---
title: "Energy or power: unit step, impulse"
subject: "Data Communication"
chapter: 2
key: "semester_5/data_communication:energy-power-check-signals"
source: https://www.bctengineer.com/q/semester_5/data_communication/energy-power-check-signals
site: BCT Engineering
---

# Energy or power: unit step, impulse

Data Communication · Chapter 2: Signals and Systems

- Asked in: 2073 Chaitra, 4 marks; 2071 Chaitra, 1+4 marks (asked 2 times)
- Video: [Energy And Power Signals | Questions 5 | Signals And Systems](https://www.youtube.com/watch?v=sG8k4WEp3Mg) — ENGINEERING TUTORIAL
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/data_communication/energy-power-check-signals
- Whole chapter: https://www.bctengineer.com/md/semester_5/data_communication/chapter-2

## Question

Define energy and power signals. Check whether the signals x(t) = u(t) and x(t) = δ(t) are energy or power type.

## Short answer

Energy signal: 0<E<∞, P=0; power signal: 0<P<∞, E=∞. u(t) has infinite energy, P=0.5 W → power signal. δ(t) has infinite undefined energy, no finite power → neither energy nor power.

## Answer

**Energy signal**: 0 < E < ∞ (and P = 0), with E = ∫|x(t)|² dt over (-∞, ∞).
**Power signal**: 0 < P < ∞ (and E = ∞), with P = lim (T→∞) (1/2T) ∫|x(t)|² dt over (-T, T).

#### x(t) = u(t)
Energy: E = ∫₀^∞ 1² dt = ∞

Power: P = lim (1/2T) ∫₀^T 1 dt = lim T/2T = **1/2**

E is infinite and P is finite, so the unit step is a **power signal** (P = 0.5 W).

#### x(t) = δ(t)
The impulse has infinite amplitude at t = 0 and zero width, and |δ(t)|² = δ(t)·δ(t) is not defined, so the energy ∫δ²(t) dt is infinite (the integral does not converge). The power, P = lim (1/2T) · ∞, is also not a finite value, so the impulse is treated as **neither an energy nor a power signal**.

Many textbooks state this directly: δ(t) has infinite energy, and since it does not satisfy 0 < P < ∞ either, it is neither.

## Check yourself

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

1. Power of u(t) is
   A. 1/2
   B. 1
   C. 0
   D. infinity
   Answer: A. lim T/2T. (Key point: Step power)

2. u(t) is
   A. energy signal
   B. power signal
   C. neither
   D. both
   Answer: B. E infinite, P finite. (Key point: Step type)

3. delta(t) is
   A. energy
   B. power
   C. neither
   D. both
   Answer: C. Energy infinite and power not finite. (Key point: Impulse)

## 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 versus power signals](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Aenergy-power-distinguish) — Data Communication, chapter 2, asked 6×
- [Causality, stability; energy and power signals](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Acausality-stability-energy-power) — 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
- [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: e^(-a|t|)u(t)](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Aenergy-power-exp-abs) — Data Communication, chapter 2

## Related in other subjects

- [Even/odd signals; energy or power check](https://www.bctengineer.com/question.md?key=semester_4%2Fsignals_and_systems%3Aeven-odd-energy-power-check) — Signals and Systems, chapter 1
- [Unit step in terms of signum; energy or power](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aunit-step-signum-energy-power) — Communication Systems, chapter 1
- [Hilbert transform properties; energy and power of unit step](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Ahilbert-properties-unit-step-energy) — Communication Systems, chapter 2
- [CT unit impulse, step and ramp relationship](https://www.bctengineer.com/question.md?key=semester_4%2Fsignals_and_systems%3Act-impulse-step-ramp) — Signals and Systems, chapter 1, asked 2×