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## Re: [Discuss-gnuradio] curve fitting data points

**From**: |
Robert McGwier |

**Subject**: |
Re: [Discuss-gnuradio] curve fitting data points |

**Date**: |
Fri, 23 Dec 2005 07:06:23 -0500 |

**User-agent**: |
Mozilla Thunderbird 1.0.2 (Windows/20050317) |

Chuck, John:

`If we know already, a priori, that the data is from a "smooth function",
``that means (moving from left to right say), the extended line or the
``extended parabola from the last two or last three points respectively is
``always a very good predictor of the next point, then I would suggest
``some form of interpolation. You can get very bad behavior from least
``squares polynomial fitting. If the data is very noisy, then it will
``not meet the smoothness assumption and some kind of least squares
``polynomial fitting will be better than interpolation so long as the
``underlying signal is well matched to the polynomial degree. If it is a
``signal with very poor signal to noise ratio (for example), these fitting
``algorithms are very problematic. Then we need to talk about
``understanding the dynamics that produce the underlying signal so that we
``can have a predictor that we can "correct" with the noisy observations.
``This is like Kalman Filtering/Smoothing. If the underlying dynamics is
``very nonlinear, or not well approximated locally by lines, as well as
``the observation of the signal, then welcome to nonlinear filtering and
``the theory of infinite dimensional functions spaces of the Hilbert type
``and stochastic driven parabolic partial differential equations. I
``needed 4.5 years to get a Ph.D. to understand the latter and that was
``the first time I could write down a real phase locked loop with
``nonlinear observation (sinusoidal phase detector) and understand the
``mechanics.
``JUST SAY NO. Doing all of these kinds of approximations, predictors,
``etc. in the real world, DSP type, control type, etc. is an art form in
``many cases based on some science or assumed knowledge. Chuck's question
``is too wide without further specifics to give it a one answer fits all.
`
Bob
John Aldridge wrote:

cswiger wrote:

`
``
`This is for the mathematicians out there - what is a simple
working algorithm for creating a function model to fit an
arbitrary number of data points.

`
``
`

You could try a least squares fitted polynomial
http://mathworld.wolfram.com/LeastSquaresFittingPolynomial.html
has a description of how it's done.

`
``
`

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