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Recent questions in Networks, Signals and Systems
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41
GATE ECE 2016 Set 3 | Question: 32
Assume that the circuit in the figure has reached the steady state before time $t = 0$ when the $3\;\Omega$ resistor suddenly burns out, resulting in an open circuit. The current $i(t)$ (in ampere) at $t=0^+$ is _______
Assume that the circuit in the figure has reached the steady state before time $t = 0$ when the $3\;\Omega$ resistor suddenly burns out, resulting in an open circuit. The...
Milicevic3306
16.0k
points
223
views
Milicevic3306
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Mar 27, 2018
Network Solution Methods
gate2016-ec-3
numerical-answers
network-solution-methods
steady-state
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–
0
votes
0
answers
42
GATE ECE 2016 Set 3 | Question: 34
The $z$-parameter matrix $\begin{bmatrix} z_{11} &z_{12}\\ z_{21} &z_{22} \end{bmatrix}$ for the two-port network shown is $\begin{bmatrix} 2 &-2\\-2 &2 \end{bmatrix} \\$ $\begin{bmatrix} 2 &2\\2 &2 \end{bmatrix} \\$ $\begin{bmatrix} 9 &-3\\6 &9 \end{bmatrix} \\$ $\begin{bmatrix} 9 &3\\6 &9 \end{bmatrix}$
The $z$-parameter matrix $\begin{bmatrix} z_{11} &z_{12}\\ z_{21} &z_{22} \end{bmatrix}$ for the two-port network shown is $\begin{bmatrix} 2 &-2\\-2 &2 \end{bmatrix} \\$...
Milicevic3306
16.0k
points
154
views
Milicevic3306
asked
Mar 27, 2018
Network Solution Methods
gate2016-ec-3
network-solution-methods
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0
votes
0
answers
43
GATE ECE 2016 Set 3 | Question: 35
A continuous-time speech signal $x_a(t)$ is sampled at a rate of $8\:kHz$ and the samples are subsequently grouped in blocks, each of size $N$. The DFT of each block is to be computed in real time using the radix-$2$ decimation-in- ... by $1$ and $-1$) and the time required for addition/subtraction is negligible, then the maximum value of $N$ is _________
A continuous-time speech signal $x_a(t)$ is sampled at a rate of $8\:kHz$ and the samples are subsequently grouped in blocks, each of size $N$. The DFT of each block is t...
Milicevic3306
16.0k
points
252
views
Milicevic3306
asked
Mar 27, 2018
Continuous-time Signals
gate2016-ec-3
numerical-answers
continuous-time-signals
discrete-fourier-transform
+
–
0
votes
0
answers
44
GATE ECE 2016 Set 3 | Question: 36
The direct form structure of an FIR (finite impulse response) filter is shown in the figure. The filter can be used to approximate a low-pass filter high-pass filter band-pass filter band-stop filter
The direct form structure of an FIR (finite impulse response) filter is shown in the figure.The filter can be used to approximate alow-pass filterhigh-pass filterband-pas...
Milicevic3306
16.0k
points
156
views
Milicevic3306
asked
Mar 27, 2018
Continuous-time Signals
gate2016-ec-3
continuous-time-signals
impulse-response
+
–
1
votes
0
answers
45
GATE ECE 2016 Set 3 | Question: 42
In the circuit shown in the figure, transistor $M1$ is in saturation and has transconductance $g_m = 0.01$ siemens. Ignoring internal parasitic capacitances and assuming the channel length modulation $\lambda$ to be zero,the small signal input pole frequency (in $kHz$) is _________
In the circuit shown in the figure, transistor $M1$ is in saturation and has transconductance $g_m = 0.01$ siemens. Ignoring internal parasitic capacitances and assuming ...
Milicevic3306
16.0k
points
150
views
Milicevic3306
asked
Mar 27, 2018
Network Solution Methods
gate2016-ec-3
numerical-answers
network-solution-methods
+
–
0
votes
0
answers
46
GATE ECE 2016 Set 3 | Question: 47
A second-order linear time-invariant system is described by the following state equations $\frac{d}{dt}x_1(t)+2x_1(t)=3u(t)$ $\frac{d}{dt}x_2(t)+x_2(t)=u(t)$ where $x_1(t)$ and $x_2(t)$ are the two ... , then the system is controllable but not observable observable but not controllable both controllable and observable neither controllable nor observable
A second-order linear time-invariant system is described by the following state equations$$\frac{d}{dt}x_1(t)+2x_1(t)=3u(t)$$$$\frac{d}{dt}x_2(t)+x_2(t)=u(t)$$where $x_1(...
Milicevic3306
16.0k
points
173
views
Milicevic3306
asked
Mar 27, 2018
Network Solution Methods
gate2016-ec-3
network-solution-methods
state-equations
+
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0
votes
0
answers
47
GATE ECE 2016 Set 3 | Question: 48
The forward-path transfer function and the feedback-path transfer function of a single loop negative feedback control system are given as $G(s)=\frac{K(s+2)}{s^2+2s+2}\;\text{and}\hspace{0.3cm}H(s)=1,$ respectively. If the variable parameter $K$ is real positive, then the location of the breakaway point on the root locus diagram of the system is _________
The forward-path transfer function and the feedback-path transfer function of a single loop negative feedback control system are given as$$G(s)=\frac{K(s+2)}{s^2+2s+2}\;\...
Milicevic3306
16.0k
points
145
views
Milicevic3306
asked
Mar 27, 2018
Network Solution Methods
gate2016-ec-3
numerical-answers
network-solution-methods
transfer-function
bode-and-root-locus-plots
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0
votes
0
answers
48
GATE ECE 2016 Set 3 | Question: 49
A wide sense stationary random process $X(t)$ passes through the LTI system shown in the figure. If the autocorrelation function of $X(t)$ is $R_X(\tau)$, then the autocorrelation function $R_Y(\tau)$ of the output $Y(t)$ ... $2R_X(\tau)-R_X(\tau-T_0)-R_X(\tau+T_0)$ $2R_X(\tau)+2R_X(\tau- 2T_0)$ $2R_X(\tau)-2R_X(\tau- 2T_0)$
A wide sense stationary random process $X(t)$ passes through the LTI system shown in the figure. If the autocorrelation function of $X(t)$ is $R_X(\tau)$, then the autoco...
Milicevic3306
16.0k
points
143
views
Milicevic3306
asked
Mar 27, 2018
Continuous-time Signals
gate2016-ec-3
continuous-time-signals
signals-and-systems
linear-time-invariant-systems
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0
votes
0
answers
49
GATE ECE 2016 Set 2 | Question: 8
The figure shown an $RLC$ circuit with a sinusoidal current source. At resonance, the ratio $\mid I_{L} \mid / \mid I_{R} \mid$, i.e., the ratio of the magnitudes of the inductor current phasor and the resistor current phasor, is ________
The figure shown an $RLC$ circuit with a sinusoidal current source. At resonance, the ratio $\mid I_{L} \mid / \mid I_{R} \mid$, i...
Milicevic3306
16.0k
points
217
views
Milicevic3306
asked
Mar 27, 2018
Network Solution Methods
gate2016-ec-2
numerical-answers
network-solution-methods
rlc-circuits
+
–
0
votes
0
answers
50
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 ________
Milicevic3306
16.0k
points
170
views
Milicevic3306
asked
Mar 27, 2018
Continuous-time Signals
gate2016-ec-2
numerical-answers
continuous-time-signals
to-be-tagged
+
–
0
votes
0
answers
51
GATE ECE 2016 Set 2 | Question: 32
A continuous-time filter with transfer function $H\left ( s \right )= \frac{2s+6}{s^{2}+6s+8}$ ... sampled at $2$ $Hz$, is identical at the sampling instants to the impulse response of the discrete time-filter. The value of $k$ is _________
A continuous-time filter with transfer function $H\left ( s \right )= \frac{2s+6}{s^{2}+6s+8}$ is converted to a discrete-time filter with transfer function $G\left ( z\r...
Milicevic3306
16.0k
points
138
views
Milicevic3306
asked
Mar 27, 2018
Network Solution Methods
gate2016-ec-2
numerical-answers
network-solution-methods
transfer-function
+
–
0
votes
0
answers
52
GATE ECE 2016 Set 2 | Question: 33
The Discrete Fourier Transform (DFT) of the $4$-point sequence $x\left [ n \right ]=\left \{ x\left [ 0 \right ],x\left [ 1 \right ], x\left [ 2 \right ], x\left [ 3 \right ] \right \}= \left \{ 3,2,3,4 \right \}$ ... $\left | \frac{X_{1}\left [ 8 \right ]}{X_{1}\left [ 11 \right ]} \right |$ is _________
The Discrete Fourier Transform (DFT) of the $4$-point sequence$x\left [ n \right ]=\left \{ x\left [ 0 \right ],x\left [ 1 \right ], x\left [ 2 \right ], x\left [ 3 \righ...
Milicevic3306
16.0k
points
148
views
Milicevic3306
asked
Mar 27, 2018
Continuous-time Signals
gate2016-ec-2
numerical-answers
continuous-time-signals
discrete-fourier-transform
+
–
0
votes
0
answers
53
GATE ECE 2016 Set 2 | Question: 34
The switch $S$ in the circuit shown has been closed for a long time. It is opened at $t = 0$ and remains open after that. Assume that the diode has zero reverse current and zero forward voltage drop. The steady state magnitude of the capacitor voltage $V_{c}$ (in volts) is ______
The switch $S$ in the circuit shown has been closed for a long time. It is opened at $t = 0$ and remains open after that. Assume that the diode has zero reverse current a...
Milicevic3306
16.0k
points
159
views
Milicevic3306
asked
Mar 27, 2018
Network Solution Methods
gate2016-ec-2
numerical-answers
network-solution-methods
diodes
steady-state
+
–
0
votes
0
answers
54
GATE ECE 2016 Set 1 | Question: 4
Which one of the following is a property of the solutions to the Laplace equation: $\nabla^2f = 0$? The solutions have neither maxima nor minima anywhere except at the boundaries. The solutions are not separable in the coordinates. The solutions are not continuous. The solutions are not dependent on the boundary conditions.
Which one of the following is a property of the solutions to the Laplace equation: $\nabla^2f = 0$?The solutions have neither maxima nor minima anywhere except at the bo...
Milicevic3306
16.0k
points
136
views
Milicevic3306
asked
Mar 27, 2018
Network Solution Methods
gate2016-ec-1
network-solution-methods
laplace-transform
+
–
0
votes
0
answers
55
GATE ECE 2016 Set 1 | Question: 7
A continuous-time function $x(t)$ is periodic with period $T$. The function is sampled uniformly with a sampling period $T_s$. In which one of the following cases is the sampled signal periodic? $T =\sqrt2 \: T_s$ $T = 1.2 \: T_s$ Always Never
A continuous-time function $x(t)$ is periodic with period $T$. The function is sampled uniformly with a sampling period $T_s$. In which one of the following cases is the ...
Milicevic3306
16.0k
points
175
views
Milicevic3306
asked
Mar 27, 2018
Continuous-time Signals
gate2016-ec-1
continuous-time-signals
sampling-theorem
+
–
0
votes
0
answers
56
GATE ECE 2016 Set 1 | Question: 9
Consider a two-port network with the transmission matrix: $T = \begin{pmatrix}A & B \\C & D\end{pmatrix}$. If the network is reciprocal, then $T^{-1} = T$ $T^2 = T$ Determinant $(T) = 0$ Determinant $(T) = 1$
Consider a two-port network with the transmission matrix: $T = \begin{pmatrix}A & B \\C & D\end{pmatrix}$. If the network is reciprocal, then $T^{-1} = T$$T^2 = T$Deter...
Milicevic3306
16.0k
points
95
views
Milicevic3306
asked
Mar 27, 2018
Network Solution Methods
gate2016-ec-1
network-solution-methods
two-port-network
+
–
0
votes
0
answers
57
GATE ECE 2016 Set 1 | Question: 10
A continuous-time sinusoid of frequency $33 Hz$ is multiplied with a periodic Dirac impulse train of frequency $46Hz$. The resulting signal is passed through an ideal analog low-pass filter with a cutoff frequency of $23Hz$. The fundamental frequency (in $Hz$) of the output is _______
A continuous-time sinusoid of frequency $33 Hz$ is multiplied with a periodic Dirac impulse train of frequency $46Hz$. The resulting signal is passed through an ideal ana...
Milicevic3306
16.0k
points
128
views
Milicevic3306
asked
Mar 27, 2018
Continuous-time Signals
gate2016-ec-1
numerical-answers
continuous-time-signals
to-be-tagged
+
–
0
votes
0
answers
58
GATE ECE 2016 Set 1 | Question: 23
The amplitude of a sinusoidal carrier is modulated by a single sinusoid to obtain the amplitude modulated signal $s(t) = 5 \cos1600 \pi t + 20 \cos 1800 \pi t + 5 \cos 2000 \pi t$. The value of the modulation index is _________
The amplitude of a sinusoidal carrier is modulated by a single sinusoid to obtain the amplitude modulated signal $s(t) = 5 \cos1600 \pi t + 20 \cos 1800 \pi t + 5 \cos 2...
Milicevic3306
16.0k
points
120
views
Milicevic3306
asked
Mar 27, 2018
Network Solution Methods
gate2016-ec-1
numerical-answers
network-solution-methods
sinusoidal-signal
+
–
0
votes
0
answers
59
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(...
Milicevic3306
16.0k
points
159
views
Milicevic3306
asked
Mar 27, 2018
Network Solution Methods
gate2016-ec-1
network-solution-methods
laplace-transform
+
–
0
votes
0
answers
60
GATE ECE 2016 Set 1 | Question: 32
A first-order low-pass filter of time constant $T$ is excited with different input signals (with zero initial conditions up to $t = 0$). Match the excitation signals $X, Y, Z$ with the corresponding time responses for $t \geq 0 $ ... $X \to R, \: Y\to P, \: Z \to Q$ $X \to P, \: Y\to R, \: Z \to Q$
A first-order low-pass filter of time constant $T$ is excited with different input signals (with zero initial conditions up to $t = 0$). Match the excitation signals $X, ...
Milicevic3306
16.0k
points
86
views
Milicevic3306
asked
Mar 27, 2018
Continuous-time Signals
gate2016-ec-1
signals-and-systems
low-pass-filters
continuous-time-signals
+
–
0
votes
0
answers
61
GATE ECE 2016 Set 1 | Question: 35
Consider the signal $x[n] = 6 \delta[n + 2] + 3 \delta[n + 1] + 8 \delta[n] + 7 \delta[n - 1] + 4 \delta[n - 2]$ If $X(e^{jw})$ is the discrete-time Fourier transform of $x[n]$, then $\frac{1}{\pi} \int\limits_{-\pi}^{\pi} X(e^{jw}) \sin^2(2\omega) d\omega$ is equal to _______
Consider the signal $$x[n] = 6 \delta[n + 2] + 3 \delta[n + 1] + 8 \delta[n] + 7 \delta[n - 1] + 4 \delta[n - 2]$$ If $X(e^{jw})$ is the discrete-time Fourier transform o...
Milicevic3306
16.0k
points
105
views
Milicevic3306
asked
Mar 27, 2018
Continuous-time Signals
gate2016-ec-1
numerical-answers
continuous-time-signals
signals-and-systems
fourier-transform
+
–
0
votes
0
answers
62
GATE ECE 2016 Set 1 | Question: 45
The open-loop transfer function of a unity-feedback control system is $G(s)= \frac{K}{s^2+5s+5}$. The value of $K$ at the breakaway point of the feedback contol system’s root-locus plot is _________
The open-loop transfer function of a unity-feedback control system is $$G(s)= \frac{K}{s^2+5s+5}$$. The value of $K$ at the breakaway point of the feedback contol system�...
Milicevic3306
16.0k
points
118
views
Milicevic3306
asked
Mar 27, 2018
Network Solution Methods
gate2016-ec-1
numerical-answers
network-solution-methods
transfer-function
bode-and-root-locus-plots
+
–
0
votes
0
answers
63
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...
Milicevic3306
16.0k
points
162
views
Milicevic3306
asked
Mar 27, 2018
Network Solution Methods
gate2016-ec-1
numerical-answers
network-solution-methods
transfer-function
+
–
0
votes
0
answers
64
GATE ECE 2016 Set 1 | Question: 47
The transfer function of a linear time invariant system is given by $H(s) = 2s^4 – 5s^3 + 5s -2$. The number of zeroes in the right half of the $s$-plane is _________
The transfer function of a linear time invariant system is given by $H(s) = 2s^4 – 5s^3 + 5s -2$. The number of zeroes in the right half of the $s$-plane is _________
Milicevic3306
16.0k
points
118
views
Milicevic3306
asked
Mar 27, 2018
Network Solution Methods
gate2016-ec-1
numerical-answers
network-solution-methods
transfer-function
+
–
0
votes
0
answers
65
GATE ECE 2015 Set 3 | Question: 6
For the circuit shown in the figure, the Thevenin equivalent voltage (in Volts) across terminals $a-b$ is _______.
For the circuit shown in the figure, the Thevenin equivalent voltage (in Volts) across terminals $a-b$ is _______.
Milicevic3306
16.0k
points
151
views
Milicevic3306
asked
Mar 27, 2018
Network Solution Methods
gate2015-ec-3
numerical-answers
network-solution-methods
thevenin-theorem
+
–
0
votes
0
answers
66
GATE ECE 2015 Set 3 | Question: 14
The circuit shown consists of J-K flip-flops, each with an active low asynchronous reset $(\overline{R_{d}}\:\text{input}).$ The counter corresponding to this circuit is a modulo-$5$ binary up counter a modulo-$6$ binary down counter a modulo-$5$ binary down counter a modulo-$6$ binary up counter
The circuit shown consists of J-K flip-flops, each with an active low asynchronous reset $(\overline{R_{d}}\:\text{input}).$ The counter corresponding to this circuit isa...
Milicevic3306
16.0k
points
230
views
Milicevic3306
asked
Mar 27, 2018
Network Solution Methods
gate2015-ec-3
network-solution-methods
flip-flops
+
–
0
votes
0
answers
67
GATE ECE 2015 Set 3 | Question: 17
The impulse response of an LTI system can be obtained by differentiating the unit ramp response differentiating the unit step response integrating the unit ramp response integrating the unit step response
The impulse response of an LTI system can be obtained by differentiating the unit ramp response differentiating the unit step response integrating the unit ramp response ...
Milicevic3306
16.0k
points
145
views
Milicevic3306
asked
Mar 27, 2018
Continuous-time Signals
gate2015-ec-3
continuous-time-signals
impulse-response
linear-time-invariant-systems
+
–
0
votes
0
answers
68
GATE ECE 2015 Set 3 | Question: 20
The phase margin (in degrees) of the system $G(s) = \dfrac{10}{s(s+10)}$ is _______.
The phase margin (in degrees) of the system $G(s) = \dfrac{10}{s(s+10)}$ is _______.
Milicevic3306
16.0k
points
147
views
Milicevic3306
asked
Mar 27, 2018
Continuous-time Signals
gate2015-ec-3
numerical-answers
continuous-time-signals
phase-delay
+
–
0
votes
0
answers
69
GATE ECE 2015 Set 3 | Question: 21
The transfer function of a first-order controller is given as $G_{C}(s) = \dfrac{K(s+a)}{s+b}$where $K,a$ and ܾ$b$ are positive real numbers. The condition for this controller to act as a phase lead compensator is $a<b$ $a>b$ $K<ab$ $K>ab$
The transfer function of a first-order controller is given as $$G_{C}(s) = \dfrac{K(s+a)}{s+b}$$where $K,a$ and ܾ$b$ are positive real numbers. The condition for this c...
Milicevic3306
16.0k
points
167
views
Milicevic3306
asked
Mar 27, 2018
Network Solution Methods
gate2015-ec-3
network-solution-methods
transfer-function
+
–
0
votes
0
answers
70
GATE ECE 2015 Set 3 | Question: 23
A message signal $m(t) = A_{m} \sin(2πf_{m}t)$ is used to modulate the phase of a carrier $A_{c} \cos(2πf_{c}t)$ to get the modulated signal $y(t) = A_{c} \cos(2πf_{c}t + m(t)).$ The bandwidth of $y(t)$ depends on $A_{m}$ but not on $f_{m}$ depends on $f_{m}$ but not on $A_{m}$ depends on both $A_{m}$ and $f_{m}$ does not depend on $A_{m}$ or $f_{m}$
A message signal $m(t) = A_{m} \sin(2πf_{m}t)$ is used to modulate the phase of a carrier $A_{c} \cos(2πf_{c}t)$ to get the modulated signal $y(t) = A_{c} \cos(2πf_{c}...
Milicevic3306
16.0k
points
96
views
Milicevic3306
asked
Mar 27, 2018
Continuous-time Signals
gate2015-ec-3
communications
calculation-of-bandwidth
+
–
1
votes
0
answers
71
GATE ECE 2015 Set 3 | Question: 31
The $ABCD$ parameters of the following $2$-port network are $\begin{bmatrix}3.5 + j2 & 20.5 \\ 20.5 & 3.5-j2 \end{bmatrix} \\$ $\begin{bmatrix}3.5 +j2 & 30.5 \\ 0.5&3.5-j2 \end{bmatrix} \\$ $\begin{bmatrix}10 &2+j0 \\2+j0 &10 \end{bmatrix} \\$ $\begin{bmatrix}7+j4 &0.5 \\ 30.5&7-j4 \end{bmatrix} $
The $ABCD$ parameters of the following $2$-port network are$\begin{bmatrix}3.5 + j2 & 20.5 \\ 20.5 & 3.5-j2 \end{bmatrix} \\$$\begin{bmatrix}3.5 +j2 & 30.5 \\ 0.5&3.5-j2 ...
Milicevic3306
16.0k
points
130
views
Milicevic3306
asked
Mar 27, 2018
Network Solution Methods
gate2015-ec-3
two-port-network
network-solution-methods
+
–
0
votes
0
answers
72
GATE ECE 2015 Set 3 | Question: 32
A network is described by the state model as $\dot{x_{1}}=2x_{1}-x_{2}+3u \\ \dot{x_{2}}=-4x_{2}-u \\ y=3x_{1}-2x_{2}$ The transfer function $H(s)\left(=\dfrac{Y(s)}{U(s)}\right)$ is $\dfrac{11s+35}{(s-2)(s+4)} \\$ $\dfrac{11s-35}{(s-2)(s+4)} \\$ $\dfrac{11s+38}{(s-2)(s+4)} \\$ $\dfrac{11s-38}{(s-2)(s+4)}$
A network is described by the state model as $$\dot{x_{1}}=2x_{1}-x_{2}+3u \\ \dot{x_{2}}=-4x_{2}-u \\ y=3x_{1}-2x_{2}$$ The transfer function $H(s)\left(=\dfrac{Y(s)}{...
Milicevic3306
16.0k
points
100
views
Milicevic3306
asked
Mar 27, 2018
Network Solution Methods
gate2015-ec-3
transfer-function
network-solution-methods
+
–
0
votes
0
answers
73
GATE ECE 2015 Set 3 | Question: 42
Suppose $x[n]$ is an absolutely summable discrete-time signal. Its $z$-transform is a rational function with two poles and two zeroes. The poles are at $z = \pm 2j.$ Which one of the following statements is TRUE for the signal $x[n]$? It is a finite duration signal It is a causal signal It is a non-causal signal It is a periodic signal.
Suppose $x[n]$ is an absolutely summable discrete-time signal. Its $z$-transform is a rational function with two poles and two zeroes. The poles are at $z = \pm 2j.$ Whic...
Milicevic3306
16.0k
points
175
views
Milicevic3306
asked
Mar 27, 2018
Continuous-time Signals
gate2015-ec-3
continuous-time-signals
signals-and-systems
fourier-transform
+
–
0
votes
0
answers
74
GATE ECE 2015 Set 3 | Question: 43
A realization of a stable discrete time system is shown in the figure. If the system is excited by a unit step sequence input $x[n ],$ the response $y[n ]$ is $4\left(-\dfrac{1}{3}\right)^{n}\:u[n]-5\left(-\dfrac{2}{3}\right)^{n}\:u[n]$ ... $5\left(\dfrac{2}{3}\right)^{n}\:u[n]-5\left(\dfrac{1}{3}\right)^{n}\:u[n]$
A realization of a stable discrete time system is shown in the figure. If the system is excited by a unit step sequence input $x[n ],$ the response $y[n ]$ is$4\left(-\df...
Milicevic3306
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143
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Milicevic3306
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Mar 27, 2018
Continuous-time Signals
gate2015-ec-3
continuous-time-signals
discrete-time-signals
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0
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0
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75
GATE ECE 2015 Set 3 | Question: 44
Let $\widetilde{x}[n] = 1 + \cos\left(\dfrac{\pi n}{8}\right)$ be a periodic signal with period $16.$ Its DFS coefficients are defined by $a_{k} = \displaystyle{}\dfrac{1}{16}\sum_{n=0}^{15}\widetilde{x}[n] \text{exp}\big(-j\dfrac{\pi}{8} kn\big)$ for all $k .$ The value of the coefficient ܽ$a_{31}$ is _______.
Let $\widetilde{x}[n] = 1 + \cos\left(\dfrac{\pi n}{8}\right)$ be a periodic signal with period $16.$ Its DFS coefficients are defined by $a_{k} = \displaystyle{}\dfrac{1...
Milicevic3306
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Mar 27, 2018
Continuous-time Signals
gate2015-ec-3
numerical-answers
continuous-time-signals
signals-and-systems
fourier-transform
periodic-signals
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0
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0
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76
GATE ECE 2015 Set 3 | Question: 45
Consider a continuous-time signal defined as $x(t)=\left(\dfrac{\sin(\pi t/2)}{(\pi t /2)}\right)\ast \sum _{n=-\infty}^{\infty}\delta(t-10n)$ where $’\ast’$ denotes the convolution operation and $t$ is in seconds. The Nyquist sampling rate $\text{(in samples/sec)}$ for $x(t)$ is _______.
Consider a continuous-time signal defined as$$x(t)=\left(\dfrac{\sin(\pi t/2)}{(\pi t /2)}\right)\ast \sum _{n=-\infty}^{\infty}\delta(t-10n)$$where $’\ast’$ denotes ...
Milicevic3306
16.0k
points
148
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Mar 27, 2018
Continuous-time Signals
gate2015-ec-3
numerical-answers
continuous-time-signals
convolution
nyquist
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0
votes
0
answers
77
GATE ECE 2015 Set 3 | Question: 46
The position control of a DC servo-motor is given in the figure. The values of the parameters are $K_{T}=1 \: N-m/A, R_{a}=1\Omega, L_{a} = 0.1H,J=5kg-m^{2},B=1N-m/(rad/sec)$ and $K_{b} = 1V/(rad/sec) .$ The steady-state position response (in radians) due to unit impulse disturbance torque $T_{d}$ is _______.
The position control of a DC servo-motor is given in the figure. The values of the parameters are $K_{T}=1 \: N-m/A, R_{a}=1\Omega, L_{a} = 0.1H,J=5kg-m^{2},B=1N-m/(rad/s...
Milicevic3306
16.0k
points
242
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Milicevic3306
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Mar 27, 2018
Network Solution Methods
gate2015-ec-3
numerical-answers
network-solution-methods
steady-state
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0
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0
answers
78
GATE ECE 2015 Set 3 | Question: 48
The characteristic equation of an LTI system is given by $F(s) = s^{5} + 2s^{4} + 3s^{3} + 6s^{2} – 4s – 8 = 0.$ The number of roots that lie strictly in the left half $s$-plane is _________.
The characteristic equation of an LTI system is given by $F(s) = s^{5} + 2s^{4} + 3s^{3} + 6s^{2} – 4s – 8 = 0.$ The number of roots that lie strictly in the left hal...
Milicevic3306
16.0k
points
111
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Mar 27, 2018
Continuous-time Signals
gate2015-ec-3
numerical-answers
continuous-time-signals
signals-and-systems
linear-time-invariant-systems
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0
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0
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79
GATE ECE 2015 Set 2 | Question: 1
The bilateral Laplace transform of a function $f(t) = \begin{cases} 1 & \text{if } a \leq t \leq b \\ 0 & \text{otherwise} \end{cases}$ is $\dfrac{a-b}{s} \\$ $\dfrac{e^{s}(a-b)}{s} \\$ $\dfrac{e^{-as}-e^{-bs}}{s} \\$ $\dfrac{e^{s(a-b)}}{s}$
The bilateral Laplace transform of a function $f(t) = \begin{cases} 1 & \text{if } a \leq t \leq b \\ 0 & \text{otherwise} \end{cases}$ is$\dfrac{a-b}{s} \\$$\dfrac{e^{s...
Milicevic3306
16.0k
points
213
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Milicevic3306
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Mar 27, 2018
Network Solution Methods
gate2015-ec-2
network-solution-methods
laplace-transform
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0
votes
0
answers
80
GATE ECE 2015 Set 2 | Question: 5
The magnitude and phase of the complex Fourier series coefficients ܽ$a_{k}$ of a periodic signal $x(t)$ are shown in the figure. Choose the correct statement from the four choices given. Notation: $C$ is the set of complex numbers, ܴ$R$ is the set of purely ... $x(t)\in P$ $x(t)\in (C-R)$ the information given is not sufficient to draw any conclusion about $x(t)$
The magnitude and phase of the complex Fourier series coefficients ܽ$a_{k}$ of a periodic signal $x(t)$ are shown in the figure. Choose the correct statement from the fo...
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16.0k
points
155
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Milicevic3306
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Mar 27, 2018
Continuous-time Signals
gate2015-ec-2
continuous-time-signals
signals-and-systems
fourier-transform
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