---
title: "Energy and power signal; bandwidth of a system"
subject: "Communication Systems"
chapter: 1
key: "semester_6/communication_systems:energy-power-bandwidth-system"
source: https://www.bctengineer.com/q/semester_6/communication_systems/energy-power-bandwidth-system
site: BCT Engineering
---

# Energy and power signal; bandwidth of a system

Communication Systems · Chapter 1: Introduction

- Asked in: 2073 Bhadra (CS I), 2+2 marks
- Video: [Energy and Power of Continuous Time Signals](https://www.youtube.com/watch?v=0Kmqp-XX_F0) — Neso Academy
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_6/communication_systems/energy-power-bandwidth-system
- Whole chapter: https://www.bctengineer.com/md/semester_6/communication_systems/chapter-1

## Question

Define Energy and Power Signal. Explain the meaning of bandwidth of a system along with necessary diagrams.

## Short answer

An energy signal has finite total energy and zero average power; a power signal has finite nonzero average power and infinite energy. System bandwidth is the frequency range where |H(f)| stays within 3 dB of its maximum (half-power): low-pass B=f_c, band-pass B=f_H-f_L. Signal passes undistorted if system bandwidth exceeds signal bandwidth.

## Answer

#### Energy and power signals
- **Energy signal:** finite total energy $0 < E = \int_{-\infty}^{\infty}|x(t)|^2dt < \infty$; its average power is zero. Example: a single pulse, $e^{-t}u(t)$.
- **Power signal:** finite non-zero average power $0 < P = \lim_{T\to\infty}\frac1T\int_{-T/2}^{T/2}|x(t)|^2dt < \infty$; its energy is infinite. Example: $A\cos\omega t$, unit step.

#### Bandwidth of a system
The **bandwidth** of a system is the range of frequencies over which it passes signals with acceptable gain, usually the range where $|H(f)|$ stays within **3 dB** of its maximum (i.e. power falls to half, amplitude to $1/\sqrt2 = 0.707$ of maximum).

- **Low-pass system:** passes $0$ to $f_c$; bandwidth $B = f_c$.
- **Band-pass system:** passes $f_L$ to $f_H$; bandwidth $B = f_H - f_L$.

```text
 |H(f)|  Low-pass             |H(f)|  Band-pass
  1 |-----.                    1 |      .---.
0.707|.....\                0.707|.....|.....|....
    |       \                    |    /       \
    +--------\--> f              +---/----+----\--> f
            fc                     fL    f0    fH
    |<- B ->|                       |<-- B -->|
```

A signal passes through a system without much distortion only if the system bandwidth is at least equal to the signal bandwidth.

## 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 power
   B. Zero energy
   C. Infinite energy and finite power
   D. Finite energy and zero average power
   Answer: D. A single pulse e^{-t}u(t) is an example. (Key point: Energy signal)

2. Which is a power signal?
   A. A single rectangular pulse
   B. e^{-t}u(t)
   C. Decaying impulse
   D. A cos(wt)
   Answer: D. Sinusoids have finite non-zero power and infinite energy. (Key point: Power signal)

3. System bandwidth is typically the range where |H(f)| stays within:
   A. 3 dB of its maximum, i.e. 0.707 of peak amplitude
   B. 10% of peak
   C. Twice the peak
   D. 1 dB of its minimum
   Answer: A. 3 dB means half power, amplitude 1/sqrt2. (Key point: 3 dB bandwidth)

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