interpolation of unevenly sampled points

*To*: mathgroup at yoda.physics.unc.edu*Subject*: interpolation of unevenly sampled points*From*: hmadorf at eso.org*Date*: Fri, 22 Jan 93 10:15:53 +0100

Ivan Vesely writes: >Hi, > >I can't seem to get anything from MathSource, so I'll try this group. > > >All I need is a way to resample a set of numbers at specific >intervals. Each x has a corresponding y, but the x's are not evenly >spaced. I'd like to space them evenly (so I can plot a surface using >Mathematica), using some simple interpolation algorithm. I'd write a >routine myself, but the problems sounds so common I thought someone >may already have written it. However, nothing this simple appears to >exist on the Mathematica archive server. > >Does anyone outhere have a "package" that will do this? >--- >Ivan Vesely, Electrical Engineering and Medical Biophysics >University of Western Ontario, vesely at next.heart.rri.uwo.ca The problem of reconstructing a continuous signal from irregular sampling is indeed a common one in signal processing. For a one-dimensional, periodic, band-limited signal it was solved in closed form by the French mathematician Cauchy in 1841. I have written a paper which discusses various sampling problems and which contains a slight generalization of Cauchy's formula. Once the continuos signal is reconstructed, it can be sampled on an arbitrary grid, e.g. a regular one. The conditions of periodicity and band-limitedness are generally not a handicap for real physical signals. Cauchy's formula can be generalized to two dimensions, more precisely to two-dimensional irregular product grids. I am prepared to mail a copy of my paper to everyone who supplies me with his/her postal address. Cheers Hans-Martin Adorf Space Telescope - European Coordinating Facility