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Questions without answers in Signals and Systems
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1
Gate EE2014
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
2
GATE201341
The impulse response of a continuous time system is given by $h(t)=\delta (t1)+\delta (t3).$ 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)
gate2013ee
impulseresponse
stepresponse
0
votes
0
answers
3
GATE201317
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)
gate2013ee
periodicity
sinusoidal
0
votes
0
answers
4
GATE20134
The impulse response a the system is $h(t)=t\:u(t).$ For an input $u(t1)$, the output is $\frac{t^2}{2}u(t)$ $\frac{t(t1)}{2}u(t1)$ $\frac{(t1)^2}{2}u(t1)$ $\frac{t^21}{2}u(t1)$
asked
Feb 12, 2017
in
Signals and Systems
by
piyag476
(
1.5k
points)
gate2013ee
fouriertransform
samplingtheorem
0
votes
0
answers
5
GATE20136
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)
gate2013ee
convolution
multiplication
addition
0
votes
0
answers
6
GATE2014334
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)
gate2014ee3
impulsetrain
lowpassfilter
0
votes
0
answers
7
GATE2014335
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)
gate2014ee3
evenfunctions
fouriertransform
0
votes
0
answers
8
GATE2014332
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)
gate2014ee3
rcfilter
rlfilter
0
votes
0
answers
9
GATE2014333
A continuoustime $LTI$ system with system function $H(w)$ has the following polezero 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)
gate2014ee3
polezeroplot
lineartimeinvariantsystem
0
votes
0
answers
10
GATE2014320
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)
gate2014ee3
oscilloscope
evenfunctions
0
votes
0
answers
11
GATE201435
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)
gate2014ee3
evenfunction
oddfunction
0
votes
0
answers
12
GATE201439
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)
gate2014ee3
fouriertransform
convolution
0
votes
0
answers
13
GATE2014310
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)
gate2014ee3
samplingfrequency
stability
numericalanswers
0
votes
0
answers
14
GATE2014234
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 $\frac{Y(z)}{X(z)}=\frac{1}{N}(\frac{1Z^{N}}{1Z^{1}})$ 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)
gate2014ee2
transferfunction
samplingpercycle
0
votes
0
answers
15
GATE2014210
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)
gate2014ee2
impulseresponse
ltisystem
0
votes
0
answers
16
GATE2014155
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)
gate2014ee1
periodicfunctions
fouriertransform
numericalanswers
0
votes
0
answers
17
GATE2014133
The function shown in the figure can be represented as $u(t)u(tT)+\frac{(tT)}{T}u(tT)\frac{(t2T)}{T}u(t2T)$ $u(t)+\frac{t}{T}u(tT)\frac{t}{T}u(t2T)$ $u(t)u(tT)+\frac{(tT)}{T}u(t)\frac{(t2T)}{T}u(t)$ $u(t)+\frac{(tT)}{T}u(tT)2\frac{(t2T)}{T}u(t2T)$
asked
Feb 12, 2017
in
Signals and Systems
by
makhdoom ghaya
(
9.3k
points)
gate2014ee1
impulsefunction
unitstepfunction
0
votes
0
answers
18
GATE2014134
Let $X(z)=\dfrac{1}{1z^{3}}$ 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)
gate2014ee1
ztransform
sausality
0
votes
0
answers
19
GATE2014135
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)
gate2014ee1
fouriertransform
unitstepfunction
continuous time
signal
0
votes
0
answers
20
GATE2014126
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)
gate2014ee1
fourier
series
expansion
fouriertransform
numericalanswers
0
votes
0
answers
21
GATE201419
$x(t)$ 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)
gate2014ee1
convolution
interval
0
votes
0
answers
22
GATE2014110
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)
gate2014ee1
squarewave
periodicfunction
fourier
series
coefficients
0
votes
0
answers
23
GATE201414
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)
gate2014ee1
laplacetransform
transferfunction
0
votes
0
answers
24
GATE2015229
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)
gate2015ee2
fourieranalysis
causalsystem
0
votes
0
answers
25
GATE2015234
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)
gate2015ee2
impulseresponse
unitstepresponse
0
votes
0
answers
26
GATE2015235
The $z$Transform of a sequence $x[n]$ is given as $X(z)=2z+44/z+3/z^{2}$. If $y[n]$ is the first difference of $x[n]$, then $Y(z)$ is given by $2z+28/z+7/z^{2}3/z^{3}$ $2z+26/z+1/z^{2}3/z^{3}$ $2z2+8/z7/z^{2}+3/z^{3}$ $4z28/z1/z^{2}+3/z^{3}$
asked
Feb 12, 2017
in
Signals and Systems
by
makhdoom ghaya
(
9.3k
points)
gate2015ee2
sequence
complexfrequencydomainrepresentation
0
votes
0
answers
27
GATE201524
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)
gate2015ee2
laplacetransform
fourierseries
0
votes
0
answers
28
GATE2015135
Consider a discrete time signal given by $x[n]= (0.25)^{n} u[n]+(0.5)^{n} u [n1]$ 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)
gate2015ee1
discretetimesignal
convergence
0
votes
0
answers
29
GATE2015128
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)
gate2015ee1
signumfunction
fourierseriesexpansion
0
votes
0
answers
30
GATE201519
A moving average function is given by $y(t) = \frac{1}{T}\int_{tT}^{t} u(\tau ) d \tau$. 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)
gate2015ee1
steadystate
sinusoidalsignal
numericalanswers
0
votes
0
answers
31
GATE2016228
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, $h(t)=e^{2t}$ 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)
gate2016ee2
evenfunctions
impulseresponse
exponentialfunction
0
votes
0
answers
32
GATE2016218
Consider a linear timeinvariant 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)
gate2016ee2
linear
translationinvariant
convolution
impulseresponse
numericalanswers
0
votes
0
answers
33
GATE2016210
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)
gate2016ee2
fourierseriescoefficient
harmonics
dirichletconditions
0
votes
0
answers
34
GATE201625
Suppose the maximum frequency in a bandlimited 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)
gate2016ee2
highpassfilter
lowpassfilter
continuoustimesignal
numericalanswers
0
votes
0
answers
35
GATE2016134
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)
gate2016ee1
mirror
signal
0
votes
0
answers
36
GATE2016135
The output of a continuoustime, linear timeinvariant system is denoted by $T\left\{x(t)\right\}$ where $x(t)$ is the input signal. A signal $z(t)$ is called eigensignal of the system $T$, when $T\left\{z(t)\right\}=\gamma z(t)$ where $\gamma$ is ... eigenvalues $\sin(t)$ is an eigensignal but $\cos(t)$ is not $\cos(t)$ and $\sin(t)$are both eigensignals with identical eigenvalues
asked
Jan 30, 2017
in
Signals and Systems
by
makhdoom ghaya
(
9.3k
points)
gate2016ee1
impulseresponse
stepresponse
convolution
0
votes
0
answers
37
GATE2016127
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)
gate2016ee1
fouriertransform
samplingtheorem
ztransform
numericalanswers
0
votes
0
answers
38
GATE201618
Consider a continuoustime system with input $x(t)$ and output $y(t)$ given by $y(t)=x(t) \cos (t)$. This system is Linear and timeinvariant Nonlinear and timeinvariant Linear and timevarying Nonlinear and timevarying
asked
Jan 30, 2017
in
Signals and Systems
by
makhdoom ghaya
(
9.3k
points)
gate2016ee1
samplingtheorem
scalingproperties
causalsystem
0
votes
0
answers
39
GATE201613
The Laplace Transform of $f(t)=e^{2t} \sin (5t)(ut)$ is $\frac{5}{s^{2}4s+29} \\ $ $\frac{5}{s^{2}+5} \\ $ $\frac{s2}{s^{2}4s+29} \\$ $\frac{5}{s +5}$
asked
Jan 30, 2017
in
Signals and Systems
by
makhdoom ghaya
(
9.3k
points)
gate2016ee1
unitstepfunction
fouriertransform
shiftingtheorems
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