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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.
`
Thanks
Matthias

**Smooth line approximating minima of a data series**,
*Matthias Brennwald* **<=**