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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 PYQ2015Networks, Signals and SystemsCircuit AnalysisMCQ · 1 mark
By performing cascading and/or summing/differencing operations using transfer function blocks G1(s)G_{1}(s ) and G2(s),G_{2}(s), one CANNOT realize a transfer function of the form
Official PYQ2015Networks, Signals and SystemsCircuit AnalysisNAT · 1 mark
A unity negative feedback system has an open-loop transfer function G(S)=Ks(s+10)G(S) = \dfrac{K}{s(s+10)}. The gain KK for the system to have a damping ratio of 0.250.25 is ________.
Official PYQ2015Networks, Signals and SystemsContinuous-time SignalsNAT · 1 mark
A sinusoidal signal of amplitude AA is quantized by a uniform quantizer. Assume that the signal utilizes all the representation levels of the quantizer. If the signal to quantization noise ratio is 31.8 dB,31.8\: dB, the number of levels in the quantizer is __________.
Official PYQ2015Networks, Signals and SystemsContinuous-time SignalsMCQ · 1 mark
The signal cos⁡(10πt+π4)\cos \left(10\pi t + \dfrac{\pi}{4}\right) is ideally sampled at a sampling frequency of 15Hz.15 Hz. The sampled signal is passed through a filter with impulse response (sin⁡(πt)πt)cos⁡(40πt–π2)\left(\dfrac{\sin (\pi t)}{\pi t}\right)\cos\left(40\pi t – \dfrac{\pi}{2}\right) The filter output is
Official PYQ2015Networks, Signals and SystemsCircuit AnalysisNAT · 2 marks
In the circuit shown, the Norton equivalent resistance (in Ω)(\text{in}\: \Omega) across terminals a−ba-b is _______.
Official PYQ2015Networks, Signals and SystemsCircuit AnalysisNAT · 2 marks
In the circuit shown, the initial voltages across the capacitors C1C_{1} and C2C_{2} are 1 V1\: V and 3 V,3\: V, respectively. The switch is closed at time t=0t = 0. The total energy dissipated (in Joules) in the resistor RR until steady state is reached, is __________.
Official PYQ2015Networks, Signals and SystemsLTI SystemsMCQ · 2 marks
Input x(t)x(t) and output y(t)y(t) of an LTI system are related by the differential equation y’’(t)–y’(t)–6y(t)=x(t).y’’(t) – y’(t) – 6y(t) = x(t). If the system is neither causal nor stable, the impulse response h(t)h(t) of the system is
Official PYQ2015Networks, Signals and SystemsDiscrete-time SignalsNAT · 2 marks
Consider two real sequences with time-origin marked by the bold value, x1[n]={1,2,3,0},  x2[n]={1,3,2,1}x_{1}[n] = \{\textbf{1},2,3,0\},\:\:x_{2}[n] = \{\textbf{1},3,2,1\} Let ܺX1(k)X_{1}(k) and ܺX2(k)X_{2}(k) be 44-point DFTs of x1[n]x_{1}[n] and x2[n]x_{2}[n], respectively. Another sequence x3[n]x_{3}[n] is derived by taking 44-point inverse DFT of X3(k)=X1(k)X2(k).X_{3}(k) = X_{1}(k)X_{2}(k). …
Official PYQ2015Networks, Signals and SystemsCircuit AnalysisNAT · 2 marks
Let x(t)=αs(t)+s(−t)x(t) = \alpha s(t) + s(-t) with s(t)=βe−4tu(t),s(t) = \beta e^{-4t}u(t), where u(t)u(t) is unit step function. If the bilateral Laplace transform of x(t)x(t) is X(s)=16s2–16  −4<Re{s}<4;X(s) = \dfrac{16}{s^{2} – 16}\:\: -4 < Re\{s\}<4; then the value of β\beta is ______.
Official PYQ2015Networks, Signals and SystemsCircuit AnalysisMCQ · 2 marks
The output of a standard second-order system for a unit step input is given as y(t)=1−23e−tcos⁡(3t−π6)y(t) = 1-\dfrac{2}{\sqrt{3}}e^{-t}\cos \left(\sqrt{3t}-\dfrac{\pi}{6}\right). The transfer function of the system is
Official PYQ2015Networks, Signals and SystemsLTI SystemsNAT · 2 marks
The transfer function of a mass-spring-damper system is given by G(S)=1Ms2+Bs+KG(S) = \dfrac{1}{Ms^{2}+Bs+K} The frequency response data for the system are given in the following table. …
Official PYQ2015Networks, Signals and SystemsCircuit AnalysisNAT · 2 marks
Two half-wave dipole antennas placed as shown in the figure are excited with sinusoidally varying currents of frequency 3 MHz3\: MHz and phase shift of π2\frac{\pi}{2} between them (the element at the origin leads in phase). If the maximum radiated EE-field at the point PP in the x−yx-y plane occurs at an azimuthal angle of 60∘,60^{\circ}, the …
Official PYQ2015Networks, Signals and SystemsCircuit AnalysisNAT · 1 mark
For the circuit shown in the figure, the Thevenin equivalent voltage (in Volts) across terminals a−ba-b is _______.
Official PYQ2015Networks, Signals and SystemsCircuit AnalysisMCQ · 1 mark
The circuit shown consists of J-K flip-flops, each with an active low asynchronous reset (Rd‾ input).(\overline{R_{d}}\:\text{input}). The counter corresponding to this circuit is
Official PYQ2015Networks, Signals and SystemsLTI SystemsMCQ · 1 mark
The impulse response of an LTI system can be obtained by
Official PYQ2015Networks, Signals and SystemsLTI SystemsNAT · 1 mark
The phase margin (in degrees) of the system G(s)=10s(s+10)G(s) = \dfrac{10}{s(s+10)} is _______.
Official PYQ2015Networks, Signals and SystemsLTI SystemsMCQ · 1 mark
The transfer function of a first-order controller is given as GC(s)=K(s+a)s+bG_{C}(s) = \dfrac{K(s+a)}{s+b}where K,aK,a and ܾbb are positive real numbers. The condition for this controller to act as a phase lead compensator is
Official PYQ2015Networks, Signals and SystemsContinuous-time SignalsMCQ · 1 mark
A message signal m(t)=Amsin⁡(2πfmt)m(t) = A_{m} \sin(2πf_{m}t) is used to modulate the phase of a carrier Accos⁡(2πfct)A_{c} \cos(2πf_{c}t) to get the modulated signal y(t)=Accos⁡(2πfct+m(t)).y(t) = A_{c} \cos(2πf_{c}t + m(t)). The bandwidth of y(t)y(t)
Official PYQ2015Networks, Signals and SystemsCircuit AnalysisMCQ · 2 marks
The ABCDABCD parameters of the following 22-port network are
Official PYQ2015Networks, Signals and SystemsCircuit AnalysisMCQ · 2 marks
A network is described by the state model as x1˙=2x1−x2+3ux2˙=−4x2−uy=3x1−2x2\dot{x_{1}}=2x_{1}-x_{2}+3u \\ \dot{x_{2}}=-4x_{2}-u \\ y=3x_{1}-2x_{2} The transfer function H(s)(=Y(s)U(s))H(s)\left(=\dfrac{Y(s)}{U(s)}\right) is