Fast Fourier Transforms Part 1: Cooley-Tukey
12 hours ago
- #algorithms
- #mathematics
- #FFT
- Connor Boyle announces a series on fast Fourier transform (FFT) algorithms, starting with the Cooley-Tukey algorithm.
- The Cooley-Tukey algorithm reduces the time complexity of the discrete Fourier transform (DFT) from O(n²) to O(n log n) for sequences of composite length.
- The algorithm works by recursively breaking down the DFT into smaller DFTs when the sequence length can be factored into smaller integers.
- The post includes mathematical formulations and visualizations to explain the algorithm's efficiency and application.
- Boyle criticizes the common misuse of 'FFT' to refer to the DFT output rather than the algorithm used to compute it, emphasizing the distinction between the two.
- The post concludes with a note on the limitations of the Cooley-Tukey algorithm for sequences of prime length and hints at future posts on alternative algorithms like Bluestein's.