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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 3254))

Abstract

This paper investigates the Signal-to-Noise Ratio (SNR) performance of the Logarithmic Number System (LNS) representation against the SNR performance of the fixed-point representation. Analytic formulas are presented for the evaluation and the comparison of the two aforementioned representations, and the superiority of the LNS representation is demonstrated. It is shown that the base b of the logarithmic representation has a major impact onto the SNR performance, the SNR dependance on the variations of the standard deviation of the analog signal, and the memory requirements for logarithmic addition and subtraction. In addition, step-by-step procedures are introduced to compute the base b that optimizes all these performance measures.

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References

  1. Swartzlander, E., Alexopoulos, A.: The sign/logarithm number system. IEEE Transactions on Computers 24, 1238–1242 (1975)

    Article  MATH  MathSciNet  Google Scholar 

  2. Arnold, M.G., Bailey, T.A., Cowles, J.R., Winkel, M.D.: Applying features of the IEEE 754 to sign/logarithm arithmetic. IEEE Transactions on Computers 41, 1040–1050 (1992)

    Article  Google Scholar 

  3. Arnold, M.G., Walter, C.: Unrestricted faithful rounding is good enough for most LNS applications. In: Proceedings of the 15th IEEE Symposium on Computer Arithmetic (ARITH15), Vail, CO, June 2001, pp. 237–246 (2001)

    Google Scholar 

  4. Paliouras, V., Stouraitis, T.: Low-power properties of the Logarithmic Number Syste. In: Proceedings of 15th Symposium on Computer Arithmetic ARITH15, Vail, CO, June 2001, pp. 229–236 (2001)

    Google Scholar 

  5. Paliouras, V.: Optimization of LNS Operations for Embedded Signal Processing Applications. In: Proceedings of IEEE International Symposium on Circuits and Systems (ISCAS 2002), Scottsdale, AZ, pp. 744–747 (2002)

    Google Scholar 

  6. Kwa, S.W., Engel, G.L., Morley, R.E.: Quantization Noise Analysis of Sign/Logarithm Data Encoders When Excited by Speech or Sinusoidal Inputs. IEEE Transactions on Signal Processing 48, 3578–3581 (2000)

    Article  MathSciNet  Google Scholar 

  7. Jayant, N., Noll, P.: Digital Coding of Waveforms. Prentice-Hall, Englewood Cliffs (1984)

    Google Scholar 

  8. Arnold, M.G.: Iterative Method for Logarithmic Subtraction. In: Proceedings of the Application-Specific Systems, Architectures, and Processoros (ASAP 2003), The Hague, Netherlands, June 24-26, pp. 315–325 (2003)

    Google Scholar 

  9. Stouraitis, T.: Logarithmic Number System: Theory, Analysis and Design. PhD thesis, University of Florida (1986)

    Google Scholar 

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© 2004 Springer-Verlag Berlin Heidelberg

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Vouzis, P., Paliouras, V. (2004). Optimal Logarithmic Representation in Terms of SNR Behavior. In: Macii, E., Paliouras, V., Koufopavlou, O. (eds) Integrated Circuit and System Design. Power and Timing Modeling, Optimization and Simulation. PATMOS 2004. Lecture Notes in Computer Science, vol 3254. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30205-6_78

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  • DOI: https://doi.org/10.1007/978-3-540-30205-6_78

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-23095-3

  • Online ISBN: 978-3-540-30205-6

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