#### Spline

The Spline filter option allows you to smooth the data by fitting a smoothing spline to it. The Smoothing Parameter value controls the amount of smoothing. However, if you want to use the "optimal" value computed by Generalized Cross-Validation (GCV) technique, you should set this value to 0. The Spline filter option is a 3D filtering option. This means deviations in all directions perpendicular to the line are affected.

How It Works: The spline filter fits a spline approximation to the data and resamples it. This way, it smoothes the data in all directions, not just radially or perpendicularly to the workplane. The fitted spline is a natural smoothing spline. It has a parameter that mediates between interpolating the data—trying to pass through every data point, which would retain all of the oscillations—and approximating the data with a successively smoother spline, in the sense that the oscillations are damped. The two limits of the smoothing parameter yield an interpolator (with all of the original oscillations) and a straight line. A zero value for the spline filter results in a spline that (asymptotically) minimizes the expected mean square error between it and the underlying, unknown, curve. You should usually use the zero value since this removes the noise yet leaves the underlying shape reasonably intact.

Math Information: Since the range of interest for the actual (internal) smoothing parameter lambda usually involves small values, the Construct Filter Feature dialog box accepts

-log10(lambda).

So, instead of 1-e-6, you just type 6. You get more smoothing for smaller values of the smoothing parameter. For example, a value of 5 for the spline filter would give you more smoothing than a value of 6.