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.*