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Previous GATE
0
votes
0
answers
1
GATE2014-1-10
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 coefficients exist and the reconstruction converges at most points. The Fourier series coefficients exist and the reconstruction converges at every point.
asked
Feb 12, 2017
in
Signals and Systems
by
makhdoom ghaya
(
9.3k
points)
gate2014-ee-1
square-wave
periodic-function
fourier
series
coefficients
+2
votes
0
answers
2
GATE2014-3-21
A state diagram of a logic gate which exhibits a delay in the output is shown in the figure, where $X$ is the don’t care condition, and $Q$ is the output representing the state. The logic gate represented by the state diagram is $XOR$ $OR$ $AND$ $NAND$
asked
Feb 12, 2017
in
Signals and Systems
by
makhdoom ghaya
(
9.3k
points)
gate2014-ee-3
delay-function
latches
0
votes
0
answers
3
GATE2015-2-34
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
asked
Feb 12, 2017
in
Signals and Systems
by
makhdoom ghaya
(
9.3k
points)
gate2015-ee-2
impulse-response
unit-step-response
+1
vote
0
answers
4
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.
asked
Jul 8, 2018
in
Signals and Systems
by
Shaurya khare
(
130
points)
0
votes
0
answers
5
GATE2014-3-34
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 $10$ $Hz$ $60$ $Hz$ $30$ $Hz$ $90$ $Hz$
asked
Feb 12, 2017
in
Signals and Systems
by
makhdoom ghaya
(
9.3k
points)
gate2014-ee-3
impulse-train
low-pass-filter
0
votes
0
answers
6
GATE2015-1-28
The signum function is given by $ sgn(x)= \begin{cases} \frac{x}{|x|};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.
asked
Feb 12, 2017
in
Signals and Systems
by
makhdoom ghaya
(
9.3k
points)
gate2015-ee-1
signum-function
fourier-series-expansion
0
votes
0
answers
7
GATE2014-1-26
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 _______
asked
Feb 12, 2017
in
Signals and Systems
by
makhdoom ghaya
(
9.3k
points)
gate2014-ee-1
fourier
series
expansion
fourier-transform
numerical-answers
0
votes
0
answers
8
GATE2015-2-4
The Laplace transform of $f(t)= 2\sqrt{t/\pi}$ is $s^{-3/2}$. The Laplace transform of $g(t)=\sqrt{1/\pi t}$ is. $3s^{-5/2} /2$ $s^{-1/2}$ $s^{1/2}$ $s^{3/2}$
asked
Feb 12, 2017
in
Signals and Systems
by
makhdoom ghaya
(
9.3k
points)
gate2015-ee-2
laplace-transform
fourier-series
0
votes
0
answers
9
GATE2014-1-55
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__________
asked
Feb 12, 2017
in
Signals and Systems
by
makhdoom ghaya
(
9.3k
points)
gate2014-ee-1
periodic-functions
fourier-transform
numerical-answers
0
votes
0
answers
10
GATE2014-1-33
The function shown in the figure can be represented as $u(t)-u(t-T)+\frac{(t-T)}{T}u(t-T)-\frac{(t-2T)}{T}u(t-2T)$ $u(t)+\frac{t}{T}u(t-T)-\frac{t}{T}u(t-2T)$ $u(t)-u(t-T)+\frac{(t-T)}{T}u(t)-\frac{(t-2T)}{T}u(t)$ $u(t)+\frac{(t-T)}{T}u(t-T)-2\frac{(t-2T)}{T}u(t-2T)$
asked
Feb 12, 2017
in
Signals and Systems
by
makhdoom ghaya
(
9.3k
points)
gate2014-ee-1
impulse-function
unit-step-function
0
votes
0
answers
11
GATE2013-41
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 $0$ $1$ $2$ $3$
asked
Feb 12, 2017
in
Signals and Systems
by
piyag476
(
1.5k
points)
gate2013-ee
impulse-response
step-response
0
votes
0
answers
12
GATE2014-3-10
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 _________.
asked
Feb 12, 2017
in
Signals and Systems
by
makhdoom ghaya
(
9.3k
points)
gate2014-ee-3
sampling-frequency
stability
numerical-answers
0
votes
0
answers
13
GATE2016-1-27
Let $S=\sum_{n=0}^{\infty} n\alpha^{n}$ where $|\alpha| < 1$. The value of $\alpha$ in the range $0 < \alpha < 1$, such that $S=2 \alpha$ is _________.
asked
Jan 30, 2017
in
Signals and Systems
by
makhdoom ghaya
(
9.3k
points)
gate2016-ee-1
fourier-transform
sampling-theorem
z-transform
numerical-answers
0
votes
0
answers
14
GATE2014-3-20
The two signals $S1$ and $S2$, shown in figure, are applied to $Y$ and $X$ deflection plates of an oscilloscope.
asked
Feb 12, 2017
in
Signals and Systems
by
makhdoom ghaya
(
9.3k
points)
gate2014-ee-3
oscilloscope
even-functions
0
votes
0
answers
15
GATE2014-1-4
Let $X(s)=\dfrac{3s+5}{s^2+10s+21}$ be the Laplace Transform of a signal $x(t)$. Then, $x(0^+) $is $0$ $3$ $5$ $21$
asked
Feb 12, 2017
in
Signals and Systems
by
makhdoom ghaya
(
9.3k
points)
gate2014-ee-1
laplace-transform
transfer-function
0
votes
0
answers
16
GATE2015-1-9
A moving average function is given by $y(t) = \frac{1}{T}\int_{t-T}^{t} u(\tau ) d \tau$. If the input $u$ is a sinusoidal signal of frequency $\frac{1}{2T}Hz$ then in steady state, the output $y$ will lag $u$ (in degree) by ______ .
asked
Feb 12, 2017
in
Signals and Systems
by
makhdoom ghaya
(
9.3k
points)
gate2015-ee-1
steady-state
sinusoidal-signal
numerical-answers
0
votes
0
answers
17
GATE2016-2-5
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 ________.
asked
Jan 30, 2017
in
Signals and Systems
by
makhdoom ghaya
(
9.3k
points)
gate2016-ee-2
high-pass-filter
low-pass-filter
continuous-time-signal
numerical-answers
0
votes
0
answers
18
GATE2014-2-34
An input signal $x(t)=2+5sin(100\pi t)$ is sampled with a sampling frequency of $400$ $Hz$ and applied to the system whose transfer function is represented by $\frac{Y(z)}{X(z)}=\frac{1}{N}(\frac{1-Z^{-N}}{1-Z^{-1}})$ where, $N$ represents the number of samples per cycle. The output $y(n)$ of the system under steady state is $0$ $1$ $2$ $5$
asked
Feb 12, 2017
in
Signals and Systems
by
makhdoom ghaya
(
9.3k
points)
gate2014-ee-2
transfer-function
sampling-per-cycle
0
votes
0
answers
19
GATE2016-1-35
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 $T\left\{z(t)\right\}=\gamma z(t)$ where $\gamma$ is ... eigenvalues $\sin(t)$ is an eigen-signal but $\cos(t)$ is not $\cos(t)$ and $\sin(t)$are both eigen-signals with identical eigenvalues
asked
Jan 30, 2017
in
Signals and Systems
by
makhdoom ghaya
(
9.3k
points)
gate2016-ee-1
impulse-response
step-response
convolution
0
votes
0
answers
20
GATE2014-3-5
A function f(t) is shown in the figure. The Fourier transform F(ω) of f(t) is real and even function of $ω$. real and odd function of $ω$. imaginary and odd function of $ω$ imaginary and even function of $ω$
asked
Feb 12, 2017
in
Signals and Systems
by
makhdoom ghaya
(
9.3k
points)
gate2014-ee-3
even-function
odd-function
0
votes
0
answers
21
GATE2014-1-34
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 $1$
asked
Feb 12, 2017
in
Signals and Systems
by
makhdoom ghaya
(
9.3k
points)
gate2014-ee-1
z-transform
sausality
0
votes
0
answers
22
GATE2014-1-35
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 $g(t)$ by $g(t)=\displaystyle{}\int_{-\infty }^{\infty }F(u)e^{-jut} du$ What is the ... . $g(t)$ would be proportional to $f(t)$ only if $f(t)$ is a sinusoidal function. $g(t)$ would never be proportional to $f(t)$.
asked
Feb 12, 2017
in
Signals and Systems
by
makhdoom ghaya
(
9.3k
points)
gate2014-ee-1
fourier-transform
unit-step-function
continuous time
signal
0
votes
0
answers
23
GATE2014-1-9
$x(t)$ 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 interval. $z(t)$ is ... $z(t)$ is zero outside of $T_x+T_y<t<{T}'_x+{T}'_y$ $z(t)$ is nonzero for $t>{T}'_x+{T}'_y$
asked
Feb 12, 2017
in
Signals and Systems
by
makhdoom ghaya
(
9.3k
points)
gate2014-ee-1
convolution
interval
0
votes
0
answers
24
GATE2015-2-35
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 $2z+2-8/z+7/z^{2}-3/z^{3}$ $-2z+2-6/z+1/z^{2}-3/z^{3}$ $-2z-2+8/z-7/z^{2}+3/z^{3}$ $4z-2-8/z-1/z^{2}+3/z^{3}$
asked
Feb 12, 2017
in
Signals and Systems
by
makhdoom ghaya
(
9.3k
points)
gate2015-ee-2
sequence
complex-frequency-domain-representation
0
votes
0
answers
25
GATE2015-1-35
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 outside the circle ... centered at origin The annular region between the two circles, both centered at origin and having radii $0.25$ and $0.5$ The entire $Z$ plane.
asked
Feb 12, 2017
in
Signals and Systems
by
makhdoom ghaya
(
9.3k
points)
gate2015-ee-1
discrete-time-signal
convergence
0
votes
0
answers
26
GATE2016-2-18
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 _________.
asked
Jan 30, 2017
in
Signals and Systems
by
makhdoom ghaya
(
9.3k
points)
gate2016-ee-2
linear
translation-invariant
convolution
impulse-response
numerical-answers
0
votes
0
answers
27
GATE2013-4
The impulse response a the system is $h(t)=t\:u(t).$ For an input $u(t-1)$, the output is $\frac{t^2}{2}u(t)$ $\frac{t(t-1)}{2}u(t-1)$ $\frac{(t-1)^2}{2}u(t-1)$ $\frac{t^2-1}{2}u(t-1)$
asked
Feb 12, 2017
in
Signals and Systems
by
piyag476
(
1.5k
points)
gate2013-ee
fourier-transform
sampling-theorem
0
votes
0
answers
28
GATE2016-1-3
The Laplace Transform of $f(t)=e^{2t} \sin (5t)(ut)$ is $\frac{5}{s^{2}-4s+29}$ $\frac{5}{s^{2}+5}$ $\frac{s-2}{s^{2}-4s+29}$ $\frac{5}{s +5}$
asked
Jan 30, 2017
in
Signals and Systems
by
makhdoom ghaya
(
9.3k
points)
gate2016-ee-1
unit-step-function
fourier-transform
shifting-theorems
0
votes
0
answers
29
GATE2013-6
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 $h_1(t)$
asked
Feb 12, 2017
in
Signals and Systems
by
piyag476
(
1.5k
points)
gate2013-ee
convolution
multiplication
addition
0
votes
0
answers
30
GATE2014-3-33
A continuous-time $LTI$ system with system function $H(w)$ has the following pole-zero plot. For this system, which of the alternatives is $TRUE$? $|H(0)|> |H(w)|;|w|> 0$ |H(w)| has multiple maxima, at $w_1$ and $w_2$ $|H(0)|< |H(w)|;|w|> 0$ |H(w)|=constant; $-\infty < w< \infty$
asked
Feb 12, 2017
in
Signals and Systems
by
makhdoom ghaya
(
9.3k
points)
gate2014-ee-3
pole-zero-plot
linear-time-invariant-system
0
votes
0
answers
31
GATE2014-3-9
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 $y(t)$= $x(2t)*x(t/2)$ is $\frac{4}{\omega ^2} \sin(\frac{\omega }{2})sin(2\omega )$ $\frac{4}{\omega ^2} \sin(\frac{\omega }{2})$ $\frac{4}{\omega ^2} \sin(2\omega )$ $\frac{4}{\omega ^2} \sin^2\omega $
asked
Feb 12, 2017
in
Signals and Systems
by
makhdoom ghaya
(
9.3k
points)
gate2014-ee-3
fourier-transform
convolution
0
votes
0
answers
32
GATE2015-2-29
Consider a signal defined by $x(t)= = \begin{cases} e^{j10 t} & \text{for} |t|\leq 1 \\ 0& \text{for } |t| > 1 \end{cases}$ Its Fourier Transform is $\frac{2 \sin (\omega -10)}{\omega - 10}$ $2e^{j10}\frac{ \sin (\omega -10)}{\omega - 10}$ $\frac{2 \sin \omega}{\omega - 10}$ $e^{j10 \omega }\frac{2 \sin\omega }{\omega }$
asked
Feb 12, 2017
in
Signals and Systems
by
makhdoom ghaya
(
9.3k
points)
gate2015-ee-2
fourier-analysis
causal-system
0
votes
0
answers
33
GATE2016-2-10
Let $f(x)$ be a real, periodic function satisfying $f(-x)=-f(x)$. The general form of its Fourier series representation would be $f(x)=a_{0}+\sum_{k=1}^{\infty}a_{k}\cos(kx)$ $f(x)=\sum_{k=1}^{\infty}b_{k}\sin(kx)$ $f(x)=a_{0}+\sum_{k=1}^{\infty}a_{2k}\cos(kx)$ $f(x)=\sum_{k=0}^{\infty}a_{2k+1}\sin(2k+1)x$
asked
Jan 30, 2017
in
Signals and Systems
by
makhdoom ghaya
(
9.3k
points)
gate2016-ee-2
fourier-series-co-efficient
harmonics
dirichlet-conditions
0
votes
0
answers
34
GATE2013-17
For a periodic signal $v(t) = 30 \sin100t +10 \cos 300t + 6 \sin (500t+\pi /4)$, the fundamental frequency in $rad/s$ is $100$ $300$ $500$ $1500$
asked
Feb 12, 2017
in
Signals and Systems
by
piyag476
(
1.5k
points)
gate2013-ee
periodicity
sinusoidal
0
votes
0
answers
35
GATE2014-3-35
A differentiable non constant even function $x(t)$ has a derivative $y(t)$, and their respective Fourier Transforms are $X(w)$ and $Y(w)$ . Which of the following statements is TRUE? $X(w)$ and $Y(w)$ are both real. $X(w)$ is real and $Y(w)$ is imaginary. $X(w)$ and $Y(w)$ are both imaginary. $X(w)$ is imaginary and $Y(w)$ is real.
asked
Feb 12, 2017
in
Signals and Systems
by
makhdoom ghaya
(
9.3k
points)
gate2014-ee-3
even-functions
fourier-transform
0
votes
0
answers
36
GATE2014-2-10
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 $e^{-3t}u(t)$ $2e^{-3t}u(t)$ $e^{-5t}u(t)$ $2e^{-5t}u(t)$
asked
Feb 12, 2017
in
Signals and Systems
by
makhdoom ghaya
(
9.3k
points)
gate2014-ee-2
impulse-response
lti-system
0
votes
0
answers
37
GATE2016-2-28
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, the minimum sampling ... $2B_{1}$ $2(B_{1}+B_{2})$ $4(B_{1}+B_{2})$ $\infty$
asked
Jan 30, 2017
in
Signals and Systems
by
makhdoom ghaya
(
9.3k
points)
gate2016-ee-2
even-functions
impulse-response
exponential-function
0
votes
0
answers
38
GATE2016-1-8
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
asked
Jan 30, 2017
in
Signals and Systems
by
makhdoom ghaya
(
9.3k
points)
gate2016-ee-1
sampling-theorem
scaling-properties
causal-system
0
votes
0
answers
39
GATE2014-3-32
A series $RLC$ circuit is observed at two frequencies. At $ω_1$=$1$ $krad/s$, 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 $w_2$=$2$ $krad/s$, the source voltage $V_2$=$100\angle 0^{\circ}$ $V$ results in a current ... $C=25 \mu F$ $R=50\Omega$ ; $L=50 mH$ ,$C=5 \mu F$ $R=50\Omega$ ; $L=5 mH$ ,$C=50 \mu F$
asked
Feb 12, 2017
in
Signals and Systems
by
makhdoom ghaya
(
9.3k
points)
gate2014-ee-3
rc-filter
rl-filter
0
votes
0
answers
40
GATE2016-1-34
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 $x_{2}(t)$ ... but $x_{1}(t) x_{2}(t)$ is real $x_{1}(t)$ and $x_{2}(t)$ are imaginary but $x_{1}(t) x_{2}(t)$ is real
asked
Jan 30, 2017
in
Signals and Systems
by
makhdoom ghaya
(
9.3k
points)
gate2016-ee-1
mirror
signal
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