Supervision : Jean-Claude BAJARD

Co-supervision : HILAIRE Thibault, LAUTER Christoph

Towards a unified code generator for libms and filters

In this thesis we develop approaches for improvement of the numerical behavior of digital filters with focus on the impact of accuracy of the computations. This work is done in the context of a reliable hardware/software code generator for Linear Time-Invariant (LTI) digital filters, in particular with Infinite Impulse Response (IIR). With this work we consider problems related to the implementation of LTI filters in Fixed-Point arithmetic while taking into account finite precision of the computations necessary for the transformation from filter to code. This point is important in the context of filters used in embedded critical systems such as autonomous vehicles. We provide a new methodology for the error analysis when linear filter algorithms are investigated from a computer arithmetic aspect. In the heart of this methodology lies the reliable evaluation of the Worst-Case Peak Gain measure of a filter, which is the l1 norm of its impulse response. The proposed error analysis is based on a combination of techniques such as rigorous Floating-Point error analysis, interval arithmetic and multiple precision implementations. This thesis also investigates the problematic of compromise between hardware cost (e.g. area) and the precision of computations during the implementation on FPGA. We provide basic brick algorithms for an automatic solution of this problem. Finally, we integrate our approaches into an open-source unifying framework to enable automatic and reliable implementation of any LTI digital filter algorithm.

2015-2020 Publications

• 2020
  • Ch. Lauter, A. Volkova : “A Framework for Semi-Automatic Precision and Accuracy Analysis for Fast and Rigorous Deep Learning”, IEEE Symposium on Computer Arithmetic (ARITH), Portland, United States (2020)
  • A. Volkova, Th. Hilaire, Ch. Lauter : “Arithmetic approaches for rigorous design of reliable Fixed-Point LTI filters”, IEEE Transactions on Computers, vol. 69 (4), pp. 489-504, (Institute of Electrical and Electronics Engineers) (2020)
• 2019
  • A. Volkova, M. Istoan, F. De Dinechin, Th. Hilaire : “Towards Hardware IIR Filters Computing Just Right: Direct Form I Case Study”, IEEE Transactions on Computers, vol. 68 (4), pp. 597-608, (Institute of Electrical and Electronics Engineers) (2019)
• 2018
  • A. Volkova : “FiXiF toolbox : validated numerics for sound digital filter implementations”, 18^th International Symposium on Scientific Computing, Computer Arithmetics and Verified Numerics., Tokyo, Japan (2018)
  • F. Qureshi, A. Volkova, Th. Hilaire, J. Takala : “Multiplierless Processing Element for Non-Power-of-Two FFTs”, (2018)
• 2017
  • A. Lozanova Volkova : “Towards a unified code generator for libms and filters”, thesis, phd defence 09/25/2017, supervision Bajard, Jean-Claude, co-supervision : Hilaire, Thibault, Lauter, Christoph (2017)
  • Th. Hilaire, A. Volkova : “Error analysis methods for the fixed-point implementation of linear systems”, 2017 IEEE International Workshop on Signal Processing Systems (SiPS), Lorient, France, (IEEE) (2017)
  • F. Qureshi, J. Takala, A. Volkova, Th. Hilaire : “Multiplierless Unified Architecture for Mixed Radix−2/3/4 FFTs”, 25^th European Signal Processing Conference, EUSIPCO 2017,, Kos island, Greece (2017)
  • A. Volkova, Ch. Lauter, Th. Hilaire : “Reliable verification of digital implemented filters against frequency specifications”, 24^th IEEE Symposium on Computer Arithmetic (ARITH 24), London, United Kingdom (2017)
• 2016
  • Th. Hilaire, A. Volkova, M. Ravoson : “Reliable fixed-point implementation of linear data-flows”, IEEE International Workshop on Signal Processing Systems (SiPS), Dallas, United States (2016)
  • A. Volkova, Ch. Lauter, Th. Hilaire : “Computing the Worst-Case Peak Gain of Digital Filter in Interval Arithmetic”, 17^th International Symposium on Scientific Computing, Computer Arithmetics and Verified Numerics., Uppsala, Sweden (2016)
• 2015
  • A. Volkova, Th. Hilaire : “FIXED-POINT IMPLEMENTATION OF LATTICE WAVE DIGITAL FILTER: COMPARISON AND ERROR ANALYSIS”, 23^rd European Signal Processing Conference, EUSIPCO 2015, Nice, France (2015)
  • A. Volkova, Th. Hilaire, Ch. Lauter : “Reliable evaluation of the Worst-Case Peak Gain matrix in multiple precision”, ARITH 22 - 22^nd IEEE Symposium on Computer Arithmetic, Lyon, France, pp. 96-103, (IEEE) (2015)
  • A. Volkova, Th. Hilaire, Ch. Lauter : “Determining fixed-point formats for a digital filter implementation using the worst-case peak gain measure”, 2015 49^th Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, United States, pp. 737-741, (IEEE) (2015)