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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