Number systems in modular rings and their applications to "error-free" computations
The article introduces and explores new systems of parallel machine arithmetic associated with the representation of data in the redundant number system with the basis, the formative sequences of degrees of roots of the characteristic polynomial of the second order recurrence. Such number systems ar...
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| Format: | Article |
| Language: | English |
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Samara National Research University
2019-10-01
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| Series: | Компьютерная оптика |
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| Online Access: | http://computeroptics.ru/KO/PDF/KO43-5/430522.pdf |
| _version_ | 1818059960622252032 |
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| author | Vladimir Chernov |
| author_facet | Vladimir Chernov |
| author_sort | Vladimir Chernov |
| collection | DOAJ |
| description | The article introduces and explores new systems of parallel machine arithmetic associated with the representation of data in the redundant number system with the basis, the formative sequences of degrees of roots of the characteristic polynomial of the second order recurrence. Such number systems are modular reductions of generalizations of Bergman's number system with the base equal to the "Golden ratio". The associated Residue Number Systems is described. In particular, a new "error-free" algorithm for calculating discrete cyclic convolution is proposed as an application to the problems of digital signal processing. The algorithm is based on the application of a new class of discrete orthogonal transformations, for which there are effective “multipication-free” implementations. |
| first_indexed | 2024-12-10T13:24:50Z |
| format | Article |
| id | doaj.art-cae47a8ad1854e5ead728adf29a3ca16 |
| institution | Directory Open Access Journal |
| issn | 0134-2452 2412-6179 |
| language | English |
| last_indexed | 2024-12-10T13:24:50Z |
| publishDate | 2019-10-01 |
| publisher | Samara National Research University |
| record_format | Article |
| series | Компьютерная оптика |
| spelling | doaj.art-cae47a8ad1854e5ead728adf29a3ca162022-12-22T01:47:14ZengSamara National Research UniversityКомпьютерная оптика0134-24522412-61792019-10-0143590191110.18287/2412-6179-2019-43-5-901-911Number systems in modular rings and their applications to "error-free" computationsVladimir Chernov0IPSI RAS – Branch of the FSRC “Crystallography and Photonics” RAS, Molodogvardeyskaya 151, 443001, Samara, Russia; Samara National Research University, Moskovskoye shosse 34, 443086, Samara, RussiaThe article introduces and explores new systems of parallel machine arithmetic associated with the representation of data in the redundant number system with the basis, the formative sequences of degrees of roots of the characteristic polynomial of the second order recurrence. Such number systems are modular reductions of generalizations of Bergman's number system with the base equal to the "Golden ratio". The associated Residue Number Systems is described. In particular, a new "error-free" algorithm for calculating discrete cyclic convolution is proposed as an application to the problems of digital signal processing. The algorithm is based on the application of a new class of discrete orthogonal transformations, for which there are effective “multipication-free” implementations.http://computeroptics.ru/KO/PDF/KO43-5/430522.pdfnumber systemmodular arithmeticdiscrete convolutionresidue number systems |
| spellingShingle | Vladimir Chernov Number systems in modular rings and their applications to "error-free" computations Компьютерная оптика number system modular arithmetic discrete convolution residue number systems |
| title | Number systems in modular rings and their applications to "error-free" computations |
| title_full | Number systems in modular rings and their applications to "error-free" computations |
| title_fullStr | Number systems in modular rings and their applications to "error-free" computations |
| title_full_unstemmed | Number systems in modular rings and their applications to "error-free" computations |
| title_short | Number systems in modular rings and their applications to "error-free" computations |
| title_sort | number systems in modular rings and their applications to error free computations |
| topic | number system modular arithmetic discrete convolution residue number systems |
| url | http://computeroptics.ru/KO/PDF/KO43-5/430522.pdf |
| work_keys_str_mv | AT vladimirchernov numbersystemsinmodularringsandtheirapplicationstoerrorfreecomputations |