Circuits and Systems, 2014, 5, 274-291 Published Online November 2014 in SciRes. http://www.scirp.org/journal/cs http://dx.doi.org/10.4236/cs.2014.511029 How to cite this paper: Mishra, B., Kochery, M., Wilson, P. and Wilcock, R. (2014) A Novel Signal Processing Coprocessor for n-Dimensional Geometric Algebra Applications. Circuits and Systems, 5, 274-291. http://dx.doi.org/10.4236/cs.2014.511029 A Novel Signal Processing Coprocessor for n-Dimensional Geometric Algebra Applications Biswajit Mishra 1 , Mittu Kochery 2 , Peter Wilson 3 , Reuben Wilcock 3 1 VLSI & Embedded Research Lab, Dhirubhai Ambani Institute of Information and Communication Technology (DAIICT), Gandhinagar, India 2 Advanced RISC Machines Ltd. (ARM), Cambridge, UK 3 School of Electronics and Computer Science, University of Southampton, Southampton, UK Email: biswajit_mishra@daiict.ac.in , mittu.kocherry@arm.com , prw@ecs.soton.ac.uk , rw3@ecs.soton.ac.uk Received 26 August 2014; revised 25 September 2014; accepted 8 October 2014 Copyright © 2014 by authors and Scientific Research Publishing Inc. This work is licensed under the Creative Commons Attribution International License (CC BY). http://creativecommons.org/licenses/by/4.0/ Abstract This paper provides an implementation of a novel signal processing co-processor using a Geome- tric Algebra technique tailored for fast and complex geometric calculations in multiple dimensions. This is the first hardware implementation of Geometric Algebra to specifically address the issue of scalability to multiple (1 - 8) dimensions. This paper presents a detailed description of the imple- mentation, with a particular focus on the techniques of optimization used to improve performance. Results are presented which demonstrate at least 3x performance improvements compared to previously published work. Keywords Geometric Algebra, Clifford Algebra, FPGA, GA Co-Processor 1. Introduction Geometric Algebra (GA) is a relatively new area of mathematics which finds applications in many different fields of research particularly in computer graphics and robotics. Traditional matrix-based methods of defining geometrical objects using vectors to characterize constructions are described in [1] [2]. A key aspect highlighted in these methods is the concept that geometric subspaces could be subject to direct computation if they were considered as basic computational elements. GA has the potential for this, as it unifies the geometric subspaces with well-defined products that have a direct geometric significance [3]-[7]. One of the issues for typical re-