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Agenda de l'ENS de Lyon

Robust tools for weighted Chebyshev approximation and applications to digital filter design

Soutenance de thèse

Mercredi 07 déc 2016
14h30
Soutenance de thèse de M. Silviu-Ioan FILIP du LIP sous la direction de M. Guillaume HANROT et sous la co-direction de M. Nicolas BRISEBARRE

Intervenant(s)

Soutenance de thèse de M. Silviu-Ioan FILIP du LIP sous la direction de M. Guillaume HANROT et sous la co-direction de M. Nicolas BRISEBARRE

Description générale
The field of signal processing methods and applications frequently relies on powerful results from numerical approximation. One such example, at the core of this thesis, is the use of Chebyshev approximation methods for designing digital filters.
In practice, the finite nature of numerical representations adds an extra layer of difficulty to the design problems we wish to address using digital filters (audio and image processing being two domains which rely heavily on filtering operations). Most of the current mainstream tools for this job are neither optimized, nor do they provide certificates of correctness. We wish to change this, with some of the groundwork being laid by the present work.
The first part of the thesis deals with the study and development of Remez/Parks-McClellan-type methods for solving weighted polynomial approximation problems in floating-point arithmetic. They are very scalable and numerically accurate in addressing finite impulse response (FIR) design problems. However, in embedded and power hungry settings, the format of the filter coefficients uses a small number of bits and other methods are needed. We propose a (quasi-)optimal approach based
on the LLL algorithm which is more tractable than exact approaches. We then proceed to integrate these aforementioned tools in a software stack for FIR filter synthesis on FPGA targets. The results obtained are both resource consumption efficient and possess guaranteed accuracy properties. In the end, we present an ongoing study on Remez-type algorithms for rational approximation problems (which can be used for infinite impulse response (IIR) filter design) and the difficulties hindering their robustness.
Complément

Amphi B – Site Monod – ENS de lyon

Disciplines