Fast Fourier Transforms (FFT) Explained: The Cooley-Tukey Algorithm
2025-09-18
This post delves into Fast Fourier Transform (FFT) algorithms, focusing on the Cooley-Tukey algorithm. It begins by defining the Discrete Fourier Transform (DFT) and highlighting its naive O(n^2) time complexity. The author then meticulously derives the Cooley-Tukey algorithm, which reduces complexity by breaking down the DFT into smaller DFTs, achieving O(n log n) for inputs of length 2^n. An interactive visualization demonstrates the algorithm's workings. The post also corrects the common misuse of 'FFT' as a synonym for 'DFT', clarifying that FFT refers to the algorithm, not the transform itself.
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