Fourier Analysis

May 8, 2026 · View on GitHub

Curriculum Module

Created with R2021b. Compatible with R2025b and later releases.

Information

This curriculum module contains interactive MATLAB® live scripts and MATLAB® apps that teaches fundamental concepts of fourier analysis.

Background

The module is taught from a signal processing perspective at a level suitable for an introductory signals and systems course. In the first lesson, students use apps to visualize Fourier series and build intuition about the frequency domain. In subsequent lessons, students study complex Fourier series, Fourier transforms, and discrete Fourier transforms. As students progress, they transition from utilizing apps to writing their own code to analyze signals. Throughout the module, students apply Fourier techniques to analyze recorded audio signals.

The instructions inside the live scripts will guide you through the exercises and activities. Get started with each live script by running it one section at a time. To stop running the script or a section midway (for example, when an animation is in progress), use the Stop button in the RUN section of the Live Editor tab in the MATLAB Toolstrip.

Contact Us

Contact the MathWorks Educator Content Development Team if you would like to request assistance, provide feedback, or if you have a question.

Prerequisites

This module assumes minimal MATLAB knowledge required for these scripts, but you could use MATLAB Onramp as a resource to acquire familiarity with live scripts and MATLAB syntax.

Getting Started

Accessing the Module

On MATLAB Online:

Use the link to download the module. You will be prompted to log in or create a MathWorks account. The project will be loaded, and you will see an app with several navigation options to get you started.

On Desktop:

Download or clone this repository. Open MATLAB, navigate to the folder containing these scripts and double-click on fourier-analysis.prj. It will add the appropriate files to your MATLAB path and open an app that asks you where you would like to start.

Ensure you have all the required products (listed below) installed. If you need to include a product, add it using the Add-On Explorer. To install an add-on, go to the Home tab and select Add-Ons > Get Add-Ons.

Products

MATLAB®, Symbolic Math Toolbox™

Scripts

FourierSeries.mlx


	In this script, students will...	Lab Assignments
	$\bullet$ Compare signals in the time and frequency domains. $\bullet$ Analyze audio signals in the frequency domain. $\bullet$ Visualize Fourier series modes. $\bullet$ Describe how phase shift is represented in a Fourier series. $\bullet$ Discuss magnitude and phase.	Lab1_FourierSeries.mlx

ComplexFourierSeries.mlx


	In this script, students will...	Lab Assignments
	$\bullet$ Compare signals in the time and frequency domains. $\bullet$ Analyze audio signals in the frequency domain. $\bullet$ Visualize Fourier series modes. $\bullet$ Describe how phase shift is represented in a Fourier series. $\bullet$ Discuss magnitude and phase.	Lab2_ComplexFourierSeries.mlx

FourierTransform.mlx


	In this script, students will...	Lab Assignments
	$\bullet$ Compare signals in the time and frequency domains. $\bullet$ Analyze audio signals in the frequency domain. $\bullet$ Visualize Fourier series modes. $\bullet$ Describe how phase shift is represented in a Fourier series. $\bullet$ Discuss magnitude and phase.	Lab3_FourierTransform.mlx

DiscreteFourierTransform.mlx


	In this script, students will...	Lab Assignments
	$\bullet$ Compare signals in the time and frequency domains. $\bullet$ Analyze audio signals in the frequency domain. $\bullet$ Visualize Fourier series modes. $\bullet$ Describe how phase shift is represented in a Fourier series. $\bullet$ Discuss magnitude and phase.	Lab4_DFT.mlx

Apps


Sine and Cosine Series app	Fourier Series app	Magnitude and Phase app	Complex Fourier Series app

Educator Resources

Educator Page

Contribute

Looking for more? Find an issue? Have a suggestion? Please contact the MathWorks Educator Content Development Team. If you want to contribute directly to this project, you can find information about how to do so in the CONTRIBUTING.md page on GitHub.