---
title: "Energy versus power signals"
subject: "Data Communication"
chapter: 2
key: "semester_5/data_communication:energy-power-distinguish"
source: https://www.bctengineer.com/q/semester_5/data_communication/energy-power-distinguish
site: BCT Engineering
---

# Energy versus power signals

Data Communication · Chapter 2: Signals and Systems

- Asked in: 2078 Bhadra, 5 marks; 2075 Chaitra, 8 marks; 2072 Chaitra, 4 marks; 2069 Chaitra, 2 marks; 2069 Asar, 4 marks; 2068 Chaitra, 2 marks (asked 6 times)
- Video: [Signal Power and Energy](https://www.youtube.com/watch?v=7I9XEhAup4c) — Iain Explains Signals, Systems, and Digital Comms
- 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-distinguish
- Whole chapter: https://www.bctengineer.com/md/semester_5/data_communication/chapter-2

## Question

Differentiate between energy and power signals with examples.

## Short answer

An energy signal has finite total energy and zero average power (e.g., a rectangular pulse), while a power signal has infinite energy but finite non-zero average power (e.g., a sinusoid A cos(ωt) has P=A²/2).

## Answer

**Energy signal**: a signal with finite total energy and zero average power. **Power signal**: a signal with finite non-zero average power and infinite energy.

Energy: E = ∫ |x(t)|² dt over (-∞, ∞)

Power: P = lim (T→∞) (1/2T) ∫ |x(t)|² dt over (-T, T)

| Point | Energy signal | Power signal |
|---|---|---|
| Energy | 0 < E < ∞ | E = ∞ |
| Average power | P = 0 | 0 < P < ∞ |
| Duration | Usually finite / decaying (aperiodic) | Usually periodic or random, lasting for all time |
| Examples | Rectangular pulse, e^(-at)u(t) with a > 0 | Sinusoid A cos(ωt), DC signal, square wave |
| Signal type | Non-periodic, transient | Periodic and some random signals |

A signal cannot be both an energy and a power signal. Some signals such as r(t) = t·u(t) are neither.

**Example 1**: x(t) = e^(-t)u(t): E = ∫₀^∞ e^(-2t) dt = 1/2 (finite), P = 0, so energy signal.

**Example 2**: x(t) = A cos(ω₀t): E = ∞ and P = A²/2 (finite), so power signal.

## Check yourself

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

1. An energy signal has
   A. infinite energy and finite power
   B. infinite both
   C. finite energy and zero average power
   D. zero energy
   Answer: C. 0 < E < infinity and P = 0. (Key point: Energy signal)

2. Which is a power signal?
   A. Rectangular pulse
   B. e^(-t)u(t)
   C. t u(t)
   D. A cos(wt)
   Answer: D. Sinusoid has E = infinity, P = A^2/2. (Key point: Power signal)

3. Energy of e^(-t)u(t) is
   A. 1/2
   B. 1
   C. infinity
   D. 0
   Answer: A. Integral of e^(-2t) = 1/2. (Key point: Example E)

4. Can a signal be both?
   A. Yes, all can
   B. No; some are neither, e.g. t u(t)
   C. Yes, periodic ones
   D. Only impulses
   Answer: B. Ramp has infinite E and P. (Key point: Both)

## Related in Data Communication

- [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
- [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×
- [Power and energy of e^(-2t)u(t)](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Apower-energy-e-2t) — 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
- [Energy or power of DT cos(3πk/16)](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Adt-signal-cos-energy-power) — Data Communication, chapter 2

## Related in other subjects

- [Define energy and power signals](https://www.bctengineer.com/question.md?key=semester_4%2Fsignals_and_systems%3Adefine-energy-power-signals) — Signals and Systems, chapter 1, asked 2×
- [Short note: Energy and power signals](https://www.bctengineer.com/question.md?key=semester_4%2Fsignals_and_systems%3Ashort-note-energy-power) — Signals and Systems, chapter 1, asked 2×
- [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
- [Energy/power signals; shifting and scaling](https://www.bctengineer.com/question.md?key=semester_4%2Fsignals_and_systems%3Aenergy-power-shifting-scaling) — Signals and Systems, chapter 1