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Analysis of Finite Word-Length Effects in Fixed-Point Systems

  • D. Menard
  • G. Caffarena
  • J. A. Lopez
  • D. Novo
  • O. Sentieys
Chapter

Abstract

Systems based on fixed-point arithmetic, when carefully designed, seem to behave as their infinite precision analogues. Most often, however, this is only a macroscopic impression: finite word-lengths inevitably approximate the reference behavior introducing quantization errors, and confine the macroscopic correspondence to a restricted range of input values. Understanding these differences is crucial to design optimized fixed-point implementations that will behave “as expected” upon deployment. Thus, in this chapter, we survey the main approaches proposed in literature to model the impact of finite precision in fixed-point systems. In particular, we focus on the rounding errors introduced after reducing the number of least-significant bits in signals and coefficients during the so-called quantization process.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • D. Menard
    • 1
  • G. Caffarena
    • 2
  • J. A. Lopez
    • 3
  • D. Novo
    • 4
  • O. Sentieys
    • 5
  1. 1.INSA Rennes, IETR, UBLRennesFrance
  2. 2.CEU San Pablo UniversityMadridSpain
  3. 3.ETSITUniversidad Politécnica de MadridMadridSpain
  4. 4.CNRSLIRMMMontpellierFrance
  5. 5.INRIAUniversity of Rennes IRennesFrance

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