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.