Computing Derivatives of Noisy Signals Using Orthogonal Functions Expansions

Computing Derivatives of Noisy Signals Using Orthogonal Functions Expansions

In many applications noisy signals are measured. These signals has to be filtered and, sometimes, their derivative have to be computed. In this paper a method for filtering the signals and computing the derivatives is presented. This method is based on expansion onto transformed Legender polynomials. Numerical examples demonstrates the efficacy of the method as well as the theoretical estimates.

Quasi-orthogonal expansions for functions in BMO

For {φ_n(x)}, x ε [0,1] an orthonormalsystem of uniformly bounded functions, ||φ_n||_{∞}≤ M

An Algorithm for Computing Derivatives of Noisy Data

Computing Derivatives of Scaling Functions and Wavelets

This paper provides a general approach to the computation, for sufficiently regular multiresolution analyses, of scaling functions and wavelets and their derivatives. Two distinct iterative schemes are used to determine the multiresolution functions, the so-called ‘cascade’ algorithm and an eigenvector-based method. We present a novel development of these procedures which not only encompasses b...

Combinatorial Orthogonal Expansions

so that amn is non-negative. In this paper we give in Theorem 1 and Theorem 2 explicit formulas for anm as a polynomial in the α ′ js, β ′ js and the γ ′ js, which give these theorems. The idea is to represent amn as a generating function of paths, whose weights are products of differences. Monotonicity hypotheses on the coefficients force the weights to be individually positive, these are the ...