---
title: "Short note: Energy and power signals"
subject: "Signals and Systems"
chapter: 1
key: "semester_4/signals_and_systems:short-note-energy-power"
source: https://www.bctengineer.com/q/semester_4/signals_and_systems/short-note-energy-power
site: BCT Engineering
---

# Short note: Energy and power signals

Signals and Systems · Chapter 1: Signals

- Asked in: 2075 Bhadra, 3 marks; 2073 Bhadra, 3 marks (asked 2 times)
- Video: [Energy Signals & Power Signals](https://www.youtube.com/watch?v=w1HU1-kGLjs) — TutorialsPoint
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/signals_and_systems/short-note-energy-power
- Whole chapter: https://www.bctengineer.com/md/semester_4/signals_and_systems/chapter-1

## Question

Write a short note on energy and power signals.

## Short answer

An energy signal has finite total energy (0<E<∞) and zero average power, e.g., a decaying exponential. A power signal has finite non-zero average power (0<P<∞) and infinite energy, e.g., a sinusoid. Some signals, like a ramp, are neither.

## Answer

Signals are classified by their energy and average power.

- **Energy signal:** total energy is finite, $0 < E < \infty$, so average power $P = 0$. Usually time-limited or decaying signals. Example: $e^{-at}u(t)$ ($a>0$), $E = 1/(2a)$.
- **Power signal:** average power is finite and non-zero, $0 < P < \infty$, so $E = \infty$. Usually periodic or everlasting signals. Example: $A\cos\omega t$, $P = A^2/2$; $u(t)$, $P = 1/2$.

$$
E = \int_{-\infty}^{\infty}|x(t)|^2\,dt, \qquad P = \lim_{T\to\infty}\frac{1}{2T}\int_{-T}^{T}|x(t)|^2\,dt
$$

(For DT signals the integrals become sums over $n$ and $2T$ becomes $2N+1$.)

| Energy signal | Power signal |
|---|---|
| $0<E<\infty$, $P=0$ | $0<P<\infty$, $E=\infty$ |
| Finite duration / decaying | Periodic / infinite duration |
| e.g. single pulse | e.g. sinusoid |

A signal cannot be both. Some signals are **neither**, e.g. $e^{2t}$ or the ramp $t\,u(t)$, where both $E$ and $P$ are infinite.

## Check yourself

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

1. For an energy signal, which holds?
   A. E = infinity, P finite
   B. 0 < E < infinity, P = 0
   C. E and P both finite non-zero
   D. E = 0, P = 1
   Answer: B. Finite energy spread over infinite time gives zero average power. (Key point: Energy signal properties)

2. For A cos(wt), the average power is:
   A. A^2
   B. A^2/2
   C. A/2
   D. 1/2a
   Answer: B. The mean of cos^2 is 1/2, so P = A^2/2 and E is infinite. (Key point: Example values)

3. Which signal is neither an energy nor a power signal?
   A. e^(-at)u(t), a>0
   B. A cos wt
   C. The ramp t u(t)
   D. u(t)
   Answer: C. A ramp grows without bound, so both E and P are infinite. (Key point: Neither class)

## Related in Signals and Systems

- [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×
- [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
- [Energy density spectrum of CT signals](https://www.bctengineer.com/question.md?key=semester_4%2Fsignals_and_systems%3Aenergy-density-spectrum) — Signals and Systems, chapter 3, asked 3×
- [Energy or power: x(t) = e^(−at)](https://www.bctengineer.com/question.md?key=semester_4%2Fsignals_and_systems%3Aenergy-power-one-sided-exponential) — Signals and Systems, chapter 1, asked 6×
- [Energy or power: x(t) = e^(−3t)](https://www.bctengineer.com/question.md?key=semester_4%2Fsignals_and_systems%3Aenergy-power-decaying-exponential) — Signals and Systems, chapter 1, asked 5×

## Related in other subjects

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- [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/power signals; periodicity of complex exponential](https://www.bctengineer.com/question.md?key=semester_7%2Fdigital_signal_analysis_and_processing%3Aenergy-power-periodic-1) — Digital Signal Analysis and Processing, chapter 1
- [Energy/power signals; periodicity of cos + sin](https://www.bctengineer.com/question.md?key=semester_7%2Fdigital_signal_analysis_and_processing%3Aenergy-power-periodic-2) — Digital Signal Analysis and Processing, chapter 1