60 solved GATE EE 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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Determine whether a signal is continuous or discrete, periodic or aperiodic, and energy or power before choosing a transform. These selected foundations connect LTI system properties, convolution, Fourier, Laplace, and Z transforms through original exercises. State region-of-convergence and causality assumptions explicitly.
Our study notes and original examples support the PYQs below; they are not official exam questions or a replacement for the current syllabus.
A continuous-time signal x(t) can be shifted, scaled, or reversed. An energy signal has finite total energy; a power signal has finite average power over an infinite interval. Periodicity requires x(t) = x(t + T) for some T > 0; the fundamental period is the smallest such T.
Check yourself: Have you confirmed finite energy or finite average power, not both?
A linear time-invariant system is fully characterised by its impulse response h(t) or h[n]. Output is the convolution of input with h: y(t) = x(t) * h(t). For causal h and causal x, the convolution integral has finite limits. Stability of a causal LTI system requires that h is absolutely integrable (or absolutely summable for discrete time).
Check yourself: Is h(t) = 0 for t < 0 if the system is causal?
The Fourier transform decomposes a signal into frequency components. Convolution in time becomes multiplication in frequency and vice versa. Parseval's theorem relates total energy in time to the integral of the squared magnitude spectrum. The transform exists for absolutely integrable signals; for power signals, use the Fourier series or generalised transforms with impulse functions.
Check yourself: Does the signal satisfy the existence condition for the transform you chose?
The bilateral Laplace transform X(s) = ∫ x(t)e^(−st) dt generalises the Fourier transform to complex s = σ + jω. The region of convergence (ROC) determines causality and stability: a causal signal has a right-sided ROC; a stable system's ROC includes the jω axis. Poles on the jω axis boundary indicate marginal stability.
Check yourself: Does the ROC include the jω axis if you need BIBO stability?
The Z-transform maps a discrete-time sequence to X(z) = Σ x[n]z^(−n). A causal sequence has an ROC outside the outermost pole. The sampling theorem states that a bandlimited signal with maximum frequency f_m can be reconstructed from samples taken at a rate exceeding 2f_m. Aliasing occurs when the sampling rate is insufficient.
Check yourself: Is the sampling rate strictly greater than twice the highest frequency component?
Original teaching example · not a PYQ
Original mini-example: find the linear convolution y[n] = x[n] * h[n], where x[n] = {1, 2, 1} for n = 0, 1, 2 and h[n] = {1, 1} for n = 0, 1, with both sequences zero elsewhere.
y[n] = {1, 3, 3, 1} for n = 0, 1, 2, 3.
Find the Laplace transform and region of convergence of x(t) = e^(−2t)u(t), where u(t) is the unit step function.
X(s) = 1/(s + 2), ROC: Re(s) > −2.
X(s) = ∫₀^∞ e^(−2t)e^(−st) dt = ∫₀^∞ e^(−(s+2)t) dt = 1/(s + 2), converging when Re(s + 2) > 0, i.e. Re(s) > −2. The ROC is right-sided, consistent with the causal signal. Since the ROC includes the jω axis, the signal is Fourier-transformable.
Supplemental reading, not an official GATE reading list or an endorsement of these notes.
Free supplemental lectures, notes, and problem sets covering LTI systems, convolution, Fourier analysis, Laplace and Z-transforms, and sampling.
This page shows 60 recent questions from the released archive, newest first. For older questions and complete papers, browse all GATE EE papers. Questions can carry more than one subject tag; counts are not marks weightage.
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