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GATE EC Networks, Signals and Systems questions

Practise Networks, Signals and Systems questions for GATE EC. Explore official PYQs and original subject-wise quizzes, check answers and view available solutions. Free, no sign-in.

Identify whether the signal and system are continuous-time or discrete-time. Check linearity, time invariance and stability before selecting a transform or response method.

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Official PYQ2022Networks, Signals and SystemsCircuit AnalysisMSQ · 2 marks
Consider an FM\text{FM} broadcast that employs the pre-emphasis filter with frequency response Hpe(ω)=1+jωω0,H_{pe}(\omega) = 1 + \frac{j \omega}{\omega_{0}}, where ω0=104  rad/sec.\omega_{0} = 10^{4} \; \text{rad/sec}. For the network shown in the figure to act as a corresponding de-emphasis filter, the appropriate pair(s) of (R,C)(R,C) values is/are _____________.
Official PYQ2022Networks, Signals and SystemsCircuit AnalysisNAT · 2 marks
A linear 2-port\text{2-port} network is shown in Fig.(a).\text{Fig.(a)}. An ideal DC\text{DC} voltage source of 10  V10 \; \text{V} is connected across Port 1.1. A variable resistance RR is connected across Port 2.2. As RR is varied, the measured voltage and current at Port 22 is shown in Fig.(b)\text{Fig.(b)} as a V2V_{2} versus −I2-I_{2} plot. Note …
Official PYQ2022Networks, Signals and SystemsDiscrete-time SignalsNAT · 2 marks
For a vector x‾=[x[0],x[1],…,x[7]],\overline{x} = \left[ x [0], x[1], \dots, x[7] \right], the 8-point\text{8-point} discrete Fourier transform (DFT)\text{(DFT)} is denoted by X‾=DFT(x‾)=[X[0],X[1],…,X[7]],\overline{X} = DFT (\overline{x}) = \left[ X [0], X[1], \dots, X[7] \right], where X[k]=∑n=07x[n]  exp(−j2π8nk).X[k] = \displaystyle \sum_{n=0}^{7} x[n] \; \text{exp} \left(-j \frac{2 \pi}{8} nk \right). Here, …
Official PYQ2021Networks, Signals and SystemsContinuous-time SignalsMCQ · 1 mark
Consider a real-valued base-band signal x(t)x(t), band limited to 10 kHz\text{10 kHz}. The Nyquist rate for the signal y(t)=x(t)x(1+t2)y\left ( t \right )=x\left ( t \right )x\left ( 1+\dfrac{t}{2} \right ) is
Official PYQ2021Networks, Signals and SystemsDiscrete-time SignalsMCQ · 1 mark
Consider two 1616-point sequences x[n]x\left [ n \right ] and h[n]h\left [ n \right ]. Let the linear convolution of x[n]x\left [ n \right ] and h[n]h\left [ n \right ] be denoted by y[n]y\left [ n \right ], while z[n]z\left [ n \right ] denotes the 1616-point inverse discrete Fourier transform (IDFT)\text{(IDFT)} of the product of the 1616-point …
Official PYQ2021Networks, Signals and SystemsCircuit AnalysisNAT · 1 mark
Consider the circuit shown in the figure. The current II flowing through the 7 Ω7\:\Omega resistor between PP and QQ (rounded off to one decimal place) is ________ AA.
Official PYQ2021Networks, Signals and SystemsCircuit AnalysisNAT · 1 mark
Consider the circuit shown in the figure. The value of v0v_{0} (rounded off to one decimal place) is _________ VV.
Official PYQ2021Networks, Signals and SystemsCircuit AnalysisMCQ · 2 marks
The switch in the circuit in the figure is in position PP for a long time and then moved to position QQ at time t=0t=0. The value of dv(t)dt\dfrac{dv\left ( t \right )}{dt} at t=0+t=0^{+} is
Official PYQ2021Networks, Signals and SystemsCircuit AnalysisMCQ · 2 marks
Consider the two-port network shown in the figure. The admittance parameters, in siemens, are
Official PYQ2021Networks, Signals and SystemsCircuit AnalysisNAT · 2 marks
In the circuit shown in the figure, the switch is closed at time t=0t=0, while the capacitor is initially charged to −5 V-5\:V (i.e., vc(0)=−5Vv_{c}(0)=-5V). The time after which the voltage across the capacitor becomes zero (rounded off to three decimal places) is ________________ ms\text{ms}.
Official PYQ2021Networks, Signals and SystemsContinuous-time SignalsNAT · 2 marks
The exponential Fourier series representation of a continuous-time periodic signal x(t)x(t) is defined as x(t)=∑k=−∞∞akejkω0tx\left ( t \right )=\sum_{k=-\infty }^{\infty }a_{k}e^{jk\omega _{0}t} where ω0\omega _0 is the fundamental angular frequency of x(t)x(t) and the coefficients of the series are aka_{k}. The following information is given about x(t)x(t) and …
Official PYQ2021Networks, Signals and SystemsLTI SystemsNAT · 2 marks
For a unit step input u[n]u[n], a discrete-time LTI\text{LTI} system produces an output signal (2δ[n+1]+δ[n]+δ[n−1])\left ( 2\delta \left [ n+1 \right ] +\delta \left [ n \right ]+\delta \left [ n-1 \right ]\right ). Let y[n]y[n] be the output of the system for an input ((12)nu[n])\left ( \left ( \dfrac{1}{2} \right )^n u\left [ n \right ]\right ). The value of y[0]y[0] is …
Official PYQ2021Networks, Signals and SystemsDiscrete-time SignalsNAT · 2 marks
Consider the signals x[n]=2n−1u[−n+2]x\left [ n \right ]=2^{n-1}u\left [ -n+2 \right ] and y[n]=2−n+2u[n+1]y\left [ n \right ]=2^{-n+2}u\left [ n+1 \right ], where u[n]u[n] is the unit step sequence. Let X(ejw)X(e^{jw}) and Y(ejw)Y(e^{jw}) be the discrete-time Fourier transform of x[n]x[n] and y[n]y[n], respectively. The value of the integral …
Official PYQ2021Networks, Signals and SystemsCircuit AnalysisNAT · 2 marks
The circuit in the figure contains a current source driving a load having an inductor and a resistor in series, with a shunt capacitor across the load. The ammeter is assumed to have zero resistance. The switch is closed at time t=0t = 0. Initially, when the switch is open, the capacitor is discharged and the ammeter reads zero ampere. After the switch is …
Official PYQ2020Networks, Signals and SystemsLTI SystemsMCQ · 1 mark
The output y[n]y[n] of a discrete-time system for an input x[n]x[n] is y[n]=max−∞≤k≤n∣x[k]∣y\left [ n \right ]=\underset{-\infty \leq k\leq n}{\text{max}} \mid x\left [ k \right ] \mid The unit impulse response of the system is
Official PYQ2020Networks, Signals and SystemsCircuit AnalysisMCQ · 1 mark
In the circuit shown below, the Thevenin voltage VTHV_{TH}is
Official PYQ2020Networks, Signals and SystemsLTI SystemsMCQ · 1 mark
The pole-zero map of a rational function G(s)G(s) is shown below. When the closed contour Γ\Gamma is mapped into the G(s)G(s)-plane, then the mapping encircles
Official PYQ2020Networks, Signals and SystemsLTI SystemsMCQ · 1 mark
Which one of the following pole-zero plots corresponds to the transfer function of an LTI\text{LTI} system characterized by the input-output difference equation given below? y[n]=∑k=03(−1)kx[n−k]y\left [ n \right ]=\sum ^{3}_{k=0}\left ( -1 \right )^{k}x\left [ n-k \right ]
Official PYQ2020Networks, Signals and SystemsCircuit AnalysisNAT · 1 mark
In the given circuit, the two-port network has the impedance matrix [Z]=[406060120]\begin{bmatrix} Z \end{bmatrix}=\begin{bmatrix} 40 & 60\\ 60& 120 \end{bmatrix}. The value of ZLZ_{L} for which maximum power is transferred to the load is _____________Ω\Omega.
Official PYQ2020Networks, Signals and SystemsCircuit AnalysisNAT · 1 mark
The current in the RL\text{RL}-circuit shown below is i(t)=10cos⁡(5t−π/4)Ai\left ( t \right )=10\cos\left ( 5t-\pi /4 \right )A. The value of the inductor (rounded off to two decimal places)\text{(rounded off to two decimal places)} is _______ H\text{H}.