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I want to numerically integrate a set of discrete values that keep arriving at constant time intervals. Which interpolation method do I choose? how to reduce the ringing artifacts if I use cubic spline interpolation?

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Could you please provide some context and clarify what you need? The title says "interpolate" but the question itself says "numerically integrate"; the two are different operations. –  whuber Jun 7 '12 at 15:44
    
and I guess what you really want to do is extrapolate. Do you have spatial data or not? –  johanvdw Jun 7 '12 at 18:47
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