Optical computing using optical flip-flops in Fourier processors: use in matrix multiplication and discrete linear transforms

Abstract

An architecture and the algorithms for matrix multiplication using optical flip-flops (OFFs) in optical processors are proposed based on residue arithmetic. The proposed system is capable of processing all elements of matrices in parallel utilizing the information retrieving ability of optical Fourier processors. The employment of OFFs enables bidirectional data flow leading to a simpler architecture and the burden of residue-to-decimal (or residue-to-binary) conversion to operation time can be largely reduced by processing all elements in parallel. The calculated characteristics of operation time suggest a promising use of the system in a real time 2-D linear transform.