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High Quality Content by WIKIPEDIA articles! In the mathematical field of harmonic analysis, the continuous Fourier transform has very precise relations with Fourier series. It is also closely related to the discrete-time Fourier transform (DTFT) and the discrete Fourier transform (DFT). The Fourier transform can be applied to time-discrete or time-periodic signals using the -Dirac formalism. In fact the Fourier series, the DTFT and the DFT can be derived all from the general continuous Fourier transform. They are, from a theoretical point of view, particular cases of the Fourier transform. In signal theory and digital signal processing (DSP), the DFT (implemented as fast Fourier transform) is extensively used to calculate approximations to the spectrum of a continuous signal, knowing only a sequence of sampled points. The relations between DFT and Fourier transform are in this case essential.