The Discrete Time Fourier Transform (DTFT) can be viewed as the limiting form of the DFT when its length is allowed to approach infinity:
The inverse DTFT is
Instead of operating on sampled signals of length (like the DFT), the DTFT operates on sampled signals defined over all integers . As a result, the DTFT frequencies form a continuum. That is, the DTFT is a function of continuous frequency , while the DFT is a function of discrete frequency , . The DFT frequencies , , are given by the angles of points uniformly distributed along the unit circle in the complex plane (see Fig.6.1). Thus, as , a continuous frequency axis must result in the limit along the unit circle in the plane. The axis is still finite in length, however, because the time domain remains sampled.