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What (who) is discrete Fourier transform - definition
Discrete Fourier transform
![FFT]] algorithm computes one cycle of the DFT and its inverse is one cycle of the DFT inverse.](https://commons.wikimedia.org/wiki/Special:FilePath/From Continuous To Discrete Fourier Transform.gif?width=200 "FFT]] algorithm computes one cycle of the DFT and its inverse is one cycle of the DFT inverse.")
TECHNIQUE USED IN ADVANCED MATHEMATICS
Discrete fourier transform; Generalized discrete Fourier transform; Discrete Fourier Transform; Shifted DFT; Centered DFT; Offset DFT; DTFS; Inverse discrete Fourier transform; Circular convolution theorem; Cross-correlation theorem; Circular cross-correlation
In mathematics, the discrete Fourier transform (DFT) converts a finite sequence of equally-spaced samples of a function into a same-length sequence of equally-spaced samples of the discrete-time Fourier transform (DTFT), which is a complex-valued function of frequency. The interval at which the DTFT is sampled is the reciprocal of the duration of the input sequence.
discrete Fourier transform
TECHNIQUE USED IN ADVANCED MATHEMATICS
Discrete fourier transform; Generalized discrete Fourier transform; Discrete Fourier Transform; Shifted DFT; Centered DFT; Offset DFT; DTFS; Inverse discrete Fourier transform; Circular convolution theorem; Cross-correlation theorem; Circular cross-correlation
<mathematics> (DFT) A Fourier transform, specialized to the
case where the abscissas are integers.
The DFT is central to many kinds of signal processing,
including the analysis and compression of video and sound
information.
A common implementation of the DFT is the {Fast Fourier
Transform} (FFT).
See also discrete cosine transform.
(1997-03-10)
Discrete Fourier transform (general)
GENERALIZATION OF FOURIER TRANSFORM TO ANY RING
Number-theoretic transform; Number theoretic transform; Discrete weighted transform; Discrete Fourier transform (general)
In mathematics, the discrete Fourier transform over an arbitrary ring generalizes the discrete Fourier transform of a function whose values are complex numbers.
