GATE Signals and Systems: Fourier analysis and sampling – Previous Year Questions

6 GATE previous year questions on Fourier analysis and sampling (Signals and Systems, Instrumentation Engineering) with answers and explanations, from every paper.

1. GATE 2022 IN Q13 (1 mark, Multiple choice) – A periodic function of period 2 is f(x)=cases-1-x,&-1 x<0\\1-x,&0<x1cases. Its Fourier series contains .
2. GATE 2022 IN Q18 (1 mark, Multiple choice) – The signal x(t) is band-limited between 100 Hz and 200 Hz. If y(t)=x(2t-5), which statement is always true?
3. GATE 2023 IN Q44 (2 marks, Multiple select) – A continuous real-valued signal x(t) has finite positive energy and is zero for all t<0. Select all signals whose continuous-time Fourier transform is…
4. GATE 2024 IN Q27 (1 mark, Numerical answer) – The Nyquist sampling frequency for x(t)=102(200 t) is Hz (nearest integer).
5. GATE 2025 IN Q48 (2 marks, Multiple choice) – Let f(t) and g(t) be continuous-time real signals. If h(t) is their cross-correlation using f(t) and g(-t), its Fourier transform H(j) equals . Here…
6. GATE 2026 IN Q18 (1 mark, Multiple choice) – A square wave signal of frequency 20 kHz is passed through an ideal low-pass filter with cut-off frequency of 21 kHz. The output signal is a .