Fourier Series Visualization Using React Hooks

“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.

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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)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:

References

• Wikipedia
• Purrier Series (Meow) and Making Images Speak
• CodingChallenges by Daniel Shiffman
• Advanced Mathematics – (Engineering Course) 高等数学（工科类）
• Signals & Systems (Second Edition) by Alan V. Oppenheim
• [干货]—Fourier级数

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