An interactive introductionFourier Transforms, Visually

Any signal — a sound, an image, a stock price — can be rebuilt out of nothing but simple sine waves. That single idea is the Fourier transform. This is a hands-on walk through what it actually means, one dial at a time.

Who this is for: you don't need calculus to get the intuition, but the real formulas are included at each step for when you want them. Every chapter has something you can drag, and nothing here is a video — it's all live and running in your browser.

Where you're headed

The chapters build on each other in order:

CHAPTER 1

Sine Waves 101

Amplitude, frequency, and phase — the three knobs that define every sine wave.
CHAPTER 2

Adding Waves Together

Stack two or more sine waves and watch a new, stranger shape emerge.
CHAPTER 3

Fourier Series

Any repeating shape — even a square wave — is a sum of sine waves. Build one out of harmonics.
CHAPTER 4

Circles Drawing Waves

The famous spinning-circles (epicycles) picture of a Fourier series, drawn live.
CHAPTER 5

Time vs. Frequency

The same signal, two views: a wiggle over time, or a bar chart of which frequencies it contains.
CHAPTER 6

Sampling & Aliasing

Computers can't store a continuous wave. What happens when you only take snapshots of it?
CHAPTER 7

The DFT & FFT

The actual algorithm: turn a list of samples into a spectrum, and why the FFT makes it fast.
CHAPTER 8

Images: The 2D FFT

The same idea in two dimensions — see an image's frequency spectrum, then blur or sharpen it by dragging a filter.
CHAPTER 9

Practical Applications

Audio EQ, JPEG, MRI, radio, WiFi, structural engineering — where all of this actually runs.