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- W2560743375 abstract "The field of signal processing methods and applications frequentlyrelies on powerful results from numerical approximation. One suchexample, at the core of this thesis, is the use of Chebyshev approximationmethods for designing digital filters.In practice, the finite nature of numerical representations adds an extralayer of difficulty to the design problems we wish to address using digitalfilters (audio and image processing being two domains which rely heavilyon filtering operations). Most of the current mainstream tools for thisjob are neither optimized, nor do they provide certificates of correctness.We wish to change this, with some of the groundwork being laid by thepresent work.The first part of the thesis deals with the study and development ofRemez/Parks-McClellan-type methods for solving weighted polynomialapproximation problems in floating-point arithmetic. They are veryscalable 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 andother methods are needed. We propose a (quasi-)optimal approach basedon the LLL algorithm which is more tractable than exact approaches.We then proceed to integrate these aforementioned tools in a softwarestack for FIR filter synthesis on FPGA targets. The results obtainedare both resource consumption efficient and possess guaranteed accuracyproperties. In the end, we present an ongoing study on Remez-type algorithmsfor rational approximation problems (which can be used for infinite impulseresponse (IIR) filter design) and the difficulties hindering their robustness." @default.
- W2560743375 created "2016-12-16" @default.
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- W2560743375 date "2016-12-07" @default.
- W2560743375 modified "2023-09-23" @default.
- W2560743375 title "Robust tools for weighted Chebyshev approximation and applications to digital filter design" @default.
- W2560743375 hasPublicationYear "2016" @default.
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