Gibbs Phenomenon in Fourier Series #maths

FULL VIDEO: https://youtu.be/2Dewmw6vp7o
Explore the fascinating world of Fourier Series and waveform synthesis! 🧐

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In this short video, we investigate what happens when we try to represent a square wave using a Fourier Series, following up on the concepts of a triangle wave representation. We start with the fundamental frequency and gradually add higher-order harmonics to approximate the square wave.

Discover the surprising result when dealing with the discontinuities of the square wave: a persistent "ringing" at the jump points! This is a classic mathematical phenomenon known as the Gibbs phenomenon. We demonstrate that no matter how many harmonics are added, this ringing (overshoot and undershoot) always shows up at the discontinuities.

Perfect for students and enthusiasts of signal processing, mathematics, and physics!

Keywords: #fouriertransform #fourierseries #gibbs #gibbsphenomenon #squarewave #trianglewave #harmonics #signalprocessing #mathematics #waveform #maths

Attributions:
The animation was created using ManimCE: The Manim Community Developers. (2025). Manim – Mathematical Animation Framework (Version v0.19.0) [Computer software]. https://www.manim.community/

Видео Gibbs Phenomenon in Fourier Series #maths канала Physics Pageant