Image courtesy of Ethan Weil / Wikimedia Commons

http://betterexplained.com/ | Article Link | by Kalid Azad

Rather than jumping into the symbols, let's experience the key idea firsthand. 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.
• Next, we'll refine the analogy into "math-English":

The Fourier Transform takes a time-based pattern, measures each "cycle ingredient" (cycle strength, offset, & rotation speed), and returns the overall "cycle recipe" (frequency graph)

Time for the equations? No! Let's get our hands dirty and experience cycles making patterns with live simulations.

If all goes well, we'll have an aha! moment and intuitively realize why the Fourier Transform is possible. We'll save the detailed math analysis for the follow-up.

This isn't a force-march through the equations, it's the casual stroll I wish I had. Onward! Read more...