Reliable verification of digital implemented filters against frequency specifications

Abstract : Reliable implementation of digital filters in finite-precision is based on accurate error analysis. However, a small error in the time domain does not guarantee that the implemented filter verifies the initial band specifications in the frequency domain. We propose a novel certified algorithm for the verification of a filter's transfer function, or of an existing finite-precision implementation. We show that this problem boils down to the verification of bounds on a rational function, and further to the positivity of a polynomial. Our algorithm has reasonable runtime efficiency to be used as a criterion in large implementation space explorations. We ensure that there are no false positives but false negative answers may occur. For negative answers we give a tight bound on the margin of acceptable specifications. We demonstrate application of our algorithm to the comparison of various finite-precision implementations of filters already fully designed.
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http://hal.upmc.fr/hal-01432000
Contributeur : Anastasia Volkova <>
Soumis le : lundi 24 avril 2017 - 15:31:26
Dernière modification le : jeudi 20 juillet 2017 - 09:28:27
Document(s) archivé(s) le : mardi 25 juillet 2017 - 16:35:36

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tf_verif_v3.pdf
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  • HAL Id : hal-01432000, version 3

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Anastasia Volkova, Christoph Lauter, Thibault Hilaire. Reliable verification of digital implemented filters against frequency specifications. 24th IEEE Symposium on Computer Arithmetic (ARITH 24), Jul 2017, London, United Kingdom. 〈http://arith24.arithsymposium.org/〉. 〈hal-01432000v3〉

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