Laplace transform of a time domain sampled data

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I have a one second voltage data sampled with 4000Hz and I can plot the voltage vs time in MATLAB. So it means I have a data matrix with with length of 4000 one column for the time in seconds the other for the voltage.

How can I take the Laplace transform of this data? Can I do it without converting it to a expressible function like poly-fit?

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divide fft of output by fft of input?

data may be noisey, may need windowing or trimming to avoid fft's spectral spreading with non exact periodic record

much more sophisticated system identification tools exist but I did just that to fit to a low order model in Python: https://stackoverflow.com/questions/42407051/suggestions-for-fitting-noisy-exponentials-with-scipy-curve-fit/42500533#42500533enter image description here