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).

smoothie-to-recipe

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

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