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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 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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Contributor : Anastasia Volkova <>
Submitted on : Sunday, April 23, 2017 - 7:22:01 PM
Last modification on : Monday, February 10, 2020 - 4:08:04 PM
Document(s) archivé(s) le : Monday, July 24, 2017 - 2:55:32 PM


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  • HAL Id : hal-01432000, version 2


Anastasia Volkova, Christoph Lauter, Thibault Hilaire. Reliable verification of digital implemented filters against frequency specifications. 2017. ⟨hal-01432000v2⟩



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