---
title: "Define LTI system and impulse response"
subject: "Data Communication"
chapter: 2
key: "semester_5/data_communication:lti-impulse-response-define"
source: https://www.bctengineer.com/q/semester_5/data_communication/lti-impulse-response-define
site: BCT Engineering
---

# Define LTI system and impulse response

Data Communication · Chapter 2: Signals and Systems

- Asked in: 2072 Kartik, 2+2 marks; 2071 Chaitra, 2 marks (asked 2 times)
- Video: [Linear Time-Invariant (LTI) Systems](https://www.youtube.com/watch?v=Y8iFJVmSQIk) — Neso Academy
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/data_communication/lti-impulse-response-define
- Whole chapter: https://www.bctengineer.com/md/semester_5/data_communication/chapter-2

## Question

Define LTI system and impulse response.

## Short answer

LTI system obeys superposition and time invariance; output is convolution y(t)=x(t)*h(t). Impuse response h(t) is the output for a unit impulse δ(t) with zero initial conditions, fully characterizing the system; e.g., RC low-pass: h(t)=(1/RC)e^{-t/RC}u(t).

## Answer

**LTI system**: a system that is both linear (it obeys superposition: additivity and homogeneity) and time-invariant (a shift in the input produces the same shift in the output). Its output for any input can be found by convolution: y(t) = x(t) * h(t) = ∫ x(τ) h(t - τ) dτ. Examples: RC filters and ideal amplifiers.

**Impulse response h(t)**: the output of a system when the input is a unit impulse δ(t) with zero initial conditions. It completely describes an LTI system: causality requires h(t) = 0 for t < 0, and stability requires ∫|h(t)| dt < ∞. For an RC low-pass filter, h(t) = (1/RC) e^(-t/RC) u(t).

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. LTI means
   A. linear and time-varying
   B. causal and stable
   C. memoryless
   D. linear and time-invariant
   Answer: D. Superposition plus shift invariance. (Key point: LTI)

2. LTI output is found by
   A. convolution x*h
   B. multiplication
   C. differentiation
   D. addition
   Answer: A. y = x * h. (Key point: Output)

3. h(t) is the output when input is
   A. unit step
   B. unit impulse
   C. sine
   D. ramp
   Answer: B. With zero initial conditions. (Key point: Impulse response)

## Related in Data Communication

- [Output of LTI with h(t) = e^(-at)u(t) and e^(at)u(-t)](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Aconvolution-exp-u-and-u-neg) — Data Communication, chapter 2, asked 3×
- [LTI output for h(t)=e^(-2t), rectangular input](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Alti-output-rect-input) — Data Communication, chapter 2, asked 3×
- [LTI output for h(t)=e^(-at)u(t), x(t)=u(t)-u(t-2)](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Alti-output-u-minus-u2) — Data Communication, chapter 2
- [Unit step response for h(t) = exp(-at)](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Aunit-step-response-exp) — Data Communication, chapter 2
- [Check LTI: y(t) = 2x(t) + 3](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Alti-check-2x-plus-3) — Data Communication, chapter 2
- [Stability of h(t) = t·e^(-3t)u(t)](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Astability-te-3t) — Data Communication, chapter 2

## Related in other subjects

- [Frequency response of a CT LTI system](https://www.bctengineer.com/question.md?key=semester_4%2Fsignals_and_systems%3Act-frequency-response) — Signals and Systems, chapter 5, asked 3×
- [First-order system impulse and step response](https://www.bctengineer.com/question.md?key=semester_4%2Fsignals_and_systems%3Afirst-order-system-response) — Signals and Systems, chapter 5
- [Frequency response; ideal LPF impulse response](https://www.bctengineer.com/question.md?key=semester_4%2Fsignals_and_systems%3Aideal-lpf-cutoff-impulse) — Signals and Systems, chapter 5, asked 2×
- [Impulse response; ideal LPF formula](https://www.bctengineer.com/question.md?key=semester_4%2Fsignals_and_systems%3Aimpulse-response-ideal-lpf) — Signals and Systems, chapter 5, asked 2×