Most viewed questions in Signals and Systems

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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)

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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)

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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)

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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)

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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)

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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)

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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)

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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)

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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)

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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)

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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)

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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)

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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)

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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)

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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)

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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)

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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)

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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)

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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)

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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)

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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)

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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)

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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)

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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)

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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)

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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)

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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)

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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)

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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)

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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)

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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)

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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)

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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)

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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)

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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)

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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)

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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)

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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)

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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)

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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)