Fourier Analysis

Learn Fourier analysis using live scripts and apps.


Updated 27 Apr 2023

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Fourier Analysis

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Curriculum Module
Created with R2021b. Compatible with R2021b and later releases.


This curriculum module teaches Fourier analysis using interactive live scripts and MATLAB® apps. 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.

Each topic includes a lab that applies the concepts taught in the lesson. The solutions are available upon instructor request. If you would like to request solutions or have a question, contact the MathWorks online teaching team.

Get started with the Fourier Analysis curriculum module by downloading and unzipping the repository. Then, double-click the project .prj file inside MATLAB. From there, you can follow the landing page instructions to get started with the examples and labs.


Module Learning Goals
1. Fourier Series

  • Compare signals in the time and frequency domains.
  • Analyze audio signals in the frequency domain.
  • Visualize Fourier series modes.
  • Describe how phase shift is represented in a Fourier series.
  • Discuss magnitude and phase.
2. Complex Fourier Series

  • Recall Euler's formula.
  • Compare complex and real Fourier series.
  • Visualize complex Fourier series.
  • Construct functions using complex Fourier series.
3. Fourier Transform

  • Compare Fourier series to the Fourier transform.
  • Evaluate the Fourier transform of a function.
  • Represent signals using continuous functions.
  • Discuss carrier waves and modulation.
  • Compare functions in the time and frequency domains using the Fourier transform.
4. Discrete Fourier Transform

  • Plot the discrete Fourier transform (DFT).
  • Use the fft function to compute the DFT.
  • Relate the DFT to the Fourier transform.
  • Apply the DFT to analyze an audio signal.


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

Suggested Prework

MATLAB Onramp – a free two-hour introductory tutorial that teaches the essentials of MATLAB.


MATLAB, Symbolic Math Toolbox™


The license for this module is available in the file in this GitHub repository.

Educator Resources

Copyright 2022 The MathWorks, Inc.

Cite As

Emma Smith Zbarsky (2023). Fourier Analysis (, GitHub. Retrieved .

MATLAB Release Compatibility
Created with R2021b
Compatible with R2021b and later releases
Platform Compatibility
Windows macOS Linux
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To view or report issues in this GitHub add-on, visit the GitHub Repository.
To view or report issues in this GitHub add-on, visit the GitHub Repository.