Question 1

What is the syllabus for Signals and Systems in GATE ECE?

Accepted Answer

GATE ECE Signals and Systems syllabus: (1) CT signals — Fourier series, Fourier transform, properties, sampling theorem, Laplace transform, transfer functions, poles/zeros, convolution, LTI systems stability. (2) DT signals — DTFT, Z-transform, properties, transfer functions, causality, stability, convolution, discrete-time system realization, filtering.

Question 2

Which topics carry the most marks in GATE from Signals and Systems?

Accepted Answer

Based on GATE trend analysis, the highest-weightage topics in Signals and Systems are: (1) Fourier Transform and its properties — 2-4 marks every year. (2) Laplace Transform and transfer functions — 2-3 marks. (3) Z-Transform — 1-2 marks. (4) Sampling theorem and aliasing — 1-2 marks. (5) LTI system properties (linearity, causality, stability) — 1-2 marks. Total: Signals and Systems typically contributes 8-12 marks in GATE ECE.

Question 3

What are LTI systems?

Accepted Answer

LTI stands for Linear Time-Invariant. An LTI system satisfies two properties: (1) Linearity — superposition holds: if x₁→y₁ and x₂→y₂, then ax₁+bx₂ → ay₁+by₂ for any constants a,b. (2) Time-Invariance — shifting the input shifts the output by the same amount: if x(t)→y(t), then x(t-τ)→y(t-τ). LTI systems are completely characterized by their impulse response h(t), and any LTI system response can be computed as the convolution y(t) = x(t)*h(t).

Signals & Systems —Complete Unit-Wise Notes

Signals & Systems —
Complete Unit-Wise Notes