When it comes to compressing & analyzing audio/video/etc, among other tasks including larger/fancier blurs, its useful to convert between a sampled signal & the sine waves making it up.

For this we use an algorithm called The Fast Fourier Transform!

It recursively splits the input samples up by odd & even indices, so it can take advantage of the cyclic nature of the relevant formula to algebraicly simplify the task into something that's reasonable to calculate.

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