Fourier Series 101

Mike's Notes

Fourier Series are fun.

• Big picture learning by video is the best approach for me to learn new maths
• Use Wolfram CDF
• Jupyter?

Resources

• https://en.wikipedia.org/wiki/Fourier_series

References

• Reference

Repository

• Home > Ajabbi Research > Library >
• Home > Handbook > 

Last Updated

11/05/2025

Fourier Series 101

By: Mike Peters

On a Sandy Beach: 09/05/2019

Mike is the inventor and architect of Pipi and the founder of Ajabbi.

"In mathematics, a Fourier series is a periodic function composed of harmonically related sinusoids, combined by a weighted summation. With appropriate weights, one cycle (or period) of the summation can be made to approximate an arbitrary function in that interval (or the entire function if it too is periodic). As such, the summation is a synthesis of another function." - Wikipedia

So what does that mean in everyday English?

Mathematicians do have a tendency to make things much more complex than they are.

I recently found this wonderful explanation of a Fourier Series on YouTube. It's well worth a watch.

• Now, the explanation on Wikipedia has made some sense.
• And Mathworld at Wolfram had this to say, which also now makes sense.
• Encyclopedia of Math was not helpful at all, at least to me.
• Just for fun from Wolfram Demonstration. Just play with the buttons and sliders.

Fourier Synthesis for Selected Waveforms by Kenny F Stephens.
Combine up to nine harmonic frequencies to visualise the resulting waveform using Fourier synthesis. Several standard waveforms are provided (sine, square, sawtooth, and triangle)."