In mathematics

Mathematics

Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

, the discrete-time Fourier transform (DTFT) is one of the specific forms of Fourier analysis. As such, it transforms one function into another, which is called the frequency domain

Frequency domain

In electronics, control systems engineering, and statistics, frequency domain is a term used to describe the domain for analysis of mathematical functions or signals with respect to frequency, rather than time....

representation, or simply the "DTFT", of the original function (which is often a function in the time-domain). But the DTFT requires an input function that is discrete. Such inputs are often created by digitally sampling

Sampling

Sampling may refer to:*Sampling , converting a continuous signal into a discrete signal*Sampling , converting continuous colors into discrete color components*Sampling , re-using portions of sound recordings in a piece...

 a continuous function, like a person's voice.

The DTFT frequency-domain representation is always a periodic function.