---
title: "Define periodic and non-periodic signals"
subject: "Data Communication"
chapter: 2
key: "semester_5/data_communication:periodic-nonperiodic-signals"
source: https://www.bctengineer.com/q/semester_5/data_communication/periodic-nonperiodic-signals
site: BCT Engineering
---

# Define periodic and non-periodic signals

Data Communication · Chapter 2: Signals and Systems

- Asked in: 2078 Kartik, 2 marks; 2075 Asoj, 2 marks; 2072 Kartik, 2 marks (asked 3 times)
- Video: [Periodic and Non-Periodic Signals](https://www.youtube.com/watch?v=Gj9pDC_OBQU) — Neso Academy
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/data_communication/periodic-nonperiodic-signals
- Whole chapter: https://www.bctengineer.com/md/semester_5/data_communication/chapter-2

## Question

Define periodic and non-periodic signals with examples.

## Short answer

A periodic signal repeats with period T (e.g., sin(ωt)), whereas a non-periodic signal does not repeat after any fixed interval (e.g., a single pulse or e⁻ᵗu(t)).

## Answer

**Periodic signal**: a signal that repeats itself at regular intervals, that is x(t) = x(t + T₀) for all t, where the smallest positive T₀ is the fundamental period. Examples: sin(ωt), a square wave, the mains supply.

**Non-periodic (aperiodic) signal**: a signal that does not repeat after any fixed time interval. Examples: a single rectangular pulse, e^(-t)u(t), speech, a unit step.

A sum of two sinusoids is periodic only if the ratio of their periods (T₁/T₂) is a rational number.

## Check yourself

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

1. Periodic means
   A. x(t) = 0
   B. x(t) never repeats
   C. x(t) = x(t + T0)
   D. x(t) = -x(t)
   Answer: C. Smallest T0 is the fundamental period. (Key point: Periodic)

2. Which is non-periodic?
   A. sin(wt)
   B. square wave
   C. mains supply
   D. e^(-t)u(t)
   Answer: D. Decaying signal does not repeat. (Key point: Non-periodic)

3. Sum of two sinusoids is periodic if
   A. T1/T2 is rational
   B. T1 = 0
   C. frequencies are irrational
   D. always
   Answer: A. Rational ratio gives a common period. (Key point: Sum)

## Related in Data Communication

- [Periodicity of sin(15πt) and sin(√2πt)](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Aperiodic-check-sinusoids) — Data Communication, chapter 2

## Related in other subjects

- [Periodic and non-periodic signals; LTI output is convolution](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aperiodic-nonperiodic-convolution) — Communication Systems, chapter 1
- [Parseval's relation for CT periodic signals](https://www.bctengineer.com/question.md?key=semester_4%2Fsignals_and_systems%3Actfs-parseval) — Signals and Systems, chapter 2, asked 4×
- [Fourier transform of CT periodic signals](https://www.bctengineer.com/question.md?key=semester_4%2Fsignals_and_systems%3Aft-periodic-signal-derivation) — Signals and Systems, chapter 3, asked 3×
- [FT of periodic signals; e^(−2|t|)sin t](https://www.bctengineer.com/question.md?key=semester_4%2Fsignals_and_systems%3Aft-periodic-damped-sine) — Signals and Systems, chapter 3, asked 2×