Matches in DBpedia 2016-04 for { <http://dbpedia.org/resource/Fractional_Fourier_transform> ?p ?o }
- 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.".
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- Fractional_Fourier_transform wikiPageExternalLink FRFT.
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- Fractional_Fourier_transform wikiPageWikiLink Automorphism.
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- Fractional_Fourier_transform wikiPageWikiLink Category:Time–frequency_analysis.
- Fractional_Fourier_transform wikiPageWikiLink Chirp.
- Fractional_Fourier_transform wikiPageWikiLink Chirp_Z-transform.
- Fractional_Fourier_transform wikiPageWikiLink Chirplet_transform.
- Fractional_Fourier_transform wikiPageWikiLink Cone-shape_distribution_function.
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- Fractional_Fourier_transform wikiPageWikiLink Convolution.
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- Fractional_Fourier_transform wikiPageWikiLink Dirac_delta_function.
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- Fractional_Fourier_transform wikiPageWikiLink Edward_Condon.
- Fractional_Fourier_transform wikiPageWikiLink Fermion.
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- Fractional_Fourier_transform wikiPageWikiLink Filter_design.
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- Fractional_Fourier_transform wikiPageWikiLink Frequency.
- Fractional_Fourier_transform wikiPageWikiLink Function_space.
- Fractional_Fourier_transform wikiPageWikiLink Harmonic_analysis.
- Fractional_Fourier_transform wikiPageWikiLink Hermite_polynomials.
- Fractional_Fourier_transform wikiPageWikiLink Integer.
- Fractional_Fourier_transform wikiPageWikiLink Integral_transform.
- Fractional_Fourier_transform wikiPageWikiLink Iterated_function.
- Fractional_Fourier_transform wikiPageWikiLink Limit_of_a_function.
- Fractional_Fourier_transform wikiPageWikiLink Linear_canonical_transformation.
- Fractional_Fourier_transform wikiPageWikiLink Linear_map.
- Fractional_Fourier_transform wikiPageWikiLink Low-pass_filter.
- Fractional_Fourier_transform wikiPageWikiLink Mathematics.
- Fractional_Fourier_transform wikiPageWikiLink Mehler_kernel.
- Fractional_Fourier_transform wikiPageWikiLink Norbert_Wiener.
- Fractional_Fourier_transform wikiPageWikiLink Parity_(mathematics).
- Fractional_Fourier_transform wikiPageWikiLink Pattern_recognition.
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- Fractional_Fourier_transform wikiPageWikiLink Quantum_circuit.
- Fractional_Fourier_transform wikiPageWikiLink Radon_transform.
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- Fractional_Fourier_transform wikiPageWikiLink Signal_processing.
- Fractional_Fourier_transform wikiPageWikiLink Sinc_function.
- Fractional_Fourier_transform wikiPageWikiLink Supersymmetry.
- Fractional_Fourier_transform wikiPageWikiLink Time–frequency_analysis.
- Fractional_Fourier_transform wikiPageWikiLink Trigonometric_functions.
- Fractional_Fourier_transform wikiPageWikiLink Unitary_operator.
- Fractional_Fourier_transform wikiPageWikiLink Wavelet_transform.
- Fractional_Fourier_transform wikiPageWikiLink Wolfram_Demonstrations_Project.
- Fractional_Fourier_transform wikiPageWikiLink Z-transform.
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- Fractional_Fourier_transform wikiPageWikiLinkText "''rotations in phase space''".
- Fractional_Fourier_transform wikiPageWikiLinkText "Fractional Fourier transform".
- Fractional_Fourier_transform wikiPageWikiLinkText "fractional Fourier transform".
- Fractional_Fourier_transform wikiPageWikiLinkText "fractional Fourier".
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- Fractional_Fourier_transform subject Category:Articles_containing_video_clips.
- 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 hypernym Family.
- Fractional_Fourier_transform type Redirect.
- Fractional_Fourier_transform type Transform.
- Fractional_Fourier_transform type Thing.
- 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 seeAlso Generalizations_of_Pauli_matrices.
- Fractional_Fourier_transform seeAlso Shift_matrices.
- Fractional_Fourier_transform sameAs Q4817582.
- Fractional_Fourier_transform sameAs تبدیل_فوریه_کسری.
- Fractional_Fourier_transform sameAs Transformada_fracional_de_Fourier.