“Coding Druid” series is my horizontal programming practice notes, each part around a topic like mathematical, physics, electronic, graphics, sound, etc., implemented in several programming languages.

Coding Druid
Part: Math
Chapter: Fourier Series
Section: Javascript (React)

In the previous Chapter, I visualized Trigonometric function (Sine and unit circle) separately using MaxMSPJavaScript (React)Python, and Unity:

This chapter I implement Fourier Series curve visualization.

### Mathematics

In mathematics, a Fourier series is a periodic function composed of harmonically related sinusoids, combined by a weighted summation.
(wikipedia)

And it can be explained as expressing a repetitive curve as sum of sine curves. (Purrier Series (Meow) and Making Images Speak)

For example, suppose there is a square wave, and it can be interpreted into sine waves:

The more sine waves you have, the preciser square wave you will get.

Now Let’s see the process of Fourier series expansion.

Assume that `f(x)` is a periodic function for `x∈[−π,π]`, and its period is `2π` .
Its expression:

Then its trigonometric expression of Fourier series (sine-cosine form) is like:

And Fourier coefficients of f(x)f(x) is:

Finally:

Above content refers to “Advanced Mathematics – (Engineering Course) (Vol.2)”

And the original Fourier series definition and detail explanation will be found in wikipedia.

Sums of lengths the first four terms, and showing how the approximation to a square wave:

### Visualization

Now to visualize this curve using React.
I have forked and refactored a sine visualization:

I will do the Fourier stuff on the basis of above code.

It’s really clear to write code using React:

Still use React Hooks to update the data binded with Components:

Final curve:

Talk is cheap. Show me the code!

This demo and the Coding Druid series is open source here:
https://github.com/avantcontra/coding-druid

You can find more resources in my site floatbug.com.

You may buy me a coffee in my Patreon. There are many articles, patches, source code and some advanced Patron-only content there.

Also you can get some free patches/codes in Gumroad shop.

Your encouragement is my driving energy!

Cheers~

Contra