Cooley-Tukey FFT and its variants - 2025.1 English - XD100

Vitis Tutorials: AI Engine Development (XD100)

Document ID
XD100
Release Date
2025-08-25
Version
2025.1 English

Usually, when the literature refers the FFT algorithm, it refers to a version of the algorithm proposed by Cooley and Tukey that is usually applied to signals that have a number of points equal to a power of two. To give a general idea, the original algorithm allows to decompose the computation of the discrete Fourier transform of a function of \(N\) points when \(N\) is a composite number $(N=N_1 \cdot N_2)\(, by computing \)N_1$ DFTs of size $N_2\(. This algorithm is often used recursively on functions having a power of 2 as number of points in order to perform a series of simple few-points DFTs, achieving a \)O(N\cdot log_2(N))$ (also called loglinear) computational complexity.