# Taking numerical Laplace transform of a tabulated data with Mathematica?

I am relatively new to the use of Mathematica in the context of numerical evaluations, therefore I would greatly appreciate a detailed answer and would like to express my gratitude towards any help in advance. Here is my question:

I have a list of data, {{t1,f1},{t2,f2},{t3,f3},...,{tn,fn}}, and I want to take a Laplace transform of this data. It would also be nice to see a plot of the data after the transformation.

• The discrete equivalent of the Laplace transform is the Z-Transform. This 16755 answer shows how you can implement a Z-transform using Sum on discrete data. This assumes uniform sampling of your data. As far as plotting it, just use 'ListPlot[transformedData]`. – N.J.Evans Oct 1 at 12:24
• Could I also suggest that you may wish to take the Fourier transform? Some details are given here. Taking the Laplace transform involves integrating your function when multiplied by Exp[-s t] where s may take any complex value. This means that you have a two parameter plot of the transform to consider (one axis real values, another imaginary values). As NJ Evans states for sampled data the Z-Transform is more standard. – Hugh Oct 1 at 18:00
• As noted, by N.J.Evans and Hugh the numerical Laplace transform is not widely used. It is difficult to advise on your best way forward without seeing the data or knowing the application. – mikado Oct 1 at 20:48