Reliable Verification of Digital Implemented Filters Against Frequency Specifications

Reliable implementation of digital filters in finiteprecision 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...

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Bibliographic Details
Main Authors: Volkova, Anastasia, Lauter, Christoph, Hilaire, Thibault
Format: Conference Proceeding
Language:English
Subjects:
Algorithm design and analysis
eigendecomposition
filters
fixed-point arithmetic
floating-point arithmetic
Frequency-domain analysis
interval arithmetic
Positivstellensatz
Reliability
rigorous computation
Signal processing algorithms
Software algorithms
transfer function
Transfer functions
Transforms
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Summary:Reliable implementation of digital filters in finiteprecision 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.
ISSN:1063-6889
DOI:10.1109/ARITH.2017.9