---
title: "Unit impulse function and its significance"
subject: "Data Communication"
chapter: 2
key: "semester_5/data_communication:unit-impulse-significance"
source: https://www.bctengineer.com/q/semester_5/data_communication/unit-impulse-significance
site: BCT Engineering
---

# Unit impulse function and its significance

Data Communication · Chapter 2: Signals and Systems

- Asked in: 2068 Chaitra, 2+2 marks
- Video: [Signals & Systems - Impulse Function](https://www.youtube.com/watch?v=gGHfj-B-w60) — TutorialsPoint
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/data_communication/unit-impulse-significance
- Whole chapter: https://www.bctengineer.com/md/semester_5/data_communication/chapter-2

## Question

Define unit impulse function. What is its significance in signal analysis?

## Short answer

The unit impulse δ(t) is zero except at t=0, infinite there, with area 1. It samples signals (sifting), characterizes LTI systems by h(t), and yields flat spectrum.

## Answer

#### Definition
The unit impulse (Dirac delta) δ(t) is zero for all t ≠ 0, has infinite height at t = 0, and has unit area: ∫ δ(t) dt = 1. It is the derivative of the unit step: δ(t) = du/dt.

#### Significance in signal analysis
- **Sifting property**: ∫ x(t) δ(t - t₀) dt = x(t₀). It samples a signal at one instant. This is the basis of ideal sampling.
- **System description**: the response of an LTI system to δ(t) is the impulse response h(t), which characterises the system completely. For any input, y(t) = x(t) * h(t).
- **Signal decomposition**: any signal is a sum of weighted, shifted impulses: x(t) = ∫ x(τ) δ(t - τ) dτ.
- **Frequency domain**: the Fourier transform of δ(t) is 1, so it contains all frequencies equally. It is used to test the frequency response of a system.
- It models very short pulses such as a lightning strike or hammer blow.

## Check yourself

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

1. The unit impulse has
   A. Unit height
   B. Zero area
   C. Finite width
   D. Zero for t≠0 and unit area
   Answer: D. Definition. (Key point: Definition)

2. Sifting property gives
   A. x(t0)
   B. x(0)
   C. 0
   D. 1
   Answer: A. Basis of sampling. (Key point: Sifting)

3. The impulse response h(t) is
   A. Output to u(t)
   B. The system output to delta(t)
   C. Input to system
   D. Derivative of input
   Answer: B. Characterises LTI systems. (Key point: Impulse response)

4. The Fourier transform of delta(t) is
   A. delta(w)
   B. 2 pi
   C. 1
   D. 0
   Answer: C. All frequencies equally. (Key point: Spectrum)

## Related in Data Communication

- [Define unit impulse and unit step](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Aunit-impulse-step-define) — Data Communication, chapter 2
- [Energy or power: unit step, impulse](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Aenergy-power-check-signals) — Data Communication, chapter 2, asked 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

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