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Smooth line approximating minima of a data series

From: Matthias Brennwald
Subject: Smooth line approximating minima of a data series
Date: Wed, 24 Feb 2010 09:04:07 +0100

Dear all

Consider a series of data values that reflect a smooth function (e.g. a low-degree polynomial), but there might be additional features in the data (e.g. narrow peaks or noise). I'd like to fit a polynomial to this data, whereby this polynomial reflects a smooth approximation of the minima of the raw data (I call this the "base line"). The following might help to illustrate what I'm trying to accomplish:

    x = [-1:0.01:1]; % x-axis values
p = [-3 2 1 0]; yp = polyval (p,x); % make up a polynomial reflecting the "base line" for illustration
    y = yp + rand(size(x)); % this would be the raw data
plot (x,y,x,yp); legend ('raw data','base line') % plot the raw data and the polynomial for illustration

Has anyone an idea of how to accomplish this? Are there standard methods? I'd appreciate any hints.


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