Laplace transform of equation from "fit"

This is a follow-up on a previous question by myself: Laplace transform of numerical data in MATLAB

I have experimentally collected data, and want to take a Laplace transformation of that. However, laplace() needs a model/equation. I find a fit equation to model my data from:

[up,lo] = envelope(dat);

x = 1:length(up);
x = x';

f = fit(x,up,'poly3');

Then for my Laplace transform I need to I pass the output of

f = fit(x,up,'poly3');

into

syms f
laplace(f)

However at the moment this spits out the transform of f:

laplace(f)

ans =

1/s^2

If this is f

f = 

     Linear model Poly3:
     f(x) = p1*x^3 + p2*x^2 + p3*x + p4
     Coefficients (with 95% confidence bounds):
       p1 =   1.772e-12  (1.593e-12, 1.951e-12)
       p2 =  -2.211e-08  (-2.483e-08, -1.939e-08)
       p3 =   2.847e-05  (1.676e-05, 4.017e-05)
       p4 =      0.2762  (0.2627, 0.2897)

How do I find the Laplace transform of f?

Solution

I'm not familiar with the output of fit, but your symbolic variable at least should be x, as that's your dependent variable. You can then build up the f yourself:

p1 =   1.772e-12;
p2 =  -2.211e-08;
p3 =   2.847e-05;
p4 =      0.2762;

syms x

f = p1*x.^3 + p2*x.^2 + p3*x + p4;

laplace(f)
ans =

(8402860860456175*((50949907131585781563392*s)/5251788037785109375 + 1))/(295147905179352825856*s^2) - 6682337467919863/(151115727451828646838272*s^3) + 26323556995364325/(2475880078570760549798248448*s^4)

fit() gives you a fitobject type variable, which, if I understand its documentation correctly, can be accessed as a structure. This means that you should be able to programmatically use the fitted parameters to build your function of symbolic x.