Fourier Transforms — ELI5

Imagine you are at a concert. The music hits your ears as one big wave of sound. But that wave is actually dozens of instruments playing at the same time — a bass guitar, a piano, a singer, drums.

A Fourier transform is like having a magic pair of headphones that separates the single wave of music back into each individual instrument. It takes something complicated and shows you all the simple pieces that make it up.

Every sound, picture, or signal you can think of is made up of simple waves added together. A Fourier transform figures out which waves and how much of each:

• Music apps use it to show you those bouncing bars that dance with the beat — each bar is a different wave frequency.
• Noise cancellation headphones use it to find the exact waves of background noise and create opposite waves to cancel them out.
• Doctors use it to turn raw MRI data into images of the inside of your body.
• Phone calls use it to compress your voice so it can travel over the internet without using too much data.

In Python, you do not need to understand the complicated math. You hand your data to a function called FFT (Fast Fourier Transform), and it gives you back the list of simple waves.

Think of it this way: if blending fruit into a smoothie is combining waves into a signal, then the Fourier transform is the machine that can taste a smoothie and tell you exactly how much of each fruit went in.

One thing to remember: The Fourier transform splits complicated signals into simple waves — and that one trick is behind music, medicine, phone calls, and nearly every piece of technology that handles waves.