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CORDIC and SVD implementation in digital hardware

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Processing of matrices, especially inversion, remains a key challenge for contemporary computing machines. Very smart algorithms were proposed many years ago, by the scientists who expected rapid development of digital hardware in the future. Many of those solutions were presumed to work on futuristic parallel devices. CORDIC and Singular Value Decomposition (SVD) are good examples here [1-3]. Eventually recent years have brought the appropriate development of digital hardware and growth of programmable logic devices complexity. There is growing interest in construction of dedicated digital hardware, according to more or less classic concepts [4-7]. This paper describes a study of hardware implementation of Singular Value Decomposition of matrix based on replicated CORDIC modules. The authors focus on comparison of architecture variants in the context of resource allocation, speed and accuracy. Similar works may be found in contemporary literature [8] showing growing interest in practical use of achievements of great mid XX-th century mathematicians. CORDIC and SVD overview CORDIC algorithm (Coordinate Rotation Digital Computer) was proposed by Volder in 1959 [2]. Originally it was used to transform polar to perpendicular coordinates and reverse. Nowadays it is extensively used in digital signal and data processing like DFT [7] and SVD [5]. It is quite universal tool which may be applied in many variants and configurations. In general CORDIC consists in iterative rotations of a vector with a predefined series of constant angles. The angles decrease in a special manner forming a series: 45°, 26.7°, 14°, 7.1°, 3.57° etc. Consecutive rotations are left or right depending on target and actual result. With growing number of rotations n, the increase in accuracy is obtained. This generic schematic may be applied in various modes, depending on needs. In rotation mode, a series of rotations is applied to a vector to reach defined [...]

Aktywowanie palladem elektrody miedziowej stosowanej jako katoda w procesie elektroredukcji kwasu 2-amino-5-nitrobenzenosulfonowego

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Przedstawiono badania nad doborem warunków prowadzenia procesu elektroredukcji kwasu 2-amino-5-nitrobenzenosulfonowego do kwasu 2,5-diaminobenzenosulfonowego z zastosowaniem elektrody miedziowej jako katody. Stwierdzono, że prowadzenie procesu na tej elektrodzie umożliwia 74-proc. redukcję kwasu 2-amino-5-nitrobenzenosulfonowego, przy czym selektywność tworzenia kwasu 2,5-diaminobenzenosulf[...]

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