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...
Полная запись метаданных
Поле DC | Значение | Язык |
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dc.contributor.author | Karkishchenko, A.N. | - |
dc.contributor.author | Mnukhin, V.B. | - |
dc.date.accessioned | 2018-05-15 13:18:36 | - |
dc.date.available | 2018-05-15 13:18:36 | - |
dc.date.issued | 2018 | - |
dc.identifier | Dspace\SGAU\20180514\69216 | ru |
dc.identifier.citation | Karkishchenko 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.1261-1266 | ru |
dc.identifier.uri | http://repo.ssau.ru/handle/Informacionnye-tehnologii-i-nanotehnologii/On-eigenvectors-of-the-discrete-Fourier-transform-over-finite-Gaussian-fields-69216 | - |
dc.description | Основная статья | ru |
dc.description.abstract | The 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.iso | en | ru |
dc.publisher | Новая техника | ru |
dc.subject | eigenvectors, discrete Fourier transform, finite fields, Gaussian fields, image compression. | ru |
dc.title | On eigenvectors of the discrete Fourier transform over finite Gaussian fields | ru |
dc.type | Article | ru |
dc.textpart | 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... | - |
Располагается в коллекциях: | Информационные технологии и нанотехнологии |
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paper_165.pdf | Основная статья | 1.06 MB | Adobe PDF | Просмотреть/Открыть |
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