Efficient (piecewise) linear minmax approximation of digital signals

Marco Dalai, Riccardo Leonardi

Abstract: Efficient geometric algorithms are provided for the linear approximation of digital signals under the uniform norm. Given a set of n points (x/sub i/, y/sub i/), i=1..n, with x/sub i/<x/sub 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 a number of segments, the solution that is l/sub /spl infin// optimal can also be found in O(n) provided that n/k = O(1).