The Fourier Transform, explained beautifully

At the Better Explained blog, Kalid Azad hits another home run with An Interactive Guide to the Fourier Transform.

Here’s a plain-English metaphor:

• What does the Fourier Transform do? Given a smoothie, it finds the recipe.
• How? Run the smoothie through filters to extract each ingredient.
• Why? Recipes are easier to analyze, compare, and modify than the smoothie itself.
• How do we get the smoothie back? Blend the ingredients.

Here’s the “math English” version of the above:

• The Fourier Transform takes a time-based pattern, measures every possible cycle, and returns the overall “cycle recipe” (the amplitude, offset, & rotation speed for every cycle that was found).

Tip from Kotke, who has a cool Fourier Transform video.