# discrete Fourier transform

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## discrete Fourier transform

[di¦skrēt für·yā ′tranz‚fȯrm] (mathematics)

A generalization of the Fourier transform to finite sets of data; for a function ƒ defined at

*N*data values, 0, 1, 2, …,*N*- 1, the discrete Fourier transform is a function, ƒ, also defined on the set (0, 1, 2, …,*N*- 1, the discrete Fourier transform is a function, ƒ, also defined on the set (0, 1, 2, …,*N*- 1), whose value at*n*is the sum over the variable*r*, from 0 through*N*-1, of the quantity*N*^{-1}ƒ(*r*) exp (-*i*2π*nr*/*N*).## discrete Fourier transform

(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.

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.

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