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International Conference on Tools and Algorithms for the Construction and Analysis of Systems

TACAS 2012: Tools and Algorithms for the Construction and Analysis of Systems pp 33–47Cite as

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A Bit Too Precise? Bounded Verification of Quantized Digital Filters

A Bit Too Precise? Bounded Verification of Quantized Digital Filters

  • Arlen Cox18,
  • Sriram Sankaranarayanan18 &
  • Bor-Yuh Evan Chang18 
  • Conference paper
  • 1628 Accesses

  • 7 Citations

Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7214)

Abstract

Digital filters are simple yet ubiquitous components of a wide variety of digital processing and control systems. Errors in the filters can be catastrophic. Traditionally digital filters have been verified using methods from control theory and extensive testing. We study two alternative verification techniques: bit-precise analysis and real-valued error approximations. In this paper, we empirically evaluate several variants of these two fundamental approaches for verifying fixed-point implementations of digital filters. We design our comparison to reveal the best possible approach towards verifying real-world designs of infinite impulse response (IIR) digital filters. Our study reveals broader insights into cases where bit-reasoning is absolutely necessary and suggests efficient approaches using modern satisfiability-modulo-theories (SMT) solvers.

Keywords

  • Impulse Response
  • Digital Filter
  • Quantization Error
  • Linear Arithmetic
  • Ellipsoidal Domain

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This material is based upon work supported by the National Science Foundation (NSF) under Grant No. 0953941. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of NSF.

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Author information

Authors and Affiliations

  1. University of Colorado, Boulder, USA

    Arlen Cox, Sriram Sankaranarayanan & Bor-Yuh Evan Chang

Authors
  1. Arlen Cox
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  2. Sriram Sankaranarayanan
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  3. Bor-Yuh Evan Chang
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Editor information

Editors and Affiliations

  1. University of California at Santa Cruz, 1156 High Street, 95064, Santa Cruz, CA, USA

    Cormac Flanagan

  2. Fakultät für Ingenieurwesen, Abteilung für Informatik und Angewandte Kognitionswissenschaft, Universität Duisburg-Essen, Lotharstraße 65, 47057, Duisburg, Germany

    Barbara König

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Cox, A., Sankaranarayanan, S., Chang, BY.E. (2012). A Bit Too Precise? Bounded Verification of Quantized Digital Filters. In: Flanagan, C., König, B. (eds) Tools and Algorithms for the Construction and Analysis of Systems. TACAS 2012. Lecture Notes in Computer Science, vol 7214. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28756-5_4

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