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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 PYQ2014Networks, Signals and SystemsLTI SystemsMCQ · 2 marks
An unforced linear time invariant (LTI) system is represented by [x1x2]=[−100−2][x1x2]\begin{bmatrix} x_1 \\ x_2 \end{bmatrix} = \begin{bmatrix} -1 & 0 \\ 0& -2 \end{bmatrix} \begin{bmatrix} x_1 \\ x_2 \end{bmatrix} If the initial conditions are x1(0)=1x_1(0)= 1 and x2(0)=−1x_2(0)= -1, the solution of the state equation is
Official PYQ2014Networks, Signals and SystemsLTI SystemsMCQ · 2 marks
Consider the state space system expressed by the signal flow diagram shown in the figure. The corresponding system is
Official PYQ2014Networks, Signals and SystemsContinuous-time SignalsNAT · 2 marks
In the figure, M(f)M(f) is the Fourier transform of the message signal m(t)m(t) where A=100A = 100 Hz and B=40B = 40 Hz. Given v(t)=cos⁡(2πfct)v(t)= \cos (2\pi f_{c}t) and w(t)=cos⁡(2π(fc+A)t)w(t)= \cos (2\pi (f_{c}+A)t), where fc>Af_{c}>A. The cutoff frequencies of both the filters are fcf_{c}. The bandwidth of the signal at the output of the modulater (in Hz) is ______.
Official PYQ2014Networks, Signals and SystemsDiscrete-time SignalsMCQ · 1 mark
For an all-pass system H(z)=(z−1−b)(1−az−1)H(z)= \frac{(z^{-1}-b)}{(1-az^{-1})}, where ∣H(e−jω)∣=1,\mid H(e^{-j\omega }) \mid= 1, for all ω\omega. If Re(a)≠0, Im(a)≠0,\text{Re}(a)\neq 0, \: \text{Im}(a)\neq 0,then bb equals
Official PYQ2014Networks, Signals and SystemsLTI SystemsMCQ · 1 mark
Consider the following block diagram in the figure. The transfer function C(s)R(s)\frac{C(s)}{R(s)} is
Official PYQ2014Networks, Signals and SystemsCircuit AnalysisNAT · 1 mark
The input −3e2tu(t),-3e^{2t}u(t), where u(t)u(t) is the unit step function, is applied to a system with transfer function s−2s+3.\frac{s-2}{s+3}. If the initial value of the output is −2-2, then the value of the output at steady state is _______.
Official PYQ2014Networks, Signals and SystemsCircuit AnalysisMCQ · 2 marks
Consider the building block called ‘Network N’ shown in the figure. Let C=100μFC= 100\mu F and R=10kΩ.R= 10 k \Omega. Two such blocks are connected in cascade, as shown in the figure. The transfer function V3(s)V1(s)\frac{V_{3}(s)}{V_{1}(s)} of the cascaded network is
Official PYQ2014Networks, Signals and SystemsCircuit AnalysisNAT · 2 marks
For the YY-network shown in the figure, the value of R1R_{1} (in Ω\Omega) in the equivalent Δ\Delta-network is __________.
Official PYQ2014Networks, Signals and SystemsLTI SystemsNAT · 2 marks
Let H1(z)=(1−pz−1)−1,H2(z)=(1−qz−1)−1,H(z)=H1(z)+rH2(z).H_{1}(z)= (1-pz^{-1})^{-1},H_{2}(z)= (1-qz^{-1})^{-1},H(z)=H_{1}(z)+rH_{2}(z). The quantities p,p, qq, rr are real numbers. Consider p=12,q=−14,∣r∣<1.p=\frac{1}{2},q=-\frac{1}{4},\mid r \mid < 1. If the zero of H(z)H(z) lies on the unit circle, then rr == _________
Official PYQ2014Networks, Signals and SystemsLTI SystemsMCQ · 2 marks
Let h(t)h(t) denote the impulse response of a causal system with transfer function 1s+1.\frac{1}{s+1}. Consider the following three statements. S1S1: The system is stable. S2S2: h(t+1)h(t)\frac{h(t+1)}{h(t)} is independent of tt for t>0t > 0. S3S3: A non-causal system with the same transfer function is stable. For the above system,
Official PYQ2014Networks, Signals and SystemsDiscrete-time SignalsNAT · 2 marks
The zz-transform of the sequence x[n]x[n] is given by X(z)=1(1−2z−1)2,X(z)=\frac{1}{(1-2z^{-1})^{2}}, with the region of convergence ∣z∣>2\mid z \mid >2. Then, x[2]x[2] is _________.
Official PYQ2014Networks, Signals and SystemsLTI SystemsNAT · 2 marks
The steady state error of the system shown in the figure for a unit step input is _________.
Official PYQ2014Networks, Signals and SystemsLTI SystemsMCQ · 2 marks
In the root locus plot shown in the figure, the pole/zero marks and the arrows have been removed. Which one of the following transfer functions has this root locus?
Official PYQ2014Networks, Signals and SystemsDiscrete-time SignalsNAT · 1 mark
A Fourier transform pair is given by (23) u[n+3]⇔FTAe−j6πf1−(23)e−j2πf\left ( \frac{2}{3} \right ) \: u[n+3] \overset{FT}{\Leftrightarrow} \frac{Ae^{-j6 \pi f}}{1- (\frac{2}{3} ) e^{-j2 \pi f}} where u[n]u[n] denotes the unit step sequence. The values of AA is ____________
Official PYQ2014Networks, Signals and SystemsLTI SystemsMCQ · 1 mark
A real-valued signal x(t)x(t) limited to the frequency band ∣f∣≤W2\mid f \mid \leq \frac{W}{2} is passed through a linear time invariant system whose frequency response is H(f)={e−j4πf,∣f∣≤W20,∣f∣>W2.H(f) = \begin{cases} e^{-j 4 \pi f}, & \mid f \mid \leq \frac{W}{2} \\ 0, & \mid f \mid > \frac{W}{2} \end{cases}. The output of the system is
Official PYQ2014Networks, Signals and SystemsLTI SystemsNAT · 1 mark
The sequence x[n]=0.5n u[n]x[n] = 0.5^n \: u[n], where u[n]u[n] is the unit step sequence, is convolved with itself to obtain y[n]y[n]. Then Σn=−∞+∞y[n]\Sigma_{n= -\infty}^{+ \infty} y[n] is _________.
Official PYQ2014Networks, Signals and SystemsCircuit AnalysisMCQ · 2 marks
The unilateral Laplace transform of f(t)f(t) is 1s2+s+1\frac{1}{s^2+s+1}. Which one of the following is the unilateral Laplace transform of g(t)=t⋅f(t)g(t) = t \cdot f(t)?
Official PYQ2014Networks, Signals and SystemsCircuit AnalysisMCQ · 2 marks
The steady state output of the circuit shown in the figure is given by y(t)=A(ω)sin⁡(ωt+ϕ(ω))y(t)=A(\omega) \sin (\omega t + \phi ( \omega)). If the amplitude ∣A(ω)∣=0.25\mid A (\omega ) \mid =0.25, then the frequency ω\omega is
Official PYQ2014Networks, Signals and SystemsCircuit AnalysisNAT · 2 marks
In the circuit shown in the figure, the value of v0(t)v_0(t) (in Volts) for t→∞t \to \infty is ___________
Official PYQ2014Networks, Signals and SystemsCircuit AnalysisNAT · 2 marks
The equivalent resistance in the infinite ladder network shown in the figure, is ReR_e. The value of Re/RR_e/R is __________