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

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Description/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.