Smoothing of Noisy Data

The function SavGo 1, m performs a Savitzky-Golay smoothing. The parameters are the x- and y-vectors, the number (n) of neighbouring left or right data points that are used for one polynomial fit (i.e. if n= 5, 2n+l=ll data points are fitted) and the degree (ndf of the polynomial to be fitted. 

It is worthwhile discussing the function SavGo 1. m in some detail. There are some interesting aspects that can illustrate a few issues of numerically reliable programming. 

It is tempting to write a routine such as SavGo l bad. m, to perform the Savitzky-Golay filtering, but we will show its numerical weakness. F is built up by the appropriate range of x-values and used to calculate the polynomial coefficients as a=F y( i-n i+n), see e.g. equation (4.31). 

These messages indicate that the rank of the matrix F is not 5, as expected for the case of a fourth order polynomial, but only 4. Why is this the case  

This is perfectly ok. However, towards the end of the loop, the matrix F looks like 

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