Computing the Worst-Case Peak Gain of Digital Filter in Interval Arithmetic

Anastasia Volkova 1 Christoph Lauter 1 Thibault Hilaire 1
1 PEQUAN - Performance et Qualité des Algorithmes Numériques
LIP6 - Laboratoire d'Informatique de Paris 6
Abstract : The Worst-Case Peak Gain (WCPG) of a Linear Time Invariant (LTI) filter is used to determine the output interval of a filter and in error propagation analysis. Previously, the authors presented an approach on the computation of the WCPG in arbitrary precision. However, the approach considered filter coefficients to be exact. We consider now LTI filters which have coefficients that are rounded prior to implementation. To provide a reliable filter implementation, these rounding errors must be taken into account in the WCPG computation. In this work we represent rounded coefficients as intervals with small radii and adapt the WCPG computation for the interval case.
Keywords : worst-case peak gain digital filters interval arithmetic
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Anastasia Volkova, Christoph Lauter, Thibault Hilaire. Computing the Worst-Case Peak Gain of Digital Filter in Interval Arithmetic. 17th International Symposium on Scientific Computing, Computer Arithmetics and Verified Numerics. , Sep 2016, Uppsala, Sweden. ⟨hal-01347634⟩

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