Paper: | SPTM-P2.7 | ||

Session: | Sampling, Extrapolation, and Interpolation | ||

Time: | Tuesday, May 18, 15:30 - 17:30 | ||

Presentation: | Poster | ||

Topic: | Signal Processing Theory and Methods: Sampling, Extrapolation, and Interpolation | ||

Title: | EFFICIENT (PIECEWISE) LINEAR MINMAX APPROXIMATION OF DIGITAL SIGNALS | ||

Authors: | Riccardo Leonardi; University of Brescia | ||

Marco Dalai; University of Brescia | |||

Abstract: | In this work efficient geometric algorithms are provided for the linear approximation of digital signals under the uniform norm. Given a set of $n$ points $(x_i,y_i)_{i=1..n}$, with $x_i<x_j$ if $i<j$, we give a new method to find the optimum linear approximation in $O(n)$. Given also an error bound, we demonstrate how to construct in $O(n)$ a non continuous piecewise solution such that the number $k$ of segments is optimal. Furthermore we show that for such number of segments, the solution that is $l_\infty$ optimal can also be found in $O(n)$ provided that $n/k=O(1)$. | ||

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