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The FID is a complex data set comprising the signals from the detectors along both the *x* and *y* axes:
*S* = *S _{x}* +

(

The Fourier transform also produces a complex spectrum. The real component of the spectrum is the *absorption* spectrum, which shows peaks at the Larmor
frequencies for the various spins. The width of the peak is determined by the *effective* *T _{2}* value:

*w* = ( π *T _{2}** )

The width of the peak (*w*) is characterized by measuring its full width at a height half way between the baseline and the peak.
(FWHM = full width at half maximum).

The imaginary component of the spectrum is the *dispersion* spectrum, which is the derivative of the absorption spectrum.

This behavior is shown in the graph below. Enter a value for *T _{2}** between 0.01 and 1 sec. Select with the absorption or dispersion signal or
both and observe the shapes of the peaks.

If the acquisition of the FID begins with the bulk magnetization perfectly aligned along the *y* axis at *t* = 0, then the *S _{x}* signal
(a cosine function) begins at a maximum and the

If the bulk magnetization does not begin perfectly aligned along the *y* axis at *t* = 0, then the absorption and
dispersion spectra are mixed.

The exercise below illustrates this effect. The simulation at the left shows the bulk magnetization as viewed along the *z* axis, which allows one to easily
observe the phase angle (the angle off the *y* axis) for the bulk magnetization at *t* = 0. There are numerous experimental issues that can cause this angle
to differ from zero. The time required for a pulse is one source of a non-zero phase angle.

- Specify a phase angle, click on
*Reset*, and observe the initial position of the bulk magnetization.

Try different values for the angle and observe the starting alignment of the bulk magnetization. - Run the simulation and collect the FID. Observe where the FID signal begins and how that starting point depends upon the phase angle.

(Only*S*is shown in the graph.)_{x} - After the FID has been recorded, plot the spectrum, which displays only the real component of the spectrum.

Observe how the absorption and dispersion spectra are mixed. - Vary the
*Phase Correction*until the displayed spectrum is the pure absorption spectrum (symmetric, positive peak).

This type of phase correction is a routine part of analyzing NMR data.

Answer the following questions by carefully observing the simulation and adjusting the phase correction.

- For what initial angle does one obtain the pure absorption spectrum?
- For what initial angle does one obtain the pure dispersion spectrum?
- For what initial angle does the spectrum contain a perfect, upside-down peak? (Why does this occur?)
- When the phase correction has been applied to obtain the absorption spectrum, how does the value of the phase correction compare with the initial angle?

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Inversion Recovery Experiment

The NMR Spectrum

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