title: Integration in the Fourier domain for restoration of a function from its slope: comparison of four methods.
abstract: In some measurement techniques the profile, f(x), of a function should be obtained from the data on measured slope f(?)(x) by integration. The slope is measured in a given set of points, and from these data we should obtain the profile with the highest possible accuracy. Most frequently, the integration is carried out by numerical integration methods [Press et al., Numerical Recipes: The Art of Scientific Computing (Cambridge U. Press, Cambridge, 1987)] that assume different kinds of polynomial approximation of data between sampling points. We propose the integration of the function in the Fourier domain, by which the most-accurate interpolation is automatically carried out. Analysis of the integration methods in the Fourier domain permits us to easily study and compare the methods' behavior.
authors.forename: J
authors.initials: J
authors.lastname: Campos
authors.forename: L P
authors.initials: LP
authors.lastname: Yaroslavsky
authors.forename: A
authors.initials: A
authors.lastname: Moreno
authors.forename: M J
authors.initials: MJ
authors.lastname: Yzuel