GATE ECE Signals and Systems notes
Use precise definitions of linearity, time invariance and stability before applying transform shortcuts.
BEFORE YOU BEGIN
Start with the right foundations
Complex exponentials, integration, summation and basic differential equations.
Original introductory notes with source references. The example is a teaching exercise, rather than an official worked solution to a GATE question. Use the full syllabus to track coverage.
01 · UNDERSTAND
Key concepts
Use these ideas to reason through a question before choosing a formula or an answer.
LTI systems
A linear time-invariant system is characterized by its impulse response. Output is convolution: an integral in continuous time and a sum in discrete time. Linearity and time invariance must both hold.
Stability
For an LTI system, BIBO stability requires the impulse response to be absolutely integrable in continuous time or absolutely summable in discrete time. A transform expression without its region of convergence may not determine causality or stability.
Sampling
For an ideal bandlimited low-pass signal with highest frequency B, sampling above 2B avoids overlapping spectral replicas. Reconstruction also assumes appropriate ideal filtering. Sampling exactly at the boundary can be ambiguous for boundary-frequency components.
02 · WORK THROUGH IT
A worked teaching example
Attempt the problem first, then trace each step and compare your reasoning.
The problem
A continuous-time causal LTI system has h(t) = exp(−2t)u(t). Is it BIBO stable?
Step-by-step reasoning
- 1
Evaluate the absolute integral over all time.
- 2
h(t) is zero for t < 0 and nonnegative for t ≥ 0.
- 3
The integral from 0 to infinity of exp(−2t) is 1/2, which is finite.
Check your result
Compare your calculation and assumptions.
Yes. Its impulse response is absolutely integrable.
03 · SPOT THE TRAPS
Common mistakes
- Assuming every linear system is time invariant.
- Dropping the region of convergence in Laplace or Z-transform questions.
- Applying a sampling formula without checking bandlimiting.
04 · CHECK YOUR UNDERSTANDING
Revision checklist
- Identify continuous versus discrete time.
- Check causality and stability separately.
- Retain transform region-of-convergence information.
Explain each point without the notes, then check it with an unfamiliar question. Print or save these notes as a PDF for your revision session.
05 · APPLY IT
Put these ideas into practice
Attempt related previous year questions and record the reasoning behind any mistakes.
Explore the archive to find a related topic for your next practice session.
Plan your next revision session
Explore topic history or move to another note.
READ FURTHER
Study references
Use the original references for a fuller explanation and more worked problems.