Why a DFT is usually called an FFT in practice

Practical implementations of the DFT are usually based on one of the Cooley-Tukey ``Fast Fourier Transform'' (FFT) algorithms [14].^8.1 For this reason, the matlab DFT function is called 'fft', and the actual algorithm used depends primarily on the transform length $N$.^8.2 The fastest FFT algorithms generally occur when $N$ is a power of 2. In practical audio signal processing, we routinely zero-pad our FFT input buffers to the next power of 2 in length (thereby interpolating our spectra somewhat) in order to enjoy the power-of-2 speed advantage. Finer spectral sampling is a typically welcome side benefit of increasing $N$ to the next power of 2. A short introduction/overview of some of the better known FFT algorithms, and some pointers to literature and online resources, are given in Appendix A.