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42
GATE ECE 2019 | Question: 33
Let the state-space representation of an LTI system be $x(t)=A x(t)+B u(t), y(t)=Cx(t)+du(t)$ where $A,B,C$ are matrices, $d$ is a scalar, $u(t)$ is the input to the system, and $y(t)$ ...
Let the state-space representation of an LTI system be $x(t)=A x(t)+B u(t), y(t)=Cx(t)+du(t)$ where $A,B,C$ are matrices, $d$ is a scalar, $u(t)$ is the input to the syst...
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44
GATE ECE 2020 | Question: 14
Which one of the following pole-zero plots corresponds to the transfer function of an $\text{LTI}$ system characterized by the input-output difference equation given below? $y\left [ n \right ]=\sum ^{3}_{k=0}\left ( -1 \right )^{k}x\left [ n-k \right ]$
Which one of the following pole-zero plots corresponds to the transfer function of an $\text{LTI}$ system characterized by the input-output difference equation given belo...
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45
GATE ECE 2013 | Question: 54
The state diagram of a system is shown below. A system is described by the state-variable equations $\dot{X}= AX+Bu;\:\: y = CX+Du$ ...
The state diagram of a system is shown below. A system is described by the state-variable equations$$\dot{X}= AX+Bu;\:\: y = CX+Du$$The state-variable equations of the sy...
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48
GATE ECE 2015 Set 2 | Question: 21
A unity negative feedback system has an open-loop transfer function $G(S) = \dfrac{K}{s(s+10)}$. The gain $K$ for the system to have a damping ratio of $0.25$ is ________.
A unity negative feedback system has an open-loop transfer function $G(S) = \dfrac{K}{s(s+10)}$. The gain $K$ for the system to have a damping ratio of $0.25$ is ________...
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49
GATE ECE 2017 Set 1 | Question: 34
The figure shows an RLC circuit excited by the sinusoidal voltage $100 \cos(3t)$ Volts, where $t$ is in seconds. The ratio $\frac{\text{amplitude of }V_{2}}{\text{amplitude of }V{1}}$ is______.
The figure shows an RLC circuit excited by the sinusoidal voltage $100 \cos(3t)$ Volts, where $t$ is in seconds. The ratio $\frac{\text{amplitude of }V_{2}}{\text{amplitu...
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52
GATE ECE 2014 Set 3 | Question: 20
Consider the following block diagram in the figure. The transfer function $\frac{C(s)}{R(s)}$ is $\frac{G_{1}G_{2}}{1+G_{1}G_{2}}$ $G_{1}G_{2}+G_{1}+1$ $G_{1}G_{2}+G_{2}+1$ $\frac{G_{1}}{1+G_{1}G_{2}}$
Consider the following block diagram in the figure. The transfer function $\frac{C(s)}{R(s)}$ is$\frac{G_{1}G_{2}}{1+G_{1}G_{2}}$$G_{1}G_{2}+G_{1}+1$$G_{1...
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53
GATE ECE 2017 Set 2 | Question: 7
An LTI system with unit sample response $h[n]=5\delta [n]-7\delta [n-1]+7\delta [n-3]-5\delta [n-4]$ is a low-pass filter high-pass filter band-pass filter band-stop filter
An LTI system with unit sample response $h[n]=5\delta [n]-7\delta [n-1]+7\delta [n-3]-5\delta [n-4]$ is a low-pass filter high-pass filter band-pass filter band-s...
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54
GATE ECE 2014 Set 3 | Question: 46
The steady state error of the system shown in the figure for a unit step input is _________.
The steady state error of the system shown in the figure for a unit step input is _________.
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55
GATE ECE 2015 Set 2 | Question: 23
The signal $\cos \left(10\pi t + \dfrac{\pi}{4}\right)$ is ideally sampled at a sampling frequency of $15 Hz.$ ... $\dfrac{15}{2}\left(\dfrac{\sin (\pi t)}{\pi t}\right)\cos\left(40\pi t - \dfrac{\pi}{2}\right)$
The signal $\cos \left(10\pi t + \dfrac{\pi}{4}\right)$ is ideally sampled at a sampling frequency of $15 Hz.$ The sampled signal is passed through a filter with impulse ...
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56
GATE ECE 2017 Set 1 | Question: 33
Let $h[n]$ ... radians. Given that $H(\omega_{0})=0$ and $0< \omega_{0} < \pi$, the value of $\omega_{0}$ (in radians) is equal to__________.
Let $h[n]$ be the impulse response of a discrete-time linear time invariant(LTI) filter. The impulse response is given by $$h[0]=\frac{1}{3}; \, h =\frac{1}{3}; \, h =\fr...
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61
GATE ECE 2019 | Question: 21
Consider the signal $f(t)=1+2 \cos(\pi t)+3 \sin \left(\dfrac{2\pi}{3}t\right)+4 \cos \left(\dfrac{\pi}{2}t+\dfrac{\pi}{4}\right)$, where $t$ is in seconds. Its fundamental time period, in seconds, is __________.
Consider the signal $f(t)=1+2 \cos(\pi t)+3 \sin \left(\dfrac{2\pi}{3}t\right)+4 \cos \left(\dfrac{\pi}{2}t+\dfrac{\pi}{4}\right)$, where $t$ is in seconds. Its fundament...
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63
GATE ECE 2016 Set 2 | Question: 10
The energy of the signal $x(t)= \frac{\sin(4\pi t)}{4\pi t}$ is ________
The energy of the signal $x(t)= \frac{\sin(4\pi t)}{4\pi t}$ is ________
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69
GATE ECE 2020 | Question: 30
For the given circuit, which one of the following is correct state equation? ...
For the given circuit, which one of the following is correct state equation? $\dfrac{\mathrm{d} }{\mathrm{d} t}\begin{bmatrix} v\\ i \end{b...
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72
GATE ECE 2017 Set 2 | Question: 5
In the circuit shown, V is a sinusoidal voltage source. The current $I$ is in phase with voltage V. The ratio$\frac{\text{amplitude of voltage across the capacitor}}{\text{amplitude of voltage across the resistor}}$ is ___________.
In the circuit shown, V is a sinusoidal voltage source. The current $I$ is in phase with voltage V. The ratio$\frac{\text{amplitude of voltage across the capacitor}}{\tex...
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73
GATE ECE 2015 Set 1 | Question: 6
In the circuit shown, at resonance, the amplitude of the sinusoidal voltage (in Volts) across the capacitor is ____________.
In the circuit shown, at resonance, the amplitude of the sinusoidal voltage (in Volts) across the capacitor is ____________.
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75
GATE ECE 2015 Set 1 | Question: 32
In the given circuit, the maximum power (in Watts) that can be transferred to the load $R_L$ is ________.
In the given circuit, the maximum power (in Watts) that can be transferred to the load $R_L$ is ________.
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76
GATE ECE 2016 Set 1 | Question: 46
The open-loop transfer function of a unity feedback control system is given by $G(s)= \frac{K}{s(s+2)}$. For the peak overshoot of the closed-loop system to a unit step input to be $10 \%$, the value of $K$ is _________
The open-loop transfer function of a unity feedback control system is given by $$G(s)= \frac{K}{s(s+2)}$$. For the peak overshoot of the closed-loop system to a unit step...
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79
GATE ECE 2016 Set 1 | Question: 30
The Laplace transform of the casual periodic square wave of period $T$ shown in the figure below is $F(S) = \frac{1}{1+e^{-sT/2}} \\$ $F(S) =\frac{1}{s(1+e^{-sT/2})} \\$ $F(S) = \frac{1}{s(1-e^{-sT})} \\$ $F(S) = \frac{1}{1-e^{-sT}}$
The Laplace transform of the casual periodic square wave of period $T$ shown in the figure below is$F(S) = \frac{1}{1+e^{-sT/2}} \\$$F(S) =\frac{1}{s(1+e^{-sT/2})} \\$$F(...
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