discrete Fourier transform


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 -1ƒ(r) exp (-inr / N).

discrete Fourier transform

(mathematics)(DFT) A Fourier transform, specialized to thecase where the abscissas are integers.

The DFT is central to many kinds of signal processing,including the analysis and compression of video and soundinformation.

A common implementation of the DFT is the Fast Fourier Transform (FFT).

See also discrete cosine transform.