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Recent questions and answers in Continuoustime Signals
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GATE ECE 2014 Set 1  Question: 17
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
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Aug 12, 2020
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GATE ECE 2020  Question: 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 $\delta \left [ n \right ].$
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Feb 13, 2020
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GATE ECE 2020  Question: 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 ... $1 + j0$ of the $G(s)$plane once in the clockwise direction.
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Feb 13, 2020
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GATE ECE 2020  Question: 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? $y\left [ n \right ]=\sum ^{3}_{k=0}\left ( 1 \right )^{k}x\left [ nk \right ]$
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Feb 13, 2020
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GATE ECE 2020  Question: 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 ... Only $X[4]$ is nonzero. Only $X[2]$ and $X[6]$ are nonzero. Only $X[3]$ and $X[5]$ are nonzero.
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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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GATE ECE 2019  Question: 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?
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Feb 12, 2019
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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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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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GATE ECE 2019  Question: 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 ... 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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Feb 12, 2019
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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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Feb 12, 2019
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12
GATE ECE 2019  Question: 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 $a_{1},a_{2},a_{3}$ ... $a_{1}=1,a_{2}=W_{6},a_{3}=W_{6}^{2}$ $a_{1}=1,a_{2}=W_{6}^{2},a_{3}=W_{6}$
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Feb 12, 2019
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GATE ECE 2019  Question: 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 $y(t)$ ...
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GATE ECE 2019  Question: 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 $n\geq4.$ 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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Feb 12, 2019
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GATE ECE 2016 Set 3  Question: 8
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 $y[n] = x[n]$ $y[n] = x[n]$ $y[n] = x[n]$ $y[n] = x[n]$
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Mar 28, 2018
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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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17
GATE ECE 2016 Set 3  Question: 35
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$2$ decimationin ... by $1$ and $1$) and the time required for addition/subtraction is negligible, then the maximum value of $N$ is _________
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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 lowpass filter highpass filter bandpass filter bandstop filter
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Mar 28, 2018
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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 $Y(t)$ ... $2R_X(\tau)R_X(\tauT_0)R_X(\tau+T_0)$ $2R_X(\tau)+2R_X(\tau 2T_0)$ $2R_X(\tau)2R_X(\tau 2T_0)$
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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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Mar 28, 2018
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0
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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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Mar 28, 2018
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22
GATE ECE 2016 Set 1  Question: 7
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
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23
GATE ECE 2016 Set 1  Question: 10
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 _______
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Mar 28, 2018
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gate2016ec1
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24
GATE ECE 2016 Set 1  Question: 32
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: $1  e^{ ... $X \to R, \: Y\to P, \: Z \to Q$ $X \to P, \: Y\to R, \: Z \to Q$
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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 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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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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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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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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29
GATE ECE 2015 Set 3  Question: 42
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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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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32
GATE ECE 2015 Set 3  Question: 45
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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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 ... $x(t)\in P$ $x(t)\in (CR)$ 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 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 _______.
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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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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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38
GATE ECE 2015 Set 2  Question: 44
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 ... $4$point inverse DFT of $X_{3}(k) = X_{1}(k)X_{2}(k).$ The value of $x_{3}[2]$ is ________.
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39
GATE ECE 2015 Set 1  Question: 17
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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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 $g(t) = x \big( \frac{t1}{2} \big)$. The average power of $g(t)$ is ________
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