I have a set of $N$ 2D points, namely ${(t_i,x_i)}^N_{i=1}$. Those points should hold the equation: $x(t) = Ae^{{-\alpha}t}\sin({\omega}t+\phi)$, Where A,$\alpha,\omega$ and $\phi$ are constants. Since these points are gained from physical measurements, they include errors and does not hold the above equation. As a result, I need to find the 'closest' function (of this form) to those points, specifically to find the above constants. Is there a way to find such a function? (via an approximation of course) maybe using the least-squares method? if so, how?
Thanks a lot in advance!
Omri