Fast Fourier Transforms Part 1: Cooley-Tukey
11 September 2025 Fast Fourier Transforms Part 1: Cooley-Tukey by Connor Boyle tags: mathematicssoftware I’m planning to write a series of posts about fast Fourier transform algorithms. This first post covers the Cooley-Tukey algorithm, which is the original and most well-known FFT algorithm. The Discrete Fourier Transform If \(x\) is a sequence of complex numbers with a length \(\lvert x \rvert\) and a starting index of 0, then the discrete Fourier transform of \(x\), \(\mathcal{F} \{ x \