Discrete-time Fourier transform (DTFT), the reverse of the Fourier series, a special case of the Z-transform around the unit circle in the complex plane
Discrete Fourier transform (DFT), occasionally called the finite Fourier transform, the Fourier transform of a discrete periodic sequence (yielding discrete periodic frequencies), which can also be thought of as the DTFT of a finite-length sequence evaluated at discrete frequencies
Fast Fourier transform (FFT), a fast algorithm for computing a Discrete Fourier transform
Fourier-transform spectroscopy, a measurement technique whereby spectra are collected based on measurements of the temporal coherence of a radiative source