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



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.
Next Section:
Fourier Transform (FT) and Inverse
Previous Section:
Overview