Fourier Transform
Every signal is a sum of pure waves. Pull them apart.
Imagine a song. It sounds complicated, but it's just a stack of single notes ringing at the same time. The Fourier transform is the machine that pulls those notes apart so you can see each one. Drag the sliders to add notes. The bottom is the song. The right side is the list of notes inside it.
What is a Fourier transform, simply?
A way to look at any signal not as a wiggle over time, but as a list of pure tones that, when added together, make that wiggle. The transform is the act of finding that list.
Why is this useful in real life?
It's how MP3 compression, JPEG images, MRI machines, and noise-cancelling headphones all work. Anywhere you want to ignore certain frequencies and keep others, the Fourier transform is doing the heavy lifting.
Why are the bars on the right discrete?
Because we're showing a Fourier *series* — a decomposition of a periodic signal into integer-frequency components. The continuous Fourier transform handles non-periodic signals; same idea, denser spectrum.
Can I share my exact slider configuration?
Yes — the URL updates as you drag. Hit Share to copy it. Whoever opens the link sees your exact wave stack.