Analysis of Finite Word-Length Effects in Fixed-Point 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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Submitted on : Monday, February 4, 2019 - 4:53:48 PM
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Daniel Ménard, Gabriel Caffarena, Juan Antonio Lopez, David Novo, Olivier Sentieys. Analysis of Finite Word-Length Effects in Fixed-Point Systems. Shuvra S. Bhattacharyya. Handbook of Signal Processing Systems, pp.1063-1101, 2019, 978-3-319-91733-7. ⟨10.1007/978-3-319-91734-4_29⟩. ⟨hal-01941888⟩

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