**"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 MaxMSP, JavaScript (React), Python, and Unity:

This chapter I implement **Fourier Series** curve visualization.

And start with **JavaScript and React** this section.

### 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 $f(x)$ 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**:

As n increases, that is, the sine wave increases, the synthesized waveform gets closer to the square wave.

#### References

**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

- Website: floatbug.com
- Github: avantcontra
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