## Discrete Time Fourier Transform (DTFT)

The*Discrete Time Fourier Transform*(DTFT) can be viewed as the limiting form of the DFT when its length is allowed to approach infinity:

(3.2) |

where denotes the

*continuous*radian frequency variable,

^{3.3}and is the signal amplitude at sample number . The inverse DTFT is

(3.3) |

which can be derived in a manner analogous to the derivation of the inverse DFT [264]. Instead of operating on sampled signals of length (like the DFT), the DTFT operates on sampled signals defined over all integers . Unlike the DFT, 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. Thus, as , a continuous frequency axis must result in the limit along the unit circle. The axis is still finite in length, however, because the time domain remains sampled.

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