FAST FOURIER TRANSFORMS
The Fast Fourier Transform (FFT) is nothing more than a computationally efficient version of the Discrete Fourier Transform (DFT): The most common approach to achieving this efficiency is to use a decimation-in-time strategy that benefits from the non-linear computational complexity of the transform:



The Radix-2 and Radix-4 algorithms are extremely popular due to their computational efficiency and relatively simple implementations:


A definitive work on the computational complexity of FFT algorithms, including benchmarks and software, can be found at parallel FFTs.