Отрывок: Proof. Indeed, F [w] = F[λv + F [v]] = λF [v] + F2[v] = λF [v] + λ2v = λ(λv + F [v]) = λw . The next result follows from the previous lemmata immediately. Proposition 1. The nonzero vectors ψ (λ) h = λφ (λ2) h + F [ φ (λ2) h ] , where λ = 1, i,−1,−i and 0 ≤ h ≤ K/2, are eigenvectors of the Fourier transform with λ as the corresponding eigenvalue. In other words, these vectors are ψ (1) h = φ (1) h + F [ φ (1) h ] = Xh −X−h + F [Xh]−F [X−h], ψ (−1) h = − φ(1)h + F [ φ (1) h ] = − Xh +X...
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dc.contributor.authorKarkishchenko, A.N.-
dc.contributor.authorMnukhin, V.B.-
dc.date.accessioned2018-05-15 13:18:36-
dc.date.available2018-05-15 13:18:36-
dc.date.issued2018-
dc.identifierDspace\SGAU\20180514\69216ru
dc.identifier.citationKarkishchenko A.N. On eigenvectors of the discrete Fourier transform over finite Gaussian fIelds / A.N. Karkishchenko, V.B. Mnukhin // Сборник трудов IV международной конференции и молодежной школы «Информационные технологии и нанотехнологии» (ИТНТ-2018) - Самара: Новая техника, 2018. - С.1261-1266ru
dc.identifier.urihttp://repo.ssau.ru/handle/Informacionnye-tehnologii-i-nanotehnologii/On-eigenvectors-of-the-discrete-Fourier-transform-over-finite-Gaussian-fields-69216-
dc.descriptionОсновная статьяru
dc.description.abstractThe problem of furnishing orthogonal systems of eigenvectors for the discrete Fourier transform (DFT) is fundamental to image processing with applications in image compression and digital watermarking. This paper studies some properties of such systems for DFT over finite fields that may be considered as ”finite complex planes”. Some applications for multiuser communication schemes are also considered.ru
dc.language.isoenru
dc.publisherНовая техникаru
dc.subjecteigenvectors, discrete Fourier transform, finite fields, Gaussian fields, image compression.ru
dc.titleOn eigenvectors of the discrete Fourier transform over finite Gaussian fieldsru
dc.typeArticleru
dc.textpartProof. Indeed, F [w] = F[λv + F [v]] = λF [v] + F2[v] = λF [v] + λ2v = λ(λv + F [v]) = λw . The next result follows from the previous lemmata immediately. Proposition 1. The nonzero vectors ψ (λ) h = λφ (λ2) h + F [ φ (λ2) h ] , where λ = 1, i,−1,−i and 0 ≤ h ≤ K/2, are eigenvectors of the Fourier transform with λ as the corresponding eigenvalue. In other words, these vectors are ψ (1) h = φ (1) h + F [ φ (1) h ] = Xh −X−h + F [Xh]−F [X−h], ψ (−1) h = − φ(1)h + F [ φ (1) h ] = − Xh +X...-
Располагается в коллекциях: Информационные технологии и нанотехнологии

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