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Pré-Publication, Document De Travail Année : 2017

Reliable verification of digital implemented filters against frequency specifications

Résumé

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 design space explorations. We ensure that there are no false positives but false negative answers may occur. For negative we give a tight bound on the margin of acceptable specifications. Numerical results illustrate the application of our approach to comparison of transfer function design tools and of the various finite-precision implementations.
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Dates et versions

hal-01432000 , version 1 (11-01-2017)
hal-01432000 , version 2 (23-04-2017)
hal-01432000 , version 3 (24-04-2017)

Identifiants

  • HAL Id : hal-01432000 , version 1

Citer

Anastasia Volkova, Christoph Lauter, Thibault Hilaire. Reliable verification of digital implemented filters against frequency specifications. 2017. ⟨hal-01432000v1⟩
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