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Recent activity in Signals and Systems

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Gate 2000 signals and systems
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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 _________.
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 _________.
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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} \\ $ $\dfrac{s-2}{s^{2}-4s+29} \\$ $\dfrac{5}{s +5}$
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}$
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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
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
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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 $0$ $1$ $2$ $5$
An input signal $x(t)=2+5 \sin(100\pi t)$ is sampled with a sampling frequency of $400$ $Hz$ and applied to the system whose transfer function is represented by $$\dfrac...
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GATE Electrical 2013 | Question: 4
The impulse response a the system is $h(t)=t\:u(t).$ For an input $u(t-1)$, the output is $\dfrac{t^2}{2}u(t) \\$ $\dfrac{t(t-1)}{2}u(t-1) \\$ $\dfrac{(t-1)^2}{2}u(t-1) \\$ $\dfrac{t^2-1}{2}u(t-1)$
The impulse response a the system is $h(t)=t\:u(t).$ For an input $u(t-1)$, the output is$\dfrac{t^2}{2}u(t) \\$$\dfrac{t(t-1)}{2}u(t-1) \\$$\dfrac{(t-1)^2}{2}u(t-1) \\$$...
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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 _________.
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 v...
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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 ________.
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 ________.
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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 _________.
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 _________.
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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 $0$ $3$ $5$ $21$
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$$21$
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GATE Electrical 2014 Set 1 | Question: 34
Let $X(z)=\dfrac{1}{1-z^{-3}}$ be the $Z$ – transform of a causal signal $x[n]$ Then, the values of $x[2]$ and $x[3]$ are $0$ and $0$ $0$ and $1$ $1$ and $0$ $1$ and $1$
Let $X(z)=\dfrac{1}{1-z^{-3}}$ be the $Z$ – transform of a causal signal $x[n]$ Then, the values of $x $ and $x[3]$ are$0$ and $0$$0$ and $1$$1$ and $0$$1$ and $1$
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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 $100$ $300$ $500$ $1500$
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$$1500$
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GATE Electrical 2013 | Question: 41
The impulse response of a continuous time system is given by $h(t)=\delta (t-1)+\delta (t-3).$ The value of the step response at $t=2$ is $0$ $1$ $2$ $3$
The impulse response of a continuous time system is given by $h(t)=\delta (t-1)+\delta (t-3).$ The value of the step response at $t=2$ is$0$$1$$2$$3$
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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.
For a peridic square wave ,which one of the following statements is TRUE?1). The fourieF series coefficients do not exist2).The Fourier series coefficients exist but the ...
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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 $e^{-3t}u(t)$ $2e^{-3t}u(t)$ $e^{-5t}u(t)$ $2e^{-5t}u(t)$
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^{...
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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
Consider a continuous-time system with input $x(t)$ and output $y(t)$ given by $y(t)=x(t) \cos (t)$.This system isLinear and time-invariantNon-linear and time-invariantLi...
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