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Mathematics

The Fast Fourier Transform (FFT)

Quick fact

The FFT reduces the number of computations from roughly N² (a million for 1000 points) to N log₂ N (about 10,000 for 1000 points) — for a 1-million-point signal, that's more than 100,000 times fewer operations.

Why this is interesting

Every time you stream music, your phone quickly figures out which frequencies are present in the audio, letting it compress and restore the sound. How can millions of data points be processed in the blink of an eye?