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Algorithm and architecture for N-D vector cross-product computation

Algorithm and architecture for N-D vector cross-product computation
Algorithm and architecture for N-D vector cross-product computation
Multi-dimensional vector cross-product has not been studied from the perspective of signal processing so far to the best of our knowledge and hence no effort has been made to develop any generalized algorithm for its hardware implementation. In this paper firstly, we identify the application domain of cross-product in signal processing and then introduce a novel recursive algorithm for generalized nD cross-product computation considering three dimensional (3D) cross product as the fundamental operation. Subsequently a generalized scheme for architecture implementation for nD cross product is proposed based on this algorithm. Secondly, we show that if 4D cross product is used as the fundamental operation for formulating nD cross product problem, then exploiting the inherent mathematical symmetry of 4D cross product it is possible to reduce the total hardware cost of nD cross product significantly at the architecture level (symmetry-based approach). Mathematical models for hardware complexity and operational delay have been formulated both for the generalized and symmetry-based approaches.
Vector Product, Cross product, Blind Source Separation, Independent Component Analysis, Hardware Architecture
1053-587X
812-826
Acharyya, Amit
f7c95a87-04ac-4d13-a74c-0c4d89b1c79c
Maharatna, Koushik
93bef0a2-e011-4622-8c56-5447da4cd5dd
Al-Hashimi, Bashir
0b29c671-a6d2-459c-af68-c4614dce3b5d
Acharyya, Amit
f7c95a87-04ac-4d13-a74c-0c4d89b1c79c
Maharatna, Koushik
93bef0a2-e011-4622-8c56-5447da4cd5dd
Al-Hashimi, Bashir
0b29c671-a6d2-459c-af68-c4614dce3b5d

Acharyya, Amit, Maharatna, Koushik and Al-Hashimi, Bashir (2011) Algorithm and architecture for N-D vector cross-product computation. IEEE Transactions on Signal Processing, 59 (2), 812-826. (doi:10.1109/TSP.2010.2090523).

Record type: Article

Abstract

Multi-dimensional vector cross-product has not been studied from the perspective of signal processing so far to the best of our knowledge and hence no effort has been made to develop any generalized algorithm for its hardware implementation. In this paper firstly, we identify the application domain of cross-product in signal processing and then introduce a novel recursive algorithm for generalized nD cross-product computation considering three dimensional (3D) cross product as the fundamental operation. Subsequently a generalized scheme for architecture implementation for nD cross product is proposed based on this algorithm. Secondly, we show that if 4D cross product is used as the fundamental operation for formulating nD cross product problem, then exploiting the inherent mathematical symmetry of 4D cross product it is possible to reduce the total hardware cost of nD cross product significantly at the architecture level (symmetry-based approach). Mathematical models for hardware complexity and operational delay have been formulated both for the generalized and symmetry-based approaches.

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Published date: March 2011
Keywords: Vector Product, Cross product, Blind Source Separation, Independent Component Analysis, Hardware Architecture
Organisations: Electronic & Software Systems

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Local EPrints ID: 271657
URI: https://eprints.soton.ac.uk/id/eprint/271657
ISSN: 1053-587X
PURE UUID: 5a6fdd78-b9a1-4487-974a-3606ecd96fac

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Date deposited: 27 Oct 2010 11:52
Last modified: 19 Jul 2019 22:12

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Contributors

Author: Amit Acharyya
Author: Koushik Maharatna
Author: Bashir Al-Hashimi

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