60 solved GATE EC questions on Signals & Systems, drawn from 10 exam years and grouped by year. Every question shows the official answer and a step-by-step solution.
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Connect continuous-time signals, discrete-time signals, and LTI systems using explicit coordinates and assumptions. These selected notes emphasize convolution and frequency interpretation, not a complete syllabus. The original calculations use abstract signals without physical implementation.
Our study notes and original examples support the PYQs below; they are not official exam questions or a replacement for the current syllabus.
Write x(t) for continuous time and x[n] for integer indices. The sequence x[n − n0] delays x[n] for positive integer n0. Reversal x[−n] reflects around zero. Lists need starting indices: shifting an origin changes convolution alignment.
Check yourself: Where does an originally nonzero sample land after the transformation?
Linearity requires T{ax1 + bx2} = aT{x1} + bT{x2}. Time invariance requires matching input and output delays. Test them independently. Fixed nonzero initial conditions can add a zero-input response, so specify when an equation-based input-output model assumes initial rest.
Check yourself: Does zero input give zero output, and does a delay commute with the system?
For an initially resting discrete-time LTI system, y[n] = Σk x[k]h[n − k]. Only overlapping nonzero samples contribute. If finite sequences occupy a through b and c through d, output is zero outside a + c through b + d; interior cancellation can still create zeros. Continuous-time convolution instead integrates over time.
Check yourself: Have you evaluated h[n − k], rather than multiplying matching list positions?
A discrete-time LTI system is causal exactly when h[n] = 0 for n < 0, and BIBO stable exactly when Σn |h[n]| is finite. A finite impulse response with finite coefficients is stable but can be noncausal if negative-index coefficients are nonzero.
Check yourself: Did you inspect negative indices separately from the absolute sum?
In cos(2πft), f is in Hz and ω = 2πf in rad/s. Sampling at fs gives Ω = 2πf/fs in rad/sample, modulo 2π. A stable LTI system scales complex exponentials by its frequency response without changing frequency; this excludes startup transients.
Check yourself: Is your frequency measured per second or per sample?
Original teaching example · not a PYQ
Original mini-example: an initially resting discrete-time LTI system has h[0] = 1 and h[1] = 3. Its input is x[−1] = 1, x[0] = 2, x[1] = −1. Both sequences are zero elsewhere. Find the full linear convolution.
y[−1] = 1, y[0] = 5, y[1] = 5, y[2] = −3; all other samples are zero.
Separately, let x[n] = x(n/1000) for x(t) = cos(2π × 125t), with t in seconds. Find ω, Ω, and the fundamental discrete period.
ω = 250π rad/s, Ω = π/4 rad/sample, and fundamental period N = 8 samples.
Sampling at 1000 samples/s gives x[n] = cos(πn/4). The smallest positive integer N satisfying (π/4)N = 2πm for integer m is 8. Samples are not seconds.
Supplemental reading, not an official GATE reading list or an endorsement of these notes.
Free convolution lecture notes for supplementary study. Compare the overlap calculation with the indexed finite example before attempting longer sequences.
This page shows 60 recent questions from the released archive, newest first. For older questions and complete papers, browse all GATE EC papers. Questions can carry more than one subject tag; counts are not marks weightage.
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