Hi David!

You could also try Loess : `https://resources.wolframcloud.com/FunctionRepository/resources/Loess/ , read that post about SMOOTHING splines https://mathematica.stackexchange.com/questions/33206/implementation-of-smoothing-splines-function

Bernstein approximation is another possibility. It depends on your goal and hypotheses...

Regards,

Claude

Hi David,

GaussianFilter is a standard smoothing method for data lists. Its the discrete version of smoothing a function with a moving average produced by the convolution of a piecewise continuous function with a Gaussian kernel ~ Exp[-x^2/sigma] of the normal distributiion.

Smoothing an Interpolation With a Gaussian Filter

This is a noisy data set from x|->(x/3)^2 Sin[2[Pi] x/22].

noisyf =  
  Array[({#, (#/3.0)^2 Sin[2 \[Pi] #/22] + 3.5 #  RandomReal[] } &), {56}, 0];

ListPlot[noisyf  ]

The data set is smoothed

 smoothf[s_]:= 
  smoothf[s] = 
(Transpose[  {#[[1]],  GaussianFilter[#[[2]], s] }] &)[Transpose[noisyf]];

Manipulate[
 Show[{ ListPlot[noisyf  , PlotStyle -> {Red, Opacity[0.5]},  Joined -> True], 
   ListPlot[smoothf[n], PlotStyle -> {Blue}, Joined -> True]}],
 {n,   Range[0, 7, 0.5]}]

Regards Roland