Laplace transform of a time domain sampled data MATLAB I have two sets of one second voltage data sampled with 4000Hz and I can plot all the voltage points vs time points 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. 

Now I have simultaneously sampled two data matrix in time domain with this way. One is input to a filter (Vin,t) the other is output (Vout,t). I want to find the transfer function both for amplitude and phase shift. 

How can I take the Laplace transform of this data? Can I do it without converting it to a expressible function like poly-fit?
Since you are sampling a real signal, you can just use the a Fourier transform, the fft function in MATLAB. You can divide the FFT of the output by the input, and then fit a curve to the result to approximate the transfer function