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- Fractional_Fourier_transform abstract "In mathematics, in the area of harmonic analysis, the fractional Fourier transform (FRFT) is a family of linear transformations generalizing the Fourier transform. It can be thought of as the Fourier transform to the n-th power, where n need not be an integer — thus, it can transform a function to any intermediate domain between time and frequency. Its applications range from filter design and signal analysis to phase retrieval and pattern recognition.The FRFT can be used to define fractional convolution, correlation, and other operations, and can also be further generalized into the linear canonical transformation (LCT). An early definition of the FRFT was introduced by Condon, by solving for the Green's function for phase-space rotations, and also by Namias, generalizing work of Wiener on Hermite polynomials.However, it was not widely recognized in signal processing until it was independently reintroduced around 1993 by several groups. Since then, there has been a surge of interest in extending Shannon's sampling theorem for signals which are band-limited in the Fractional Fourier domain.A completely different meaning for "fractional Fourier transform" was introduced by Bailey and Swartztrauber as essentially another name for a z-transform, and in particular for the case that corresponds to a discrete Fourier transform shifted by a fractional amount in frequency space (multiplying the input by a linear chirp) and evaluating at a fractional set of frequency points (e.g. considering only a small portion of the spectrum). (Such transforms can be evaluated efficiently by Bluestein's FFT algorithm.) This terminology has fallen out of use in most of the technical literature, however, in preference to the FRFT. The remainder of this article describes the FRFT.See also the chirplet transform for a related generalization of the Fourier transform.".
- Fractional_Fourier_transform wikiPageExternalLink FractionalFourierTransform.
- Fractional_Fourier_transform wikiPageExternalLink 11.pdf..
- Fractional_Fourier_transform wikiPageExternalLink FRFT.
- Fractional_Fourier_transform wikiPageExternalLink tfd.sourceforge.net.
- Fractional_Fourier_transform wikiPageExternalLink wileybook.html.
- Fractional_Fourier_transform wikiPageID "1103773".
- Fractional_Fourier_transform wikiPageRevisionID "591356560".
- Fractional_Fourier_transform hasPhotoCollection Fractional_Fourier_transform.
- Fractional_Fourier_transform subject Category:Fourier_analysis.
- Fractional_Fourier_transform subject Category:Integral_transforms.
- Fractional_Fourier_transform subject Category:Time–frequency_analysis.
- Fractional_Fourier_transform comment "In mathematics, in the area of harmonic analysis, the fractional Fourier transform (FRFT) is a family of linear transformations generalizing the Fourier transform. It can be thought of as the Fourier transform to the n-th power, where n need not be an integer — thus, it can transform a function to any intermediate domain between time and frequency.".
- Fractional_Fourier_transform label "Fractional Fourier transform".
- Fractional_Fourier_transform label "Transformada fracional de Fourier".
- Fractional_Fourier_transform label "分數傅立葉變換".
- Fractional_Fourier_transform sameAs Transformada_fracional_de_Fourier.
- Fractional_Fourier_transform sameAs m.0468f8.
- Fractional_Fourier_transform sameAs Q4817582.
- Fractional_Fourier_transform sameAs Q4817582.
- Fractional_Fourier_transform wasDerivedFrom Fractional_Fourier_transform?oldid=591356560.
- Fractional_Fourier_transform isPrimaryTopicOf Fractional_Fourier_transform.