GATE Signals and Systems: Signals and Sampling – Previous Year Questions

6 GATE previous year questions on Signals and Sampling (Signals and Systems, Biomedical Engineering) with answers and explanations, from every paper.

1. GATE 2021 BM Q42 (2 marks, Multiple choice) – An analog signal sampled at 100 MHz produces 1024 samples. Only those samples are used for a 1024-point FFT. Find adjacent frequency-bin separation in…
2. GATE 2022 BM Q14 (1 mark, Multiple choice) – A real continuous-time signal has the magnitude spectrum shown. After sampling at angular frequency 100 rad/s, to what nonnegative baseband frequency…
3. GATE 2022 BM Q15 (1 mark, Multiple choice) – The discrete signals x[n] and y[n] are shown. Find their zero-lag cross-correlation rₓᵧ[0] using the average over the eight shown samples. The source…
4. GATE 2022 BM Q18 (1 mark, Multiple choice) – Find the time separation in seconds between corresponding peaks of v₁(t)=2cos(6t+60°) and v₂(t)=−3sin(6t).
5. GATE 2023 BM Q33 (1 mark, Numerical answer) – A band-limited continuous signal has X(f)=1- f /200 for f 200 Hz and zero otherwise. It is uniformly impulse-sampled at 600 Hz, giving spectrum Xₛ(f).…
6. GATE 2025 BM Q36 (2 marks, Multiple choice) – For x(t)=20(100 t)+36(150 t)-2(300 t) with t in seconds, which sampling frequency permits accurate reconstruction?