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

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Handbook of Signal Processing Systems

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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Authors and Affiliations

  1. INSA Rennes, IETR, UBL, Rennes, France

    D. Menard

  2. CEU San Pablo University, Madrid, Spain

    G. Caffarena

  3. ETSIT, Universidad Politécnica de Madrid, Madrid, Spain

    J. A. Lopez

  4. CNRS, LIRMM, Montpellier, France

    D. Novo

  5. INRIA, University of Rennes I, Rennes, France

    O. Sentieys

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  1. D. Menard
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  4. D. Novo
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  5. O. Sentieys
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Correspondence to D. Menard .

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  1. Department of ECE and UMIACS, University of Maryland, College Park, MD, USA

    Shuvra S. Bhattacharyya

  2. Leiden Embedded Research Center, Leiden University Leiden Institute Advanced Computer Science, Leiden, The Netherlands

    Ed F. Deprettere

  3. RWTH Aachen University Software for Systems on Silicon, Aachen, Germany

    Rainer Leupers

  4. Department of Pervasive Computing, Tampere University of Technology, Tampere, Finland

    Jarmo Takala

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Menard, D., Caffarena, G., Lopez, J.A., Novo, D., Sentieys, O. (2019). Analysis of Finite Word-Length Effects in Fixed-Point Systems. In: Bhattacharyya, S., Deprettere, E., Leupers, R., Takala, J. (eds) Handbook of Signal Processing Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-91734-4_29

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