# 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 -1ƒ(r) exp (-inr / 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.
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Due to its important properties, quaternion discrete Fourier transform (QDFT) and its counterparts quaternion discrete cosine transform (QDCT) and quaternion wavelet transform have been widely used and applied to both single and two dimensional signals in the fields of image processing, radar, robotics and cryptographic.
The discrete Fourier transform is easily to implement and its computational cost is very low.
Enkhbold method are spectrum analysis using Discrete Fourier Transform described in Section 2.
Park, "2D discrete Fourier transform on sliding windows," IEEE Transactions on Image Processing, vol.
Keywords: Circular convolution, circular deconvolution, discrete Fourier transform, circular convolution equations.
The entries of the inverse of a right circulant matrix can be solved using the Inverse Discrete Fourier transform
Keywords: linear models, optimal design, orthogonal designs, discrete Fourier transform, power spectral density, construction
The discrete Fourier transform of the time series h(t) is obtained as
Therefore, even in the absence of guard bands, DWT-OFDM can combat narrowband interference better than the traditional discrete Fourier transform systems and is inherently more robust in terms of inter carrier interference (ICI) which is the most detrimental feature in DFT-OFDM systems .
The computational fluid dynamics visualization and analysis software provides support for unsteady analysis solutions including new tools for time-dependent solutions and discrete Fourier transform.
RN](x), is the inverse discrete Fourier transform of classical cross-spectrum, given by

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