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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 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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https://hal.sorbonne-universite.fr/hal-01432000
Contributor : Anastasia Volkova <>
Submitted on : Wednesday, January 11, 2017 - 2:07:56 PM
Last modification on : Monday, February 10, 2020 - 4:08:04 PM
Document(s) archivé(s) le : Friday, April 14, 2017 - 4:45:24 PM

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  • HAL Id : hal-01432000, version 1

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

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