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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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20 on this page
Official PYQ2015Networks, Signals and SystemsDiscrete-time SignalsMCQ · 2 marks
Suppose x[n]x[n] is an absolutely summable discrete-time signal. Its zz-transform is a rational function with two poles and two zeroes. The poles are at z=±2j.z = \pm 2j. Which one of the following statements is TRUE for the signal x[n]x[n]?
Official PYQ2015Networks, Signals and SystemsDiscrete-time SignalsMCQ · 2 marks
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],x[n ], the response y[n]y[n ] is
Official PYQ2015Networks, Signals and SystemsDiscrete-time SignalsNAT · 2 marks
Let x~[n]=1+cos⁡(πn8)\widetilde{x}[n] = 1 + \cos\left(\dfrac{\pi n}{8}\right) be a periodic signal with period 16.16. Its DFS coefficients are defined by ak=116∑n=015x~[n]exp(−jπ8kn)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.k . The value of the coefficient ܽa31a_{31} is _______.
Official PYQ2015Networks, Signals and SystemsContinuous-time SignalsNAT · 2 marks
Consider a continuous-time signal defined as x(t)=(sin⁡(πt/2)(πt/2))∗∑n=−∞∞δ(t−10n)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 tt is in seconds. The Nyquist sampling rate (in samples/sec)\text{(in samples/sec)} for x(t)x(t) is _______.
Official PYQ2015Networks, Signals and SystemsCircuit AnalysisNAT · 2 marks
The position control of a DC servo-motor is given in the figure. The values of the parameters are KT=1 N−m/A,Ra=1Ω,La=0.1H,J=5kg−m2,B=1N−m/(rad/sec)K_{T}=1 \: N-m/A, R_{a}=1\Omega, L_{a} = 0.1H,J=5kg-m^{2},B=1N-m/(rad/sec) and Kb=1V/(rad/sec).K_{b} = 1V/(rad/sec) . The steady-state position response (in radians) due to unit impulse disturbance torque TdT_{d} is _______.
Official PYQ2015Networks, Signals and SystemsLTI SystemsNAT · 2 marks
The characteristic equation of an LTI system is given by F(s)=s5+2s4+3s3+6s2–4s–8=0.F(s) = s^{5} + 2s^{4} + 3s^{3} + 6s^{2} – 4s – 8 = 0. The number of roots that lie strictly in the left half ss-plane is _________.
Official PYQ2014Networks, Signals and SystemsCircuit AnalysisMCQ · 1 mark
Consider the configuration shown in the figure which is a portion of a larger electrical network For R=1 ΩR = 1\: \Omega and currents i1=2A,i4=−1A,i5=−4A,i_{1} = 2A,i_{4} = -1A,i_{5} = -4A, which one of the following is TRUE?\textbf{TRUE}?
Official PYQ2014Networks, Signals and SystemsLTI SystemsMCQ · 1 mark
A discrete-time signal x[n]=sin⁡(π2n),nx[n] = \sin(\pi^{2}n),n being an integer, is
Official PYQ2014Networks, Signals and SystemsLTI SystemsNAT · 1 mark
A continuous, linear time-invariant filter has an impulse response h(t)h(t) described by h(t)={3for 0≤t≤30otherwiseh(t) = \begin{cases}3 & \text{for } 0 \leq t \leq 3 \\ 0 & \text{otherwise} \end{cases} When a constant input of value 55 is applied to this filter, the steady state output is ________.
Official PYQ2014Networks, Signals and SystemsLTI SystemsNAT · 1 mark
The forward path transfer function of a unity negative feedback system is given by G(s)=K(s+2)(s−1)G(s) = \frac{K}{(s+2)(s-1)}. The value of KK which will place both the poles of the closed-loop system at the same location, is _______.
Official PYQ2014Networks, Signals and SystemsCircuit AnalysisMCQ · 1 mark
A two-port network has scattering parameters given by [S]=[s11s12s21s22].[S] = \begin{bmatrix}s_{11} &s_{12} \\s_{21} &s_{22} \end{bmatrix}. If the port-2 of the two-port is short circuited, the s11s_{11} parameter for the resultant one-port network is
Official PYQ2014Networks, Signals and SystemsCircuit AnalysisNAT · 2 marks
A YY-network has resistances of 10Ω10\Omega each in two of its arms, while the third arm has a resistance of 11Ω.11\Omega. In the equivalent Δ\Delta – network, the lowest value (in Ω)\Omega) among the three resistances is ______.
Official PYQ2014Networks, Signals and SystemsCircuit AnalysisMCQ · 2 marks
A 230 V230\: V rms source supplies power to two loads connected in parallel. The first load draws 10 kW10 \: kW at 0.80.8 leading power factor and the second one draws 10 kVA10\: kVA at 0.80.8 lagging power factor. The complex power delivered by the source is
Official PYQ2014Networks, Signals and SystemsDiscrete-time SignalsNAT · 2 marks
Consider a discrete time periodic signal x[n]=sin⁡(πns).x[n] = \sin(\frac{\pi n}{s}). Let aka_{k} be the complex Fourier series coefficients of x[n].x[n]. The coefficients {ak}\{a_{k}\} are non-zero when k=Bm ±1,k = Bm\: \pm 1, where mm is any integer. The value of BB is ______.
Official PYQ2014Networks, Signals and SystemsCircuit AnalysisMCQ · 1 mark
Norton’s theorem states that a complex network connected to a load can be replaced with an equivalent impedance
Official PYQ2014Networks, Signals and SystemsDiscrete-time SignalsMCQ · 1 mark
Let x[n]=x[−n]x[n] = x[-n]. Let X(z)X(z) be the zz-transform of x[n]x[n]. If 0.5+j0.250.5 + j 0.25 is a zero of X(z)X(z), which one of the following must also be a zero of x(z)x(z)
Official PYQ2014Networks, Signals and SystemsLTI SystemsMCQ · 1 mark
For the following system, when X1(s)=0X_{1} (s) = 0, the transfer function Y(s)X2(s)\frac{Y(s)}{X_{2}(s)} is
Official PYQ2014Networks, Signals and SystemsCircuit AnalysisNAT · 2 marks
In the h-parameter model of the 22-port network given in the figure shown, the value of h22h_{22} (in S) is ______ .
Official PYQ2014Networks, Signals and SystemsCircuit AnalysisNAT · 2 marks
In the magnetically coupled circuit shown in the figure, 56%56 \% of the total flux emanating from one coil links the other coil. The value of the mutual inductance (in H) is ____ .
Official PYQ2014Networks, Signals and SystemsLTI SystemsNAT · 2 marks
Consider a discrete-time signal x[n]={nfor 0≤n≤100otherwise x[n]= \begin{cases} n & \text{for } 0\leq n\leq 10 \\ 0 & \text{otherwise }\end{cases} If y[n]y[n] is the convolution of x[n]x[n] with itself, the value of y[4]y[4] is _______ .