When it comes to mathematics, the average person can probably get through most of life well enough with just basic algebra. Some simple statistical concepts would be helpful, and a little calculus couldn’t hurt. But that leaves out a lot of interesting mathematical concepts that really do have applications in everyday life and are just plain fascinating in their own right.

Chief among these concepts is the Fourier transform, which is the key to understanding everything from how JPEGs work to how we can stream audio and video over the Internet. To help get your mind around the concept, [Jez Swanson] has this interactive Fourier transform visualizer that really drives home the important points. This is high-level stuff; it just covers the basic concepts of a Fourier transform, how they work, and what they’re good for in everyday life. There are no equations, just engaging animations that show how any function can be decomposed into a set of sine waves. One shows the approximation of a square wave with a slider to control to vary the number of component sine waves; a button lets you hear the resulting sound getting harsher as it approaches a true square wave. There’s also a great bit on epicycles and SVGs, and one of the best introductions to encoding images as JPEGs that we’ve seen. The best part: all the code behind the demos is available on GitHub.

In terms of making Fourier transform concepts accessible, we’d put [Jez]’s work right up there with such devices as the original Michelson harmonic analyzer, or even its more recent plywood reproduction. Plus the interactive demos were a lot of fun to play with.

[via the Adafruit blog]

Coolest visualization of the Fourier I have seen- kudos for open sourcing the site too

Powerful way of getting a point across.

BTW Nice job on the changes HaD.

I felt the same. I hated doing Fourier transforms but that interactive demo was mind blowing.

There’s me thinking that making a sine wave (or two) fit my data was a hack. Now I know that mathematicians are hackers as well!

Wow. Being able to draw something and see it at work instantly was freaking awesome!

This was an excellent example of clear math explanation and showing practically and simply how it works, without direct equations.

I almost wonder if you couldn’t write an entire book on math like this without equations but just showing practical examples of what different concepts in math fundamental or otherwise can be used for. This might be a very clever way of getting more people to see the beauty and usefulness behind every day math.

Well done to the creator

Eventually one has to come to grips with the gritty nitty, but I have always thought (over the last few years anyway) that an entire semester could be devoted to the unit circle. There’s so much there.

http://www.jezzamon.com/fourier/index.html addres is labeled as game site so our websebse doesnt let go in to this site. Please change your meta data for not blocked by websense :)

All of that and no mention of the Homer Curve? For shame, HaD!

That’s awesome! BTW I’m impressed the site works perfectly well in a mobile browser.

This is super – also of note is Dan Shiffman’s excellent Coding Train on the same subject > https://www.youtube.com/watch?v=MY4luNgGfms

THis one is very well made as well, and goes a bit deaper in the topic:

https://jackschaedler.github.io/circles-sines-signals/index.html

This is amazing work! If the author of this site is reading this, I want to say thank you for your wonderful work!

There’s a quote somewhere that goes something like this – Only the knowledgeable person can explain you something complex as such that it will seem simple enough.. This guy hit the spot there.. he can be a great teacher at some university once he’s done with working for the search company..

I’m glad that he provided links to the maths bits as well..