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Recent questions and answers in Signals and Systems
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1
Gate 2000 signals and systems
Hanuma
asked
in
Signals and Systems
Mar 17, 2021
by
Hanuma
120
points
0
votes
0
answers
2
GATE Electrical 2020 | Question: 10
Consider a linear time-invariant system whose input $\text{r(t)}$ and output $\text{y(t)}$ are related by the following differential equation: $\frac{d^{2}y\left ( t \right )}{dt^{2}}+4y\left ( t \right )=6r\left ( t \right )$ The poles of this system are at $+2j,-2j$ $+2,-2$ $+4,-4$ $+4j,-4j$
go_editor
asked
in
Signals and Systems
Feb 28, 2020
by
go_editor
1.9k
points
gate2020-ee
signals-and-systems
linear-time-invariant-system
1
vote
0
answers
3
Gate EE-2014
For a peridic square wave ,which one of the following statements is TRUE? 1). The fourieF series coefficients do not exist 2).The Fourier series coefficients exist but the reconstruction converges at most point. I know the correct answer is 2). But I need some explanation.
Shaurya khare
asked
in
Signals and Systems
Jul 8, 2018
by
Shaurya khare
130
points
0
votes
0
answers
4
GATE Electrical 2013 | Question: 41
The impulse response of a continuous time system is given by $h(t)=\delta (t-1)+\delta (t-3).$ The value of the step response at $t=2$ is $0$ $1$ $2$ $3$
piyag476
asked
in
Signals and Systems
Feb 12, 2017
by
piyag476
1.5k
points
gate2013-ee
impulse-response
step-response
0
votes
0
answers
5
GATE Electrical 2013 | Question: 17
For a periodic signal $v(t) = 30 \sin100t +10 \cos 300t + 6 \sin (500t+\pi /4)$, the fundamental frequency in $rad/s$ is $100$ $300$ $500$ $1500$
piyag476
asked
in
Signals and Systems
Feb 12, 2017
by
piyag476
1.5k
points
gate2013-ee
periodicity
sinusoidal
0
votes
0
answers
6
GATE Electrical 2013 | Question: 6
Two systems with impulse responses $h_1(t)$ and $h_2(t)$ are connected in cascade.then the overall impulse response of the cascaded system is given by Product of $h_1(t)$ and $h_2(t)$ Sum of $h_1(t)$ and $h_2(t)$ convolution of $h_1(t)$ and $h_2(t)$ subtraction of $h_2(t)$ from $h_1(t)$
piyag476
asked
in
Signals and Systems
Feb 12, 2017
by
piyag476
1.5k
points
gate2013-ee
convolution
multiplication
addition
0
votes
0
answers
7
GATE Electrical 2013 | Question: 4
The impulse response a the system is $h(t)=t\:u(t).$ For an input $u(t-1)$, the output is $\dfrac{t^2}{2}u(t) \\$ $\dfrac{t(t-1)}{2}u(t-1) \\$ $\dfrac{(t-1)^2}{2}u(t-1) \\$ $\dfrac{t^2-1}{2}u(t-1)$
piyag476
asked
in
Signals and Systems
Feb 12, 2017
by
piyag476
1.5k
points
gate2013-ee
fourier-transform
sampling-theorem
0
votes
0
answers
8
GATE Electrical 2014 Set 3 | Question: 35
A differentiable non constant even function $x(t)$ has a derivative $y(t)$, and their respective Fourier Transforms are $X(\omega)$ and $Y(\omega)$. Which of the following statements is TRUE? $X(\omega)$ and $Y(\omega)$ ... imaginary. $X(\omega)$ and $Y(\omega)$ are both imaginary. $X(\omega)$ is imaginary and $Y(\omega)$ is real.
makhdoom ghaya
asked
in
Signals and Systems
Feb 12, 2017
by
makhdoom ghaya
9.3k
points
gate2014-ee-3
even-functions
fourier-transform
0
votes
0
answers
9
GATE Electrical 2014 Set 3 | Question: 32
A series $RLC$ circuit is observed at two frequencies. At $ω_1=1 \text{ krad/s}$, we note that source voltage $V_1=100\angle 0^{\circ} \: V$ results in a current $I_1=0.03\angle 31^{\circ}$ $A$. At $w_2=2 \text{ krad/s}$ ... $R=50\Omega$ ; $L=50 mH$ ,$C=5 \mu F$ $R=50\Omega$ ; $L=5 mH$ ,$C=50 \mu F$
makhdoom ghaya
asked
in
Signals and Systems
Feb 12, 2017
by
makhdoom ghaya
9.3k
points
gate2014-ee-3
rc-filter
rl-filter
0
votes
0
answers
10
GATE Electrical 2014 Set 3 | Question: 33
A continuous-time $LTI$ system with system function $H(w)$ has the following pole-zero plot. For this system, which of the alternatives is $TRUE$? $\mid H(0)\mid > \mid H(w)\mid ;\mid w\mid > 0$ $\mid H(w) \mid$ has multiple maxima, at $w_1$ ... $\mid H(w)\mid =$ constant; $-\infty < w< \infty$
makhdoom ghaya
asked
in
Signals and Systems
Feb 12, 2017
by
makhdoom ghaya
9.3k
points
gate2014-ee-3
pole-zero-plot
linear-time-invariant-system
0
votes
0
answers
11
GATE Electrical 2014 Set 3 | Question: 34
A sinusoid $x(t)$ of unknown frequency is sampled by an impulse train of period $20$ $ms$. The resulting sample train is next applied to an ideal lowpass filter with a cutoff at $25$ $Hz$. The filter output is seen to be a sinusoid of frequency $20$ $Hz$. This means that $x(t)$ has a frequency of $10$ $Hz$ $60$ $Hz$ $30$ $Hz$ $90$ $Hz$
makhdoom ghaya
asked
in
Signals and Systems
Feb 12, 2017
by
makhdoom ghaya
9.3k
points
gate2014-ee-3
impulse-train
low-pass-filter
0
votes
0
answers
12
GATE Electrical 2014 Set 3 | Question: 20
The two signals $S1$ and $S2$, shown in figure, are applied to $Y$ and $X$ deflection plates of an oscilloscope. The waveform displayed on the screen is
makhdoom ghaya
asked
in
Signals and Systems
Feb 12, 2017
by
makhdoom ghaya
9.3k
points
gate2014-ee-3
oscilloscope
even-functions
0
votes
0
answers
13
GATE Electrical 2014 Set 3 | Question: 10
For the signal $f(t)=3 \sin8 \pi t+6 \sin 12\pi t+ \sin14\pi t$ , the minimum sampling frequency (in $Hz$) satisfying the Nyquist criterion is _________.
makhdoom ghaya
asked
in
Signals and Systems
Feb 12, 2017
by
makhdoom ghaya
9.3k
points
gate2014-ee-3
sampling-frequency
stability
numerical-answers
0
votes
0
answers
14
GATE Electrical 2014 Set 3 | Question: 9
A signal is represented by $x(t)=\begin{cases} 1 & \mid t \mid<1 \\ 0 & \mid t \mid >1 \end{cases}$ The Fourier transform of the convolved signal $y(t)$= $x(2t)*x(t/2)$ ... $\dfrac{4}{\omega ^2} \sin(2\omega ) \\$ $\dfrac{4}{\omega ^2} \sin^2\omega $
makhdoom ghaya
asked
in
Signals and Systems
Feb 12, 2017
by
makhdoom ghaya
9.3k
points
gate2014-ee-3
fourier-transform
convolution
0
votes
0
answers
15
GATE Electrical 2014 Set 2 | Question: 34
An input signal $x(t)=2+5 \sin(100\pi t)$ is sampled with a sampling frequency of $400$ $Hz$ ... where, $N$ represents the number of samples per cycle. The output $y(n)$ of the system under steady state is $0$ $1$ $2$ $5$
makhdoom ghaya
asked
in
Signals and Systems
Feb 12, 2017
by
makhdoom ghaya
9.3k
points
gate2014-ee-2
transfer-function
sampling-per-cycle
0
votes
0
answers
16
GATE Electrical 2014 Set 2 | Question: 10
Consider an $LTI$ system with impulse response $h(t)=e^{-5t}u(t)$ . If the output of the system is $y(t)=e^{-3t}u(t)-e^{-5t}u(t)$ then the input, $x(t)$, is given by $e^{-3t}u(t)$ $2e^{-3t}u(t)$ $e^{-5t}u(t)$ $2e^{-5t}u(t)$
makhdoom ghaya
asked
in
Signals and Systems
Feb 12, 2017
by
makhdoom ghaya
9.3k
points
gate2014-ee-2
impulse-response
lti-system
0
votes
0
answers
17
GATE Electrical 2014 Set 1 | Question: 55
The figure shows one period of the output voltage of an inverter.$\alpha$ should be chosen such that $60^{\circ}<\alpha <90^{\circ}$. If $rms$ value of the fundamental component is $50V$, then $\alpha$ in degree is__________
makhdoom ghaya
asked
in
Signals and Systems
Feb 12, 2017
by
makhdoom ghaya
9.3k
points
gate2014-ee-1
periodic-functions
fourier-transform
numerical-answers
0
votes
0
answers
18
GATE Electrical 2014 Set 1 | Question: 33
The function shown in the figure can be represented as $u(t)-u(t-T)+\dfrac{(t-T)}{T}u(t-T)-\frac{(t-2T)}{T}u(t-2T) \\$ $u(t)+\dfrac{t}{T}u(t-T)-\dfrac{t}{T}u(t-2T) \\$ $u(t)-u(t-T)+\dfrac{(t-T)}{T}u(t)-\dfrac{(t-2T)}{T}u(t) \\$ $u(t)+\dfrac{(t-T)}{T}u(t-T)-2\dfrac{(t-2T)}{T}u(t-2T)$
makhdoom ghaya
asked
in
Signals and Systems
Feb 12, 2017
by
makhdoom ghaya
9.3k
points
gate2014-ee-1
impulse-function
unit-step-function
0
votes
0
answers
19
GATE Electrical 2014 Set 1 | Question: 35
Let $f(t)$ be continuous time signal and let $F(w)$be its Fourier Transform defined by $F(\omega )=\displaystyle{}\int_{-\infty }^{\infty }f(t)e^{-j\omega t} dt$ define $g(t)$ ... $f(t)$ only if $f(t)$ is a sinusoidal function. $g(t)$ would never be proportional to $f(t)$.
makhdoom ghaya
asked
in
Signals and Systems
Feb 12, 2017
by
makhdoom ghaya
9.3k
points
gate2014-ee-1
fourier-transform
unit-step-function
continuous time
signal
0
votes
0
answers
20
GATE Electrical 2014 Set 1 | Question: 34
Let $X(z)=\dfrac{1}{1-z^{-3}}$ be the $Z$ – transform of a causal signal $x[n]$ Then, the values of $x[2]$ and $x[3]$ are $0$ and $0$ $0$ and $1$ $1$ and $0$ $1$ and $1$
makhdoom ghaya
asked
in
Signals and Systems
Feb 12, 2017
by
makhdoom ghaya
9.3k
points
gate2014-ee-1
z-transform
sausality
0
votes
0
answers
21
GATE Electrical 2014 Set 1 | Question: 26
Let $g:[0,\infty )\rightarrow [0,\infty )$ be a function defined by $g(x)=x-[x]$, where $[x]$ represents the integer part of $x.($That is, it is the largest integer which is less than or equal to $x).$ The value of the constant term in the Fourier series expansion of $g(x)$ is _______
makhdoom ghaya
asked
in
Signals and Systems
Feb 12, 2017
by
makhdoom ghaya
9.3k
points
gate2014-ee-1
fourier
series
expansion
fourier-transform
numerical-answers
0
votes
0
answers
22
GATE Electrical 2014 Set 1 | Question: 10
For a periodic square wave, which one of the following statements is TRUE? The Fourier series coefficients do not exist. The Fourier series coefficients exist but the reconstruction converges at no point. The Fourier series ... the reconstruction converges at most points. The Fourier series coefficients exist and the reconstruction converges at every point.
makhdoom ghaya
asked
in
Signals and Systems
Feb 12, 2017
by
makhdoom ghaya
9.3k
points
gate2014-ee-1
square-wave
periodic-function
fourier
series
coefficients
0
votes
0
answers
23
GATE Electrical 2014 Set 1 | Question: 9
$x(t)$ is nonzero only for $T_x<t<{T}'x$ , and similarly, $y(t)$ is non zero only for $T_y<t<{T}'y$. Let $z(t)$ be convolution of $x(t)$ and $y(t).$ Which one of the following statements is TRUE? $z(t)$ can be nonzero over an unbounded ... $z(t)$ is zero outside of $T_x+T_y<t<{T}'_x+{T}'_y$ $z(t)$ is nonzero for $t>{T}'_x+{T}'_y$
makhdoom ghaya
asked
in
Signals and Systems
Feb 12, 2017
by
makhdoom ghaya
9.3k
points
gate2014-ee-1
convolution
interval
0
votes
0
answers
24
GATE Electrical 2014 Set 1 | Question: 4
Let $X(s)=\dfrac{3s+5}{s^2+10s+21}$ be the Laplace Transform of a signal $x(t)$. Then, $x(0^+) $is $0$ $3$ $5$ $21$
makhdoom ghaya
asked
in
Signals and Systems
Feb 12, 2017
by
makhdoom ghaya
9.3k
points
gate2014-ee-1
laplace-transform
transfer-function
0
votes
0
answers
25
GATE Electrical 2015 Set 2 | Question: 35
The $z$-Transform of a sequence $x[n]$ is given as $X(z)=2z+4-4/z+3/z^{2}$. If $y[n]$ is the first difference of $x[n]$, then $Y(z)$ is given by $2z+2-8/z+7/z^{2}-3/z^{3}$ $-2z+2-6/z+1/z^{2}-3/z^{3}$ $-2z-2+8/z-7/z^{2}+3/z^{3}$ $4z-2-8/z-1/z^{2}+3/z^{3}$
makhdoom ghaya
asked
in
Signals and Systems
Feb 12, 2017
by
makhdoom ghaya
9.3k
points
gate2015-ee-2
sequence
complex-frequency-domain-representation
0
votes
0
answers
26
GATE Electrical 2015 Set 2 | Question: 34
For linear time invariant systems, that are Bounded Input Bounded Output stable, which one of the following statements is TRUE? The impulse response will be integrable, but may not be absolutely integrable. The unit impulse response will have finite support. The unit step response will be absolutely integrable. The unit step response will be bounded
makhdoom ghaya
asked
in
Signals and Systems
Feb 12, 2017
by
makhdoom ghaya
9.3k
points
gate2015-ee-2
impulse-response
unit-step-response
0
votes
0
answers
27
GATE Electrical 2015 Set 2 | Question: 29
Consider a signal defined by $x(t)= \begin{cases} e^{j10 t} & \text{for } \mid t \mid \leq 1 \\ 0& \text{for } \mid t \mid > 1\end{cases}$ Its Fourier Transform is $\dfrac{2 \sin (\omega -10)}{\omega - 10}\\$ ... $\dfrac{2 \sin \omega}{\omega - 10} \\$ $e^{j10 \omega }\dfrac{2 \sin\omega }{\omega }$
makhdoom ghaya
asked
in
Signals and Systems
Feb 12, 2017
by
makhdoom ghaya
9.3k
points
gate2015-ee-2
fourier-analysis
causal-system
0
votes
0
answers
28
GATE Electrical 2015 Set 1 | Question: 35
Consider a discrete time signal given by $x[n]= (-0.25)^{n} u[n]+(0.5)^{n} u [-n-1]$ The region of convergence of its $Z$-transform would be The region inside the circle of radius $0.5$ and centered at origin The region ... origin The annular region between the two circles, both centered at origin and having radii $0.25$ and $0.5$ The entire $Z$ plane.
makhdoom ghaya
asked
in
Signals and Systems
Feb 12, 2017
by
makhdoom ghaya
9.3k
points
gate2015-ee-1
discrete-time-signal
convergence
0
votes
0
answers
29
GATE Electrical 2015 Set 1 | Question: 28
The signum function is given by $sgn(x)= \begin{cases} \dfrac{x}{ \mid x \mid }; x \neq 0& \\ 0;x=0& \end{cases}$ The Fourier series expansion of $sgn (\cos (t) )$ has Only sine terms with all harmonics. Only cosine terms with all harmonics. Only sine terms with even numbered harmonics. Only cosine terms with odd numbered harmonics.
makhdoom ghaya
asked
in
Signals and Systems
Feb 12, 2017
by
makhdoom ghaya
9.3k
points
gate2015-ee-1
signum-function
fourier-series-expansion
0
votes
0
answers
30
GATE Electrical 2015 Set 1 | Question: 9
A moving average function is given by $y(t) = \dfrac{1}{T} \displaystyle \int_{t-T}^{t} u(\tau ) d \tau$. If the input $u$ is a sinusoidal signal of frequency $\dfrac{1}{2T}Hz$ then in steady state, the output $y$ will lag $u$ (in degree) by __________ .
makhdoom ghaya
asked
in
Signals and Systems
Feb 12, 2017
by
makhdoom ghaya
9.3k
points
gate2015-ee-1
steady-state
sinusoidal-signal
numerical-answers
0
votes
0
answers
31
GATE Electrical 2016 Set 2 | Question: 28
Let $x_{1}(t)\leftrightarrow X_{1}(\omega )$ and $x_{2}(t)\leftrightarrow X_{2}(\omega )$ be two signals whose Fourier Transforms are as shown in the figure below. In the figure, $h(t)=e^{-2|t|}$ denotes the impulse response. For the system shown above ... can be uniquely reconstructed from its samples, is $2B_{1}$ $2(B_{1}+B_{2})$ $4(B_{1}+B_{2})$ $\infty$
makhdoom ghaya
asked
in
Signals and Systems
Jan 30, 2017
by
makhdoom ghaya
9.3k
points
gate2016-ee-2
even-functions
impulse-response
exponential-function
0
votes
0
answers
32
GATE Electrical 2016 Set 2 | Question: 18
Consider a linear time-invariant system with transfer function $H(s)=\frac{1}{(s+1)}$ If the input is $\cos(t)$ and the steady state output is $A \cos(t+\alpha)$ then the value of $A$ is _________.
makhdoom ghaya
asked
in
Signals and Systems
Jan 30, 2017
by
makhdoom ghaya
9.3k
points
gate2016-ee-2
linear
translation-invariant
convolution
impulse-response
numerical-answers
0
votes
0
answers
33
GATE Electrical 2016 Set 2 | Question: 5
Suppose the maximum frequency in a band-limited signal $x(t)$ is $5 kHz$. Then, the maximum frequency in $x(t)\cos(2000\pi t)$, in $kHz$, is ________.
makhdoom ghaya
asked
in
Signals and Systems
Jan 30, 2017
by
makhdoom ghaya
9.3k
points
gate2016-ee-2
high-pass-filter
low-pass-filter
continuous-time-signal
numerical-answers
0
votes
0
answers
34
GATE Electrical 2016 Set 1 | Question: 35
The output of a continuous-time, linear time-invariant system is denoted by $T\left\{x(t)\right\}$ where $x(t)$ is the input signal. A signal $z(t)$ is called eigen-signal of the system $T$, when $T\left\{z(t)\right\}=\gamma z(t)$ ... $\cos(t)$ is not $\cos(t)$ and $\sin(t)$are both eigen-signals with identical eigenvalues
makhdoom ghaya
asked
in
Signals and Systems
Jan 30, 2017
by
makhdoom ghaya
9.3k
points
gate2016-ee-1
impulse-response
step-response
convolution
0
votes
0
answers
35
GATE Electrical 2016 Set 1 | Question: 34
Suppose $x_{1}(t)$ and $x_{2}(t)$ have the Fourier transforms as shown below. Which one of the following statements is TRUE? $x_{1}(t)$ and $x_{2}(t)$ are complex and $x_{1}(t) x_{2}(t)$is also complex with nonzero imaginary part $x_{1}(t)$ and $x_{2}(t)$ ... $x_{1}(t)$ and $x_{2}(t)$ are imaginary but $x_{1}(t) x_{2}(t)$ is real
makhdoom ghaya
asked
in
Signals and Systems
Jan 30, 2017
by
makhdoom ghaya
9.3k
points
gate2016-ee-1
mirror
signal
0
votes
0
answers
36
GATE Electrical 2016 Set 1 | Question: 27
Let $S=\sum_{n=0}^{\infty} n\alpha^{n}$ where $\mid \alpha \mid < 1$. The value of $\alpha$ in the range $0 < \alpha < 1$, such that $S=2 \alpha$ is _________.
makhdoom ghaya
asked
in
Signals and Systems
Jan 30, 2017
by
makhdoom ghaya
9.3k
points
gate2016-ee-1
fourier-transform
sampling-theorem
z-transform
numerical-answers
0
votes
0
answers
37
GATE Electrical 2016 Set 1 | Question: 8
Consider a continuous-time system with input $x(t)$ and output $y(t)$ given by $y(t)=x(t) \cos (t)$. This system is Linear and time-invariant Non-linear and time-invariant Linear and time-varying Non-linear and time-varying
makhdoom ghaya
asked
in
Signals and Systems
Jan 30, 2017
by
makhdoom ghaya
9.3k
points
gate2016-ee-1
sampling-theorem
scaling-properties
causal-system
0
votes
0
answers
38
GATE Electrical 2016 Set 1 | Question: 3
The Laplace Transform of $f(t)=e^{2t} \sin (5t)(ut)$ is $\dfrac{5}{s^{2}-4s+29} \\ $ $\dfrac{5}{s^{2}+5} \\ $ $\dfrac{s-2}{s^{2}-4s+29} \\$ $\dfrac{5}{s +5}$
makhdoom ghaya
asked
in
Signals and Systems
Jan 30, 2017
by
makhdoom ghaya
9.3k
points
gate2016-ee-1
unit-step-function
fourier-transform
shifting-theorems
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