Exercise: Parameters of an FID Signal

In this exercise, we will find the optimized parameters of a raw FID signal.

We'll cover the following

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

Decay curves are given by the equation:

eαte^{-\alpha t} and eαt-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: fof_o and α\alpha.

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