GATE Signals and Systems: Laplace and Fourier Transforms – Previous Year Questions
9 GATE previous year questions on Laplace and Fourier Transforms (Signals and Systems, Biomedical Engineering) with answers and explanations, from every paper.
- GATE 2020 BM Q18 – X(s) is the Laplace transform of x(t). Assuming x(0)=0, find the Laplace transform of dx(t)/dt.
- GATE 2021 BM Q15 – Let X(jω) be the Fourier transform of x(t), with X(j)=10e-j f( f)/( f) and ω=2πf. Evaluate 12 -X(j)\,d.
- GATE 2021 BM Q37 – A unit step is applied at t=0 to a system with H(s)=(1-s/ z)/(1+s/ p). Find y(0⁺).
- GATE 2022 BM Q38 – A system has the magnitude and phase responses shown. For step input x(t)=u(t), its output crosses zero at t=t d>0. Find t d in μs.
- GATE 2022 BM Q42 – Let g(t)=df(t)/dt and F(s)=(1+s)/(s2+12s+32) be the Laplace transform of f(t). Find g(0), interpreted as the right-hand derivative of the ordinary…
- GATE 2023 BM Q39 – The bilateral Laplace transforms of x₁(t)=e⁻ᵗu(t) and x₂(t)=eᵗu(−t) are X₁(s) and X₂(s), respectively. Which statement is true?
- GATE 2024 BM Q22 – Find the continuous-time Fourier transform of e- 2t , with kernel e⁻ʲωᵗ.
- GATE 2024 BM Q30 – The periodic square wave shown has cosine/sine Fourier coefficients an,bn. Find a1/a3 to one decimal place.
- GATE 2026 BM Q27 – x[n] is real and odd. Which describes its DTFT X(ej)?