Re: [Discuss-gnuradio] curve fitting data points

[Robert McGwier]

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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