Remove Undercuts

Remove undercuts from an x,y data set. This can make it possible to interpolate a data set that otherwise could not be.

function [xout,yout]=undercutRemoval(xin,yin,varargin)

Remove undercuts from an x,y dataset.

An undercut or uppercut (collectively, undercuts) in an x,y data set is one or more data points whose x values are less than or equal to previous x-values. In other words, an undercut is a data segment that "curves back on itself". Data sets with undercuts cannot be interpolated with interp1(). Removing the undercuts will make the data interpolate-able. The user may specify one of four methods, or not. Method 1 is the default. Figure below shows the difference between methods.

• Method 1: Remove down-going undercuts by a two-pass approach
• Method 2: Remove up-going uppercuts by a two-pass approach
• Method 3: Remove under- and uppercuts, proceeding from beginning to end
• Method 4: Remove under- and uppercuts, proceeding from end to beginning

See undercutRemovalTest.m for a demonstration of the function and example of the different methods. The demonstration program uses data in file undercutdata.txt.

I beleive the following statements are true, but have not proved them:

• Method 1 has an upward bias, i.e. mean(yout)>=mean(yin)
• Method 2 has a downward bias, i.e. mean(yout)<=mean(yin)
• Methods 3,4 are unbiased, i.e. exp.val(mean(yout))=exp.val.(mean(yin))