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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https://hal.sorbonne-universite.fr/hal-01432000
Contributor : Anastasia Volkova <>
Submitted on : Monday, April 24, 2017 - 3:31:26 PM
Last modification on : Thursday, March 21, 2019 - 2:22:07 PM
Long-term archiving on : Tuesday, July 25, 2017 - 4:35:36 PM

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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. ⟨hal-01432000v3⟩

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