GATE EE 2027 · SUBJECT 04 / 10

Signals & Systems: Syllabus, Topics & Reference Books

Continuous/discrete signals, LTI systems, Fourier analysis, sampling, Laplace and Z transforms.

Read syllabus topics ↓Download GATE EE syllabus ↗

Signals & Systems syllabus topics

The following topic groups come from the syllabus content included in this study hub. Consult the official GATE 2027 website for examination updates.

  1. Representation of continuous and discrete time signals,
  2. shifting and scaling properties,
  3. linear time invariant and causal systems,
  4. Fourier series representation of continuous and discrete time periodic signals,
  5. sampling theorem,
  6. Applications of Fourier Transform for continuous and discrete time signals,
  7. Laplace Transform and Z transform.
  8. R.M.S. value, average value calculation for any general periodic waveform.

How to prepare this subject

  1. Check topic coverage. Work through the groups above and mark unfamiliar concepts.
  2. Learn and practise. Study one relevant reference book, then solve worked examples without looking at the solutions.
  3. Apply concepts. Use GATE EE previous-year questions to assess where you need additional practice.
  4. Revise and test. Create a short formula or concept sheet and reattempt questions you initially missed.

Recommended reference books

These are textbook suggestions for studying this subject, not a mandatory purchase list.

  • Signals and Systems — A. V. Oppenheim, A. S. Willsky & S. H. Nawab
  • Linear Systems and Signals — B. P. Lathi

Free resources for practice

Use the downloadable question-paper collection and year-wise weightage report as supporting study materials.

Download GATE EE papers (2007–2026) ↓View subject-wise weightage analysis PDF ↗Open interactive subject tracker ↗Past papers by year →Create a study schedule →Free EE mock test →

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STEP-BY-STEP LEARNING

Convolution of two causal exponential signals

Solve a continuous-time LTI response by convolution and verify the answer with Laplace transforms.

Key learning goal: Set the correct integration limits for causal signals, evaluate the convolution integral and cross-check the result using partial fractions.

Read the detailed worked example and self-check question →

Quick concept check: Replace h(t) with e⁻²ᵗu(t), identical to x(t). What is y(t)?

Check the answer

The integral becomes ∫₀ᵗ e⁻²τ e⁻²(t−τ)dτ = te⁻²ᵗ for t ≥ 0. Therefore y(t) = te⁻²ᵗu(t).

Common pitfalls: Using integration limits from −∞ to +∞ without checking where the signals are nonzero. Treating e⁻²ᵗ × e⁻³ᵗ as the time-domain convolution.