---
title: "Applications of Fourier series"
subject: "Data Communication"
chapter: 3
key: "semester_5/data_communication:fourier-series-applications"
source: https://www.bctengineer.com/q/semester_5/data_communication/fourier-series-applications
site: BCT Engineering
---

# Applications of Fourier series

Data Communication · Chapter 3: Signal Analysis

- Asked in: 2079 Baisakh, 2 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/data_communication/fourier-series-applications
- Whole chapter: https://www.bctengineer.com/md/semester_5/data_communication/chapter-3

## Question

Mention any two applications of Fourier series.

## Short answer

Two key applications: (1) analyzing periodic signal harmonics to determine bandwidth and filter effects; (2) computing linear circuit response to non-sinusoidal inputs by superposition of harmonic responses.

## Answer

1. **Signal analysis and filtering**: a periodic signal (such as a square wave or a rectified waveform) is split into harmonics, so that the bandwidth needed and the effect of a filter or channel can be found. Harmonics beyond the system bandwidth are removed.
2. **Circuit and power analysis**: the response of linear circuits to non-sinusoidal periodic inputs (rectifiers, switching waveforms) is found by applying each harmonic separately and adding the results; it is also used for harmonic distortion in power systems.

Other uses include communication (modulation, spectrum analysers), heat conduction, vibration analysis and image/audio compression.

## Check yourself

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

1. Fourier series splits a periodic signal into
   A. Impulses
   B. Steps
   C. Random noise
   D. Harmonics
   Answer: D. Basic idea. (Key point: Signal analysis)

2. Non-sinusoidal periodic input response is found by
   A. Applying each harmonic separately and adding
   B. Using one cycle only
   C. Ignoring harmonics
   D. Using the DC term only
   Answer: A. Superposition. (Key point: Circuits)

3. Harmonics beyond system bandwidth are
   A. Amplified
   B. Removed
   C. Ignored in the input
   D. Doubled
   Answer: B. Filter effect. (Key point: Filtering)

## Related in Data Communication

- [Properties of continuous-time Fourier series](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Afourier-series-properties) — Data Communication, chapter 3
- [Fourier series of half-wave rectified sine](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Afs-half-wave-rectified) — Data Communication, chapter 3
- [Fourier series of full-wave rectified sine](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Afs-full-wave-rectified) — Data Communication, chapter 3
- [Fourier series vs Fourier transform](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Afs-vs-ft) — Data Communication, chapter 3
- [Fourier series coefficients of a square wave](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Afs-coefficients-square-wave) — Data Communication, chapter 3
- [Multiplexing: definition and applications](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Amux-define-why) — Data Communication, chapter 6, asked 5×

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- [Fourier series of two-sided sawtooth with V](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_circuit_theory%3Afourier-sawtooth-two-sided-v) — Electrical Circuit Theory, chapter 6
- [Fourier series vs transform; DTFT of aⁿ](https://www.bctengineer.com/question.md?key=semester_4%2Fsignals_and_systems%3Afs-vs-ft-dtft-geometric) — Signals and Systems, chapter 3
- [Derive exponential Fourier series (CT)](https://www.bctengineer.com/question.md?key=semester_4%2Fsignals_and_systems%3Actfs-exponential-derivation) — Signals and Systems, chapter 2, asked 15×
- [Derive the discrete-time Fourier series](https://www.bctengineer.com/question.md?key=semester_4%2Fsignals_and_systems%3Adtfs-derivation) — Signals and Systems, chapter 2, asked 15×