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Mathematics

Fast Fourier Transform (FFT)

Quick fact

The FFT reduces the work of computing N frequency components from about N² operations to N log N operations—for a 1-second audio clip with 44,100 samples, that's roughly 600,000 times fewer multiplications.

Why this is interesting

You use the Fast Fourier Transform dozens of times a day—every time you stream a song, take a photo, or make a phone call. But how does your device separate a jumble of noise into beautiful individual frequencies so quickly?