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LNS Extensions

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LNS Extensions

If you scare easily, might want to look away... but there's an extension of the LNS that's called the “Multi-Dimensional Logarithmic Number System” (MDLNS). Its theory is based on the “Multiple-Base Number System” (MBNS). MDLNS and MBNS have both found some applications in digital signal processing.

Research papers on LNS extensions: List of research papers on advanced LNS issues:

  1. Vassil Dimitrov, Graham Jullien, Roberto Muscedere, 2012, Multiple-Base Number System: Theory and Applications, (Circuits and Electrical Engineering Book 2), Part of: Circuits and Electrical Engineering (2 books), Jan 24, 2012 https://www.amazon.com/Multiple-Base-Number-System-Applications-Engineering-ebook/dp/B00847CSAG/ (General book with a section on MDLNS.)
  2. V. S. Dimitrov, J. Eskritt, L. Imbert, G. A. Jullien, and W. C. Miller, 2001, The use of the multi-dimensional logarithmic number system in DSP applications, in Proc. 15th IEEE Symp. Comput. Arith., Vail, CO, USA, Jun. 2001, pp. 247–254, https://ieeexplore.ieee.org/document/930126
  3. Vassil S. Dimitrov, Graham A. Jullien, Konrad Walus, 2002, Digital filtering using the multidimensional logarithmic number system, Proceedings Volume 4791, Advanced Signal Processing Algorithms, Architectures, and Implementations XII; (2002) https://doi.org/10.1117/12.452047
  4. H. Li; G.A. Jullien; V.S. Dimitrov; M. Ahmadi; W. Miller, 2002, A 2-digit multidimensional logarithmic number system filterbank for a digital hearing aid architecture, 2002 IEEE International Symposium on Circuits and Systems. Proceedings (Cat. No.02CH37353), https://ieeexplore.ieee.org/abstract/document/1011464
  5. R. Muscedere, V. S. Dimitrov, G. A. Jullien, and W. C. Miller. 2002, Efficient conversion from binary to multi-digit multi-dimensional logarithmic number systems using arrays of range addressable look-up tables, Proc. 21st IEEE International Conference on Application-specific Systems, Architectures and Processors (ASAP), pages 130-138, 2002. https://ieeexplore.ieee.org/document/1030711
  6. Leila Sepahi, 2012, Improved MDLNS Number System Addition and Subtraction by Use of the Novel Co-Transformation, Masters Thesis, University of Windsor, https://scholar.uwindsor.ca/cgi/viewcontent.cgi?article=1139&context=etd
  7. J.-M. Muller, A. Scherbyna and A. Tisserand, 1998, Semi-Logarithmic Number Systems, IEEE Trans. Computers, vol. 47, No. 2, pp. 145-151, 1998, https://ieeexplore.ieee.org/document/663760 PDF: https://perso.ens-lyon.fr/jean-michel.muller/IEEETC-Fev98.pdf
  8. R Muscedere, 2003, Difficult operations in the multi-dimensional logarithmic number system, Ph.D. Thesis, Electrical and Computer Engineering, University of Windsor, https://scholar.uwindsor.ca/cgi/viewcontent.cgi?article=2741&context=etd
  9. J. Eskritt, R. Muscedere, G.AJullien, V.S.Dimitrov and W.C.Miller, 2000, A 2-digit DBNS filter architecture, IEEE Workshop on Signal Processing, Louisiana, Oct. 2000, https://ieeexplore.ieee.org/document/886743
  10. V.S. Dimitrov, G.A. Jullien and W.C. Miller, Theory and applications of the double-base number system, IEEE Trans. an Computers, vol. 48, No. IO, pp. 1098-1 106, Oct. 1999, https://ieeexplore.ieee.org/document/805158
  11. V.S. Dimitrov, S. Sadeghi-Emamchaie, G.A. Jullien and W.C. Miller, 1996, A near canonic double-base number system with applications in DSP, SPlE Conference on Signal Processing Algorithms, vol. 2846, pp.14-25. 1996, https://doi.org/10.1117/12.255433
  12. G. A. Jullien, V. S. Dimitrov, B. Li, W. C. Miller, A..Lee, and M. Ahmadi, 1999, A Hybrid DBNS Processor for DSP, Computation, Proc. Int. IEEE Symp. Circuits and Systems, Orlando, https://www.researchgate.net/publication/221381797_A_hybrid_DBNS_processor_for_DSP_computation
  13. Ewe, Chun Te, 2009, A new number representation for hardware implementation of DSP algorithms, Ph.D. thesis, Imperial College London, https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.501468 (Dual fixed-point number system; has some LNS content.)
  14. Vassil S. Dimitrov, Graham A. Jullien, Konrad Walus, 2002, Digital filtering using the multidimensional logarithmic number system, Proceedings Volume 4791, Advanced Signal Processing Algorithms, Architectures, and Implementations XII; (2002), International Symposium on Optical Science and Technology, 2002, Seattle, WA, United States, https://doi.org/10.1117/12.452047

For more research papers on LNS extensions, see https://www.aussieai.com/research/logarithmic#extend.

 

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