 The FFT works by taking a sampled signal and dividing those samples into smaller and smaller groups until there are only two samples per group. It then calculates a discrete Fourier transform for each group by multiplying the second sample by a twiddle factor, then adding the two samples together to produce the first result and subtracting them to produce the second result. The same calculation is repeated on each group's results again and again as the algorithm advances. This core process is therefore repeated many times and can be visualized using a butterfly diagram. A single butterfly, also known as an inner butterfly, will be repeated again and again, interleaving with other butterflies until the FFT for the entire signal has been calculated. To find out more, check out my series of books on how the Fourier transform works by going to howthetransformworks.com slash books.