JavaScript (React) Fourier Series Visualization

The [Coding Druid] series is my cross-platform programming practice notes. Each episode focuses on a theme (math, physics, electronics, graphics, sound...), implemented in several programming languages. Leveling up warrior, mage, healer, and rogue simultaneously — tanking, DPSing, healing, and escaping all at once.

Coding Druid - Math Chapter - Fourier Series Visualization: JavaScript (React) Implementation

The previous chapter covered trigonometric function visualization, implemented in MaxMSP, JavaScript (React), Python, and Unity:

This chapter is about revisiting the terror once dominated by Fourier — tackling Fourier Series visualization. I can't help but recall that sunset run years ago, when I scored 7 out of 100 on the calculus exam.

When discussing Fourier transform/Fourier analysis, it's usually divided into two parts: Fourier Series and Continuous Fourier Transform. This chapter focuses on Fourier Series.

In mathematics, a Fourier series can be seen as a periodic function composed of a set of sinusoidal curves, combined through weighted summation. (Wikipedia)

For example, a periodic square wave can be decomposed into multiple sine waves. The more sine waves added, the closer the composite curve approximates a square wave.

This article is quite long as it includes the math foundations. Please refer to the original Chinese article for the full mathematical derivations and detailed React SVG implementation.

Final result:

Talk is cheap. Show me the code!

The code for this and most of the [Coding Druid] series is open-sourced here: https://github.com/avantcontra/coding-druid

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Contra