---
title: "Causality, stability; energy and power signals"
subject: "Data Communication"
chapter: 2
key: "semester_5/data_communication:causality-stability-energy-power"
source: https://www.bctengineer.com/q/semester_5/data_communication/causality-stability-energy-power
site: BCT Engineering
---

# Causality, stability; energy and power signals

Data Communication · Chapter 2: Signals and Systems

- Asked in: 2070 Chaitra, 3+5 marks
- Video: [Energy and Power Signals | Solved Problems / Examples](https://www.youtube.com/watch?v=bZgQD_7d5VM) — Shrenik Jain
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/data_communication/causality-stability-energy-power
- Whole chapter: https://www.bctengineer.com/md/semester_5/data_communication/chapter-2

## Question

Define causality and stability properties of systems. What are energy and power signals. Explain with example.

## Short answer

A causal system's output depends only on present/past inputs. BIBO stability means bounded input yields bounded output; for LTI, ∫|h|dt<∞. An energy signal has finite energy E=∫|x|²dt, zero power (e.g., e^{-t}u(t)). A power signal has finite power P=lim(1/2T)∫|x|²dt, infinite energy (e.g., A cos ω₀t).

## Answer

#### Causality
A system is **causal** if the output at time t depends only on the present and past values of the input (not the future). Example: y(t) = x(t) + x(t - 1) is causal; y(t) = x(t + 1) is non-causal. For an LTI system, h(t) = 0 for t < 0.

#### Stability
A system is **BIBO stable** if every bounded input gives a bounded output. For an LTI system, ∫|h(t)| dt < ∞. Example: h(t) = e^(-2t)u(t) is stable (∫ = 1/2); h(t) = u(t) (integrator) is unstable.

#### Energy and power signals
- **Energy signal**: finite energy 0 < E = ∫|x(t)|² dt < ∞, and zero average power. Example: x(t) = e^(-t)u(t) has E = 1/2.
- **Power signal**: finite average power 0 < P = lim (1/2T) ∫_{-T}^{T}|x(t)|² dt < ∞, with infinite energy. Example: x(t) = A cos(ω₀t) has P = A²/2.

Periodic signals are power signals; non-periodic decaying (finite-duration) signals are energy signals. No signal is both.

## Check yourself

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

1. An LTI system is causal if
   A. h(t) = 0 for t < 0
   B. h(t) = 0 for t > 0
   C. h is even
   D. h is bounded
   Answer: A. No response before the impulse. (Key point: LTI causal)

2. An energy signal has
   A. Infinite energy
   B. Finite nonzero energy and zero average power
   C. Finite power and infinite energy
   D. Zero energy
   Answer: B. Definition. (Key point: Energy signal)

3. Which is a power signal?
   A. e^(-t)u(t)
   B. A rectangular pulse
   C. A cos(w0 t)
   D. delta(t) shifted
   Answer: C. Periodic signals have finite power A^2/2 and infinite energy. (Key point: Power signal)

## Related in Data Communication

- [Energy versus power signals](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Aenergy-power-distinguish) — Data Communication, chapter 2, asked 6×
- [Basic properties of systems](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Asystem-properties) — Data Communication, chapter 2, asked 3×
- [Recursive/nonrecursive systems; stability](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Arecursive-nonrecursive-stability) — Data Communication, chapter 2
- [Stable/unstable systems; test stability](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Astability-define-test-72c) — 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×
- [Invertibility; properties of y[n], y(t)](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Ainvertibility-system-properties) — Data Communication, chapter 2

## Related in other subjects

- [Stability and causality of LTI systems](https://www.bctengineer.com/question.md?key=semester_7%2Fdigital_signal_analysis_and_processing%3Astability-causality-lti) — Digital Signal Analysis and Processing, chapter 1
- [LTI system: linearity, stability, TI, causality](https://www.bctengineer.com/question.md?key=semester_4%2Fsignals_and_systems%3Alti-properties-four) — Signals and Systems, chapter 5, asked 2×
- [LTI: causality and stability](https://www.bctengineer.com/question.md?key=semester_4%2Fsignals_and_systems%3Alti-causality-stability) — Signals and Systems, chapter 5
- [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×