STUDY MATERIAL · GATE EC · EE · IN
GATE Signals and Systems previous year questions and notes
Every Signals and Systems question from 21 GATE papers (2018–2026), solved step by step and checked against the organising institute’s official answer key — with notes for each topic, a formula sheet and practice questions.
- previous-year questions
- 123previous-year questions
- worked solutions, checked against the key
- 118worked solutions, checked against the key
- GATE papers, 2018–2026
- 21GATE papers, 2018–2026
- topics with notes
- 9topics with notes
TOPICS
Nine topics, in the order they are taught
Cut from the official GATE 2027 syllabus. Each topic has notes, the formulas you need, every previous-year question on it with a checked solution, and practice questions.
- TOPIC 01
Signals: types, operations, energy, power and averages
This topic sets up the vocabulary for the whole Signals and Systems unit: how signals are classified, the standard building-block signals and the unit impulse, how time shifting, scaling and reversal act on a signal, and how to compute energy, power, average and RMS values.
18 previous-year questions · 25 marks · 5 practice
- TOPIC 02
LTI systems: properties, impulse response, convolution and correlation
A linear time-invariant (LTI) system is described completely by its impulse response $h(t)$ or $h[n]$.
31 previous-year questions · 47 marks · 5 practice
- TOPIC 03
Fourier series
A Fourier series writes a periodic signal as a sum of sinusoids at integer multiples of one fundamental frequency, so a question about a waveform becomes a question about a list of coefficients.
11 previous-year questions · 18 marks · 6 practice
- TOPIC 04
Fourier transform, frequency response, group and phase delay
The Fourier transform describes a signal by how much of each frequency it contains, and the frequency response $H(j\omega)$ describes how an LTI system scales and phase-shifts each of those frequencies.
22 previous-year questions · 33 marks · 6 practice
- TOPIC 05
Laplace transform, poles, zeros and system functions
The Laplace transform turns the differential equation of a continuous-time LTI system into algebra in the complex variable $s = \sigma + j\omega$, and its region of convergence (ROC) decides which time signal an algebraic $X(s)$ actually stands for.
8 previous-year questions · 13 marks · 7 practice
- TOPIC 06
Sampling and reconstruction
Sampling turns a continuous-time signal into a sequence of numbers; the sampling theorem says when those numbers still carry the whole signal, and reconstruction says how an ideal lowpass filter rebuilds it from them.
8 previous-year questions · 13 marks · 6 practice
- TOPIC 07
z-transform and discrete-time systems
The z-transform turns a sequence into a function of a complex variable $z$, so that convolution becomes multiplication and a difference equation becomes an algebraic equation.
12 previous-year questions · 16 marks · 6 practice
- TOPIC 08
DTFT, DFT and FFT
The DTFT gives the spectrum of a discrete-time signal as a continuous function of digital frequency that repeats every $2\pi$.
11 previous-year questions · 21 marks · 5 practice
- TOPIC 09EC · IN SYLLABUS ONLY
FIR and IIR filters
FIR and IIR filters are the two families of digital filters.
2 previous-year questions · 3 marks · 5 practice
WHERE THE QUESTIONS FALL
123 questions, by topic and year
Counts across the EC, EE and IN papers of each year. A count of what was asked, not a forecast of what will be. The topic tags are IAE’s reading of each question, and every question links back to its paper.
| Topic | 2018 | 2020 | 2022 | 2023 | 2024 | 2025 | 2026 | Total |
|---|---|---|---|---|---|---|---|---|
| Signals basics | 4 | 2 | · | 3 | 3 | 2 | 4 | 18 |
| LTI & convolution | 1 | 4 | 5 | 6 | 5 | 6 | 4 | 31 |
| Fourier series | 2 | · | 1 | 1 | · | 3 | 4 | 11 |
| Fourier transform | 3 | 3 | 4 | 6 | 2 | 3 | 1 | 22 |
| Laplace | · | 2 | 1 | 1 | 2 | · | 2 | 8 |
| Sampling | 1 | 1 | · | 2 | 2 | 1 | 1 | 8 |
| z-transform | 2 | 3 | · | 1 | 3 | 1 | 2 | 12 |
| DTFT & DFT | 2 | 2 | 1 | 2 | 3 | 1 | · | 11 |
| FIR & IIR filters | · | · | 1 | · | 1 | · | · | 2 |
GATE ECE question papers with solutions: 2026, 2025, 2024, 2023, 2022, 2020, 2018
GATE EE question papers with solutions: 2026, 2025, 2024, 2023, 2022, 2020, 2018
GATE IN question papers with solutions: 2026, 2025, 2024, 2023, 2022, 2020, 2018
The 2019 and 2021 papers are not yet included: the copies we host are image scans that do not carry the official key, so no solution to them could be checked.
How we check solutions: editorial standards.
Signals and Systems formulas by topic
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THE OFFICIAL SYLLABUS
What each paper lists under Signals and Systems
Verbatim from the GATE 2027 syllabus PDFs. EE and IN give Signals and Systems a section of its own (Section 4 in both); EC prints it inside Section 2, “Networks, Signals and Systems”, after the circuit topics. EE’s syllabus does not name FIR or IIR filters — its only filters are the active filters of analog electronics — which is why the filters topic is marked EC and IN.
GATE EC
LTI systems: definition and properties, causality, stability, impulse response, convolution, poles and zeroes, frequency response, group delay, phase delay. Continuous-time Signals: Fourier series and Fourier transform, Nyquist sampling theorem, sampling and reconstruction. Discrete-time Signals: DTFT, DFT, z-transform, FIR and IIR filter design.
GATE EE
Representation of continuous and discrete time signals, shifting and scaling properties, linear time invariant and causal systems, Fourier series representation of continuous and discrete time periodic signals, sampling theorem, Applications of Fourier Transform for continuous and discrete time signals, Laplace Transform and Z transform. R.M.S. value, average value calculation for any general periodic waveform.
GATE IN
Periodic, aperiodic and impulse signals; sampling; Fourier series, Laplace, Fourier and z-transforms, DFT and FFT; continuous-time and discrete-time systems, transfer function, linear time invariant systems, impulse response, frequency response, pulse transfer function; convolution, correlation; basics of IIR and FIR filters.
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