I would like to fit two parameters $K_1$ and $k_2$ in the problem $f(t)*C_a(t) = C_E(t)$ where $*$ represents the convolution operator and $f(t) = K_1 e^{-k_2 t}$. $C_a(t)$ and $C_E(t)$ are given discrete input data.
I see two alternatives:
- Deconvolve an approximation of $f(t)$ out of $C_E$ using the MATLAB command deconv and thereafter use lsqcurvefit to fit $f(t)$ to the result of the deconvolution.
- Construct another function $g(t) = f(t)*C_a(t)$ and thereafter perform the curvefitting with lsqcurvefit directly with $g(t)$ to minimize $||C_E(t) - g(t)||_2$.
Can anyone tell if I should expect any difference between the solutions obtained from the different approaches?