Algorithm and Architecture for N-D Vector Cross-Product Computation

摘要

Multidimensional 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.