22 March 2018 - 15h00
Towards reliable implementation of digital filters. How digital signal processing and computer arithmetic meet (candidate poste MCF)
by Anastasia Volkova from LIP, ENS de Lyon
Abstract: This work focuses on the improvement of numerical algorithms for the rigorous design of linear digital filters for signal processing.
Assuming exact real arithmetic, the theory of these filters has been firmly established for a long time.
However, many problems arise when confronted with the practice: the coefficients of the filters are represented on a small number of bits, the arithmetic operations are not exact, etc. We wish, at the same time, for the implementation to be efficient in terms of computation speed, circuit area, power consumption, etc. In practice, designers often find solutions via empirical approaches, and validate them with tests that are far from exhaustive. This way of implementing the filters is ideal for certain applications such as telecommunications, but not for critical applications for example related to transport and aeronautics.
In this work we cover the whole chain of linear filter design: from transfer functions to reliable and efficient software/hardware implementations.
We provide a new methodology for error analysis of linear filter algorithms from the point of view of computer arithmetic. The proposed error analysis is based on the combination of techniques such as Floating Point Error Analysis, Interval Arithmetic, and Multiple-Precision Implementations. We provide basic algorithmic blocks for efficient FPGA implementations. All implementations are reliable (in terms of precision constraints) by construction.
Finally, we integrate our approach in a code generator to allow the automatic and reliable implementation of any digital linear filter algorithm.