Design and implementation of the Walsh–Hadamard transform on a ternary optical computer
- 11 October 2021
- journal article
- research article
- Published by Optica Publishing Group in Applied Optics
- Vol. 60 (30), 9254-9262
- https://doi.org/10.1364/ao.435457
Abstract
Walsh–Hadamard is a commonly used mathematical transformation, a mathematical method for spectrum analysis in the real number domain, which has been widely used in many fields such as digital signal processing, spectral modulation, and image processing. Based on the characteristics of the ternary optical computer with a large number of processor bits, reconfigurable bit functions, and parallel computation, a ternary optical processor with all bits allocated is given, and the transformations T , W , T ′ , W ′ , T 2 of modified signed-digit (MSD) addition are reconfigured. On this basis, by configuring A d d e r N MSD adders on the optical processor, the N -point Walsh–Hadamard transform fast parallel computing approach is given. It requires only 3 × ⌊ N / A d d e r N ⌋ clock cycles to compute the Walsh–Hadamard transform of N points under parallel computing. Furthermore, complexity analysis shows that the clock cycles in an electronic computer are N / 3 times that of in a ternary optical computer under the fully parallel optical computation. The experiment of the Walsh–Hadamard transform with eight points shows that parallel optical computing has more advantages than the conventional electronic computer in fast computing the problems with characteristics of parallel computing. At the same time, it highlights the advantages and potential of ternary optical computers in data-intensive computing.Funding Information
- National Natural Science Foundation of China (61572305, 61672006)
- National Key Research and Development Program of China (2017YFE0117500)
This publication has 23 references indexed in Scilit:
- Hadamard Matrix Design for a Low-Cost Indoor Positioning System in Visible Light CommunicationIEEE Photonics Journal, 2017
- Algorithm of Walsh-Hadamard Transform with Optical ApproachJournal of Information and Computational Science, 2013
- Principles, structures, and implementation of reconfigurable ternary optical processorsScience China Information Sciences, 2011
- Principles and construction of MSD adder in ternary optical computerScience China Information Sciences, 2010
- Carry-free vector-matrix multiplication on a dynamically reconfigurable optical platformApplied Optics, 2010
- Fast Algorithm for Walsh Hadamard Transform on Sliding WindowsIEEE Transactions on Pattern Analysis and Machine Intelligence, 2009
- Ternary Optical Computer ArchitecturePhysica Scripta, 2005
- Asymptotics of the goodness-of-fit test for a partial linear model with randomly censored dataScience China Mathematics, 2003
- Fast algorithm for calculation of both Walsh-Hadamard and Fourier transforms (FWFTs)Electronics Letters, 1989
- A sequency-ordered fast Walsh transformIEEE Transactions on Audio and Electroacoustics, 1972