I am reading about NMR, and from what I'm understanding it should give information on the transition energies in the spectrum of the nuclear spin in a magnetic field.
What I don't understand is how this information is accessed during the experiment.
The NMR measurement is usually described as: a magnetic field $H_0$ polarizes the sample along a certain direction; then a short pulse of an auxiliary magnetic field alters the direction of the magnetization, which then starts to precess around $H_0$. The changing magnetization induces a current the coils of the NMR machine which is measured and gives the precession frequency. The magnetization gradually aligns with $H_0$, leading to a diminishing current intensity. The decrease in intensity gives the nuclear relaxation rate.
A first question is: is the above description of the measurement correct?
A second question is: How do we extract the information on the energy levels $E_m$, or their separation, from the precession frequency? If not from the precession, how is the energy spectrum obtained?