The GATE Grind

GATE Signals and Systems: Signals and linear time-invariant systems – Previous Year Questions

17 GATE previous year questions on Signals and linear time-invariant systems (Signals and Systems, Instrumentation Engineering) with answers and explanations, from every paper.

  1. GATE 2021 IN Q14 (1 mark, Multiple choice) – The input–output relationship of an LTI system is shown. For the input x[n] shown below it, the peak output value is .
  2. GATE 2021 IN Q18 (1 mark, Multiple choice) – The signal (2 t) is .
  3. GATE 2021 IN Q53 (2 marks, Numerical answer) – Given y(t)=e-3tu(t)*u(t+3), where * denotes convolution, ty(t) is (two decimal places).
  4. GATE 2021 IN Q55 (2 marks, Numerical answer) – A sinusoid (2 t)u(t) is applied to G(s)=1/(s+1), where u is the unit step. The steady-state output amplitude is .
  5. GATE 2022 IN Q14 (1 mark, Multiple choice) – The output is related to the input by y(t)=x(t)(2 t). This system is .
  6. GATE 2023 IN Q21 (1 mark, Multiple choice) – A system has Y(s)/X(s)=(s-)/(s+). If u(t) is the unit step, which input gives steady-state output y(t)=( t)?
  7. GATE 2023 IN Q28 (1 mark, Numerical answer) – Let x[n]=u[-n+5]-u[n+3], where u[n]=1 for n0 and zero for n<0. The smallest n for which x[n]=0 is .
  8. GATE 2023 IN Q29 (1 mark, Numerical answer) – A continuous-time periodic signal x(t) has fundamental period 100 s. If y(t)=x(4t), its fundamental period is s (nearest integer).
  9. GATE 2023 IN Q36 (2 marks, Multiple choice) – An LTI system has impulse response h(t)=(t)+0.5(t-4), where is the continuous-time unit impulse. For x(t)=(7 t/4), its output is
  10. GATE 2024 IN Q13 (1 mark, Multiple choice) – A discrete-time sequence is x[n]=[1,2,3,4] for 0 n3. Its zero-lag autocorrelation is
  11. GATE 2025 IN Q16 (1 mark, Multiple choice) – Let the continuous-time signal be x(t)=ej9t+ej5t, where j=-1 and t is in seconds. The fundamental period of x(t) , in seconds, is
  12. GATE 2025 IN Q51 (2 marks, Multiple select) – Choose the eigenfunctions of stable linear time-invariant continuous-time systems.
  13. GATE 2026 IN Q19 (1 mark, Multiple choice) – Given x(t)=4(15 t)+7(4 t), where t is in seconds, the fundamental period of x(t) is seconds.
  14. GATE 2026 IN Q20 (1 mark, Multiple choice) – Among the following, the differential equation(s) not representative of a linear dynamical system is/are . (i) d2xdt2+2tdxdt+x(t)=u(t) (ii)…
  15. GATE 2026 IN Q41 (2 marks, Multiple choice) – A signal x(t) is shown in the first graph. The plot of y(t)=1-x(4-t) is shown in . The candidate plots are labeled A–D in the figure.
  16. GATE 2026 IN Q42 (2 marks, Multiple choice) – List I gives system responses to an input, and List II gives system properties. Choose the correct matching. List I: (M) x2(t); (N) x(-t); (O) x(3-t)…
  17. GATE 2026 IN Q57 (2 marks, Numerical answer) – Let f(t)=cases1,&t[0,2],\\-t+3,&t[2,3],\\0,&otherwise.cases Then -f()\,d= . (Rounded off to one decimal place.)