The GATE Grind

GATE Signals and Systems: Representation of continuous and discrete time signals, shifting and scaling properties – Previous Year Questions

8 GATE previous year questions on Representation of continuous and discrete time signals, shifting and scaling properties (Signals and Systems, Electrical Engineering) with answers and explanations, from every paper.

  1. GATE 2016 EE Q19 (1 mark, Multiple choice) – The value of -+ e-t (2t - 2) \, dt, where (t) is the Dirac delta function, is
  2. GATE 2018 EE Q48 (2 marks, Multiple choice) – Consider the two continuous-time signals defined below: x 1(t)= t for -1 t1 (0 otherwise), and x 2(t)=1- t for -1 t1 (0 otherwise). These signals are…
  3. GATE 2018 EE Q49 (2 marks, Multiple choice) – The signal energy of the continuous-time signal x(t)=[(t-1)u(t-1)]-[(t-2)u(t-2)]-[(t-3)u(t-3)]+[(t-4)u(t-4)] is
  4. GATE 2020 EE Q16 (1 mark, Multiple choice) – x R and x A are, respectively, the rms and average values of x(t)=x(t-T), and similarly, y R and y A are, respectively, the rms and average values of…
  5. GATE 2023 EE Q49 (2 marks, Numerical answer) – The period of the discrete-time signal x[n] described by the equation below is N= (Round off to the nearest integer). x[n]=1+3(158n+34)-5(3n-4)
  6. GATE 2024 EE Q53 (2 marks, Numerical answer) – If the energy of a continuous-time signal x(t) is E and the energy of the signal 2x(2t-1) is cE, then c is (rounded off to 1 decimal place).
  7. GATE 2025 EE Q21 (1 mark, Multiple choice) – Consider a continuous-time signal x(t)=-t2\u(t+4)-u(t-4)\ where u(t) is the continuous-time unit step function. Let (t) be the continuous-time unit…
  8. GATE 2026 EE Q12 (1 mark, Multiple choice) – Let x c(t) be any continuous-time periodic signal with period T. It is sampled uniformly with a sampling period T s, where T s T, resulting in the…