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Recent questions tagged signalsandsystems
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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
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jothee
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1.4k
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gate2020ec
continuoustimesignals
signalsandsystems
discretetimesignals
impulseresponse
0
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0
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2
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.
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Feb 13
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jothee
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1.4k
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gate2020ec
continuoustimesignals
signalsandsystems
polezero
0
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0
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3
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
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jothee
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1.4k
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gate2020ec
continuoustimesignals
signalsandsystems
discretetimesignals
0
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0
answers
4
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
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jothee
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1.4k
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gate2020ec
numericalanswers
continuoustimesignals
signalsandsystems
fouriertransform
0
votes
0
answers
5
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
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Arjun
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1.4k
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gate2019ec
continuoustimesignals
signalsandsystems
discretetimesignals
0
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0
answers
6
GATE2019 EC: 5
Let $Y(s)$ be the unitstep response of a causal system having a transfer function $G(s)= \dfrac{3s}{(s+1)(s+3)}$ that is ,$Y(s)=\dfrac{G(s)}{s}.$ The forced response of the system is $u(t)2e^{t}u(t)+e^{3t}u(t)$ $2u(t)2e^{t}u(t)+e^{3t}u(t)$ $2u(t)$ $u(t)$
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Feb 12, 2019
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by
Arjun
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1.4k
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gate2019ec
networksolutionmethods
signalsandsystems
transferfunction
0
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0
answers
7
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 $N_{p}=5, N_{z}=2$ $N_{p}=6, N_{z}=3$ $N_{p}=7, N_{z}=4$ $N_{p}=4, N_{z}=2$
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Feb 12, 2019
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Arjun
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1.4k
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gate2019ec
continuoustimesignals
signalsandsystems
ltisystems
0
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0
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8
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 __________.
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Feb 12, 2019
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Arjun
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1.4k
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gate2019ec
numericalanswers
continuoustimesignals
signalsandsystems
0
votes
0
answers
9
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).
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Feb 12, 2019
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by
Arjun
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1.4k
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gate2019ec
numericalanswers
signalsandsystems
basebandsignal
0
votes
0
answers
10
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
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by
Arjun
(
1.4k
points)
gate2019ec
continuoustimesignals
signalsandsystems
fouriertransform
0
votes
0
answers
11
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
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by
Arjun
(
1.4k
points)
gate2019ec
continuoustimesignals
signalsandsystems
ltisystems
0
votes
0
answers
12
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
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by
Arjun
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1.4k
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gate2019ec
numericalanswers
continuoustimesignals
signalsandsystems
discretetime
0
votes
0
answers
13
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
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by
Milicevic3306
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15.7k
points)
gate2016ec3
continuoustimesignals
signalsandsystems
discretetimesignals
0
votes
0
answers
14
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 _________
asked
Mar 28, 2018
in
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Milicevic3306
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15.7k
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gate2016ec3
numericalanswers
continuoustimesignals
signalsandsystems
0
votes
0
answers
15
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
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Mar 28, 2018
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Milicevic3306
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gate2016ec3
continuoustimesignals
signalsandsystems
filters
0
votes
0
answers
16
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
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Milicevic3306
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15.7k
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gate2016ec3
continuoustimesignals
signalsandsystems
ltisystems
0
votes
0
answers
17
GATE2016210
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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Milicevic3306
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15.7k
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gate2016ec2
numericalanswers
signalsandsystems
0
votes
0
answers
18
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 _________
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Mar 28, 2018
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Milicevic3306
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15.7k
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gate2016ec2
numericalanswers
continuoustimesignals
signalsandsystems
discretefouriertransform
0
votes
0
answers
19
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
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Mar 28, 2018
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Milicevic3306
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gate2016ec1
continuoustimesignals
signalsandsystems
0
votes
0
answers
20
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 _______
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Mar 28, 2018
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Milicevic3306
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15.7k
points)
gate2016ec1
numericalanswers
continuoustimesignals
signalsandsystems
0
votes
0
answers
21
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
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by
Milicevic3306
(
15.7k
points)
gate2016ec1
signalsandsystems
lowpassfilters
0
votes
0
answers
22
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
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Milicevic3306
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15.7k
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gate2016ec1
numericalanswers
continuoustimesignals
signalsandsystems
fouriertransform
0
votes
0
answers
23
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 $f_{m}$
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Mar 28, 2018
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Milicevic3306
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gate2015ec3
signalsandsystems
0
votes
0
answers
24
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
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Milicevic3306
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15.7k
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gate2015ec3
continuoustimesignals
signalsandsystems
fourierseries
0
votes
0
answers
25
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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by
Milicevic3306
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15.7k
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gate2015ec3
numericalanswers
continuoustimesignals
signalsandsystems
fourierseries
periodicsignals
0
votes
0
answers
26
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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Milicevic3306
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15.7k
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gate2015ec3
numericalanswers
continuoustimesignals
signalsandsystems
0
votes
0
answers
27
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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Milicevic3306
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15.7k
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gate2015ec3
numericalanswers
continuoustimesignals
signalsandsystems
ltisystems
0
votes
0
answers
28
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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Milicevic3306
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15.7k
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gate2015ec2
continuoustimesignals
signalsandsystems
fourierseries
0
votes
0
answers
29
GATE2015220
For the signal flow graph shown in the figure, the value of $\dfrac{C(s)}{R(s)}$ is $\dfrac{G_{1}G_{2}G_{3}G_{4}}{1  G_{1}G_{2}H_{1}  G_{3}G_{4}H_{2}  G_{2}G_{3}H_{3} +G_{1}G_{2}G_{3}G_{4}H_{1}H_{2}} \\$ ... $\dfrac{1}{1  G_{1}G_{2}H_{1}  G_{3}G_{4}H_{2}  G_{2}G_{3}H_{3} +G_{1}G_{2}G_{3}G_{4}H_{1}H_{2}}$
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Mar 28, 2018
in
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Milicevic3306
(
15.7k
points)
gate2015ec2
signalsandsystems
0
votes
0
answers
30
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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Milicevic3306
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15.7k
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gate2015ec2
continuoustimesignals
signalsandsystems
ltisystems
0
votes
0
answers
31
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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Mar 28, 2018
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Milicevic3306
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gate2015ec2
numericalanswers
signalsandsystems
0
votes
0
answers
32
GATE2015123
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 highpass signal lowpass signal bandpass signal double sideband suppressed carrier signal
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gate2015ec1
signalsandsystems
0
votes
0
answers
33
GATE2015131
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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Mar 28, 2018
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gate2015ec1
numericalanswers
continuoustimesignals
signalsandsystems
zero
0
votes
0
answers
34
GATE2015151
In the system shown in Figure (a), $m(t)$ is a lowpass signal with bandwidth $W$ Hz. The frequency response of the bandpass filter $H(f)$ is shown in Figure (b). If it is desired that the output signal $z(t)=10x(t)$, the maximum value of $W$ (in Hz) should be strictly less than _____________.
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Mar 28, 2018
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Milicevic3306
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15.7k
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gate2015ec1
numericalanswers
signalsandsystems
0
votes
0
answers
35
GATE2014417
A Fourier transform pair is given by $\bigg ( \frac{2}{3} \bigg ) \: u[n+3] \overset{FT}{\Leftrightarrow} \frac{Ae^{j6 \pi f}}{1 (\frac{2}{3} ) e^{j2 \pi f}}$ where $u[n]$ denotes the unit step sequence. The values of $A$ is ____________
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Mar 26, 2018
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Milicevic3306
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gate2014ec4
numericalanswers
continuoustimesignals
signalsandsystems
fouriertransform
0
votes
0
answers
36
GATE2014418
A realvalued 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 $x(t+4)$ $x(t4)$ $x(t+2)$ $x(t2)$
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Mar 26, 2018
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Milicevic3306
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gate2014ec4
signalsandsystems
realvaluedsignal
0
votes
0
answers
37
GATE2014419
The sequence $x[n] = 0.5^n \: u[n]$, where $u[n]$ is the unit step sequence, is convolved with itself to obtain $y[n]$. Then $\Sigma_{n= \infty}^{+ \infty} y[n]$ is _________.
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Mar 26, 2018
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Milicevic3306
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gate2014ec4
numericalanswers
signalsandsystems
0
votes
0
answers
38
GATE2014443
A stable linear time variant (LTI) system has a transfer function $H(s) = \frac{1}{s^2+s6}$. To make this system casual it needs to be cascaded with another LTI system having a transfer function $H_1(s)$. A correct choice for $H_1(s)$ among the following options is $s+3$ $s2$ $s6$ $s+1$
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Mar 26, 2018
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Milicevic3306
(
15.7k
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gate2014ec4
continuoustimesignals
signalsandsystems
ltisystems
0
votes
0
answers
39
GATE2014444
A casual LTI system has zero initial conditions and impulse response $h(t)$. Its input $x(t)$ and output $y(t)$ are related through the linear constantcoefficient differential equation $\frac{d^2y(t)}{dt^2} + a \frac{dy(t)}{dt}+a^2y(t)=x(t).$ Let another signal $g(t)$ ... $G(s)$ is the Laplace transform of $g(t)$, then the number of poles of $G(s)$ is _________.
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Mar 26, 2018
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Milicevic3306
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15.7k
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gate2014ec4
numericalanswers
continuoustimesignals
signalsandsystems
ltisystems
0
votes
0
answers
40
GATE2014445
The $N$point DFT $X$ of a sequence $x[n]$, $0 \leq n \leq N1$ is given by $X[k] = \frac{1}{\sqrt{N}} \Sigma_{n=0}^{N1} x[n] e^{j \frac{2\pi}{N}nk}, \: \: \: 0 \leq k \leq N1.$ Denote this relation as $X=DFT(x)$. For $N=4$, which ... $x = \begin{bmatrix} 1 & 3 & 2 & 2 \end{bmatrix}$ $x = \begin{bmatrix} 1 & 2 & 2 & 3 \end{bmatrix}$
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Mar 26, 2018
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gate2014ec4
continuoustimesignals
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dft
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