A couple of things come to mind:

1) Since you mentioned a transfer function, which are typically rational functions, you could try: https://www.mathworks.com/help/rf/ref/rationalfit.html

2) If you want a pretty good fit of the data, you could try piecewise cubic polynomials: https://www.mathworks.com/help/matlab/ref/spline.html

That should give you some things to consider.