FOURIER TRANSFORM SERIES

From front on, though, these look like circles. If we take a look from the side, they look like sine waves. The thing is, the sine waves it creates are not just regular sine waves, but they’re 3D. Now at the start, I said it splits things into sine waves. This next part looks cool, but also gives you a bit more understanding of what the Fourier transform does. Ok, now let's dig more into the Fourier transform. So in this case, we can use Fourier transforms to get an understanding of the fundamental properties of a wave, and then we can use that for things like compression. This is essentially what MP3s do, except they're more clever about which frequencies they keep and which ones they throw away.

Our end result won't be the same, but it'll sound pretty similar to a person. Then we can compress the sound by ignoring the smaller frequencies. What we can do instead is represent it as a bunch of sine waves.

FOURIER TRANSFORM SERIES

Normally on a computer we store a wave as a series of points. By using a Fourier transform, we can get the important parts of a sound, and only store those to end up with something that's pretty close to the original sound. We can actually use the fact that the wave is pretty similar to our advantage. Move the slider to see how as we add more sine waves, it gets closer and closer to your drawingĪgain, aside from the extra wigglyness, the wave looks pretty similar with just half of the sine waves. This process works like that for any repeating line. When you listen to the wave, you'll hear the sound get lower, because we're removing the higher frequencies. We just need the rest of the small ones to make the wigglyness flatten out. With the slider halfway, we have the general shape of the wave, but it's all wiggly. Visually, you'll notice that actually the first few sine waves are the ones that make the biggest difference. As we add up more and more sine waves the pattern gets closer and closer to the square wave we started with.ĭrag the slider above to play with how many sine waves there are. We need a lot of them this time – technically an infinite amount to perfectly represent it. It might not look like it, but it also can be split up into sine waves. We can also use this process on waves that don't look like they're made of sine waves. We can understand how high or low a sound is, or figure out what note it is. The most obvious example is sound – when we hear a sound, we don’t hear that squiggly line, but we hear the different frequencies of the sine waves that make up the sound.īeing able to split them up on a computer can give us an understanding of what a person actually hears. We usually call them the wave's frequencies. Why? Turns out a lot of things in the real world interact based on these sine waves. In this example, you can almost do it in your head, just by looking at the original wave. The Fourier transform is a way for us to take the combined wave, and get each of the sine waves back out. That is, when we add up the two sine waves we get back the original wave.

This wavy pattern here can be split up into sine waves. First up we're going to look at waves - patterns that repeat over time. Let’s start with some simple examples and work our way up. As usual, the name comes from some person who lived a long time ago called Fourier.

Put simply, the Fourier transform is a way of splitting something up into a bunch of sine waves. If you want to know more about the how, there's some further reading suggestions below! So what is this thing? There's a bunch of interesting maths behind it, but it's better to start with what it actually does, and why you'd want to use it first. We're going to leave the mathematics and equations out of it for now.

Some pointless but cool uses of Fourier transforms.

Some practical uses of Fourier transforms.

I'm going to explain how that animation works, and along the way explain Fourier transforms!īy the end you should have a good idea about And how you can make pretty things with it, like this thing: This is an explanation of what a Fourier transform does, and some different ways it can be useful. An Interactive Introduction to Fourier Transforms An Interactive Introduction to Fourier Transformsįourier transforms are a tool used in a whole bunch of different things.