In
mathematics, the
discrete-time Fourier transform (
DTFT) is a form of
Fourier analysis that is applicable to the uniformly-spaced samples of a continuous function. The term
discrete-time refers to the fact that the transform operates on discrete data (samples) whose interval often has units of time. From only the samples, it produces a function of frequency that is a
periodic summation of the
continuous Fourier transform of the original continuous function. Under certain theoretical conditions, described by the
sampling theorem, the original continuous function can be recovered perfectly from the DTFT and thus from the original discrete samples. The DTFT itself is a continuous function of frequency, but discrete samples of it can be readily calculated via the
discrete Fourier transform (DFT) (see Sampling the DTFT), which is by far the most common method of modern Fourier analysis.