Number systems in modular rings and their applications to 'error-free' computations
| Autor: | Vladimir Chernov |
|---|---|
| Jazyk: | English<br />Russian |
| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Компьютерная оптика, Vol 43, Iss 5, Pp 901-911 (2019) |
| Druh dokumentu: | article |
| ISSN: | 2412-6179 0134-2452 |
| DOI: | 10.18287/2412-6179-2019-43-5-901-911 |
| Popis: | 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. |
| Databáze: | Directory of Open Access Journals |
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