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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.


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


has a description of how it's done.

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