![]() We change our notion of quantity from "single items" (lines in the sand, tally system) to "groups of 10" (decimal) depending on what we're counting. Onward!Ī math transformation is a change of perspective. This isn't a force-march through the equations, it's the casual stroll I wish I had. We'll save the detailed math analysis for the follow-up. If all goes well, we'll have an aha! moment and intuitively realize why the Fourier Transform is possible. Time for the equations? No! Let's get our hands dirty and experience how any pattern can be built with cycles, with live simulations. 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).Here's the "math English" version of the above: How do we get the smoothie back? Blend the ingredients.Why? Recipes are easier to analyze, compare, and modify than the smoothie itself.How? Run the smoothie through filters to extract each ingredient.What does the Fourier Transform do? Given a smoothie, it finds the recipe.Rather than jumping into the symbols, let's experience the key idea firsthand. ![]() Unfortunately, the meaning is buried within dense equations: ![]() The Fourier Transform is one of deepest insights ever made. ![]()
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