X(\tau- 2T_0)$
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signals-and-systems
linear-time-invariant-systems
0
votes
0
answers
20
GATE ECE 2016 Set 2 | Question: 10
The energy of the signal $x(t)= \frac{\sin(4\pi t)}{4\pi t}$ is ________
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gate2016-ec-2
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continuous-time-signals
to-be-tagged
0
votes
0
answers
21
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 _________
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gate2016-ec-2
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continuous-time-signals
discrete-fourier-transform
0
votes
0
answers
22
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
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gate2016-ec-1
continuous-time-signals
sampling-theorem
0
votes
0
answers
23
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 _______
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continuous-time-signals
to-be-tagged
0
votes
0
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24
GATE ECE 2016 Set 1 | Question: 32
A first-order low-pass 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 $ ... $X \to R, \: Y\to P, \: Z \to Q$ $X \to P, \: Y\to R, \: Z \to Q$
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signals-and-systems
low-pass-filters
continuous-time-signals
0
votes
0
answers
25
GATE ECE 2016 Set 1 | Question: 35
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 discrete-time 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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numerical-answers
continuous-time-signals
signals-and-systems
fourier-transform
0
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0
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26
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
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impulse-response
linear-time-invariant-systems
0
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27
GATE ECE 2015 Set 3 | Question: 20
The phase margin (in degrees) of the system $G(s) = \dfrac{10}{s(s+10)}$ is _______.
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phase-delay
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28
GATE ECE 2015 Set 3 | Question: 23
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 $f_{m}$
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communications
calculation-of-bandwidth
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0
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29
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.
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fourier-transform
0
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30
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 $4\left(-\dfrac{1}{3}\right)^{n}\:u[n]-5\left(-\dfrac{2}{3}\right)^{n}\:u[n]$ ... $5\left(\dfrac{2}{3}\right)^{n}\:u[n]-5\left(\dfrac{1}{3}\right)^{n}\:u[n]$
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31
GATE ECE 2015 Set 3 | Question: 44
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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fourier-transform
periodic-signals
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32
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 _______.
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convolution
nyquist
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33
GATE ECE 2015 Set 3 | Question: 48
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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34
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 $x(t)$
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35
GATE ECE 2015 Set 2 | Question: 18
Two causal discrete-time 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 $\dfrac{2}{z(z-1)^{2}},$ the value of $x[2]$ is _______.
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36
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 $15 Hz.$ ... $\dfrac{15}{2}\left(\dfrac{\sin (\pi t)}{\pi t}\right)\cos\left(40\pi t - \dfrac{\pi}{2}\right)$
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sampling-theorem
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37
GATE ECE 2015 Set 2 | Question: 43
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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linear-time-invariant-systems
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0
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38
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 ________.
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continuous-time-signals
discrete-fourier-transform
0
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39
GATE ECE 2015 Set 1 | Question: 17
The result of the convolution $x(-t) * \delta (-t-t_0)$ is $x(t+t_0)$ $x(t-t_0)$ $x(-t+t_0)$ $x(-t – t_0)$
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signals-and-system
convolution
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0
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40
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 ________
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