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

# Define unit impulse and unit step

Data Communication · Chapter 2: Signals and Systems

- Asked in: 2071 Shrawan, 2 marks
- Video: [Elementary Signals - Unit Step and  unit impulse.](https://www.youtube.com/watch?v=T8ubEdWjcuk) — HANU7
- 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-step-define
- Whole chapter: https://www.bctengineer.com/md/semester_5/data_communication/chapter-2

## Question

Define unit impulse and unit step function.

## Short answer

Unit step u(t)=1 for t≥0, 0 for t<0. Unit impulse δ(t)=0 for t≠0, ∫δ(t)dt=1; it is the derivative of u(t), and sifting property gives ∫x(t)δ(t-t₀)dt = x(t₀).

## Answer

**Unit step function u(t)**: equals 1 for t ≥ 0 and 0 for t < 0.

```text
u(t)
1 |      ________
  |     |
0 +-----+-------> t
```

**Unit impulse function δ(t)**: zero everywhere except t = 0, where it is infinite, and its total area is one:

δ(t) = 0 for t ≠ 0, and ∫ δ(t) dt = 1.

It is the derivative of the unit step: δ(t) = du(t)/dt. Its sifting property is ∫ x(t) δ(t - t₀) dt = x(t₀).

## Check yourself

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

1. The unit step u(t) equals
   A. 1 for t <= 0
   B. 0 for t >= 0
   C. Infinite at 0
   D. 1 for t >= 0, 0 for t < 0
   Answer: D. Definition. (Key point: Unit step)

2. What is the area of the unit impulse?
   A. 1
   B. 0
   C. Infinity
   D. 2 pi
   Answer: A. Integral of delta(t) is 1. (Key point: Impulse area)

3. How are impulse and step related?
   A. u(t) = d delta/dt
   B. delta(t) = du/dt
   C. delta(t) = u(t)^2
   D. They are unrelated
   Answer: B. The impulse is the derivative of the step. (Key point: Relation)

4. The sifting property says the integral of x(t)delta(t-t0) is
   A. x(0)
   B. 0
   C. x(t0)
   D. 1
   Answer: C. The impulse picks the value at t0. (Key point: Sifting)

## Related in Data Communication

- [Unit impulse function and its significance](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Aunit-impulse-significance) — 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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