Task

In Fourier transform nuclear magnetic resonance spectroscopy, free induction decay (FID) is the observable Nuclear Magnetic Resonance (NMR) signal generated by non-equilibrium nuclear spin magnetization precessing about the magnetic field. The signal has decayed oscillations and is defined by the equation:

$$y(t)=[sin(2\pi f_ot)]e^{-\alpha t}$$

Decay curves are given by the equation:

$e^{-\alpha t}$ and $-e^{-\alpha t}$

In this exercise, you are given raw data directly from an NMR system and will fit the curve to reduce RMSE and find the unknown coefficients: $f_o$ and $\alpha$.