discrete Fourier transform

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discrete Fourier transform

[di¦skrēt für·yā ′tranz‚fȯrm]
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

(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.
References in periodicals archive ?
A method that uses the Discrete Fourier Transform (DKr) was recently developed in the literature (see [3]).
The right figure shows the magnitude of the discrete Fourier transform of the corresponding fan beam kernel, [v'.
An Owner's Manual for the Discrete Fourier Transform, SIAM, Philadelphia, 1995.
Fast algorithms for the nonequispaced discrete Fourier transform have already been known a couple of years.
Emphasis on the discrete Fourier transform and on commonly used filter design methods are key features of the text.
The spectral repetition in (c) is a periodic function with discrete Fourier transform shown in (d).
Based on the advanced Multi-Accelerator-Platform-Engine for Baseband (MAPLE-B) technology developed by Freescale, the device is designed to accelerate Turbo and Viterbi decoding, Fast Fourier Transform (FFT), Inverse Fast Fourier Transform (IFFT), Discrete Fourier Transform (DFT) and Inverse Discrete Fourier Transform (IDFT) operations currently performed in FPGA or custom ASIC devices.
He includes special topics and applications such as the discrete Fourier transform, Fraunhofer diffraction and Fourier optics.
Data Transmission by Frequency-Division Multiplexing Using the Discrete Fourier Transform.
A fully embedded modified Discrete Fourier Transform (DFT) burst demodulation scheme provides significant gain in determining head position also reducing the latency of the servo loop.
0 implements the efficient Cooley-Tukey algorithm for computing discrete Fourier transforms, delivering a hardware accelerated flexible, area efficient and fully configurable radix-2 DIT burst I/O FFT.
2003) features new and updated content, including a chapter on magnetic resonance imaging, a revised section on the relationship between the continuum and discrete Fourier transforms, a new section on Grangreat's formula, and an improved description of the gridding method.

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