## 5 - Anti-echo file

For aluminum-27 (I = 5/2), which has a positive gyromagnetic ratio,
and for 3QMAS experiment performed with the
two-pulse program,
the antiecho f^{anti-echo}(t_{1}, t_{2}) signal
is related to the cosine S^{cos}(t_{1}, t_{2})
and sine S^{sin}(t_{1}, t_{2}) signals by:

f^{anti-echo}(t_{1}, t_{2})
= S^{cos}(t_{1}, t_{2})
- i*S^{sin}(t_{1}, t_{2}) .

To get -i*S^{sin}(t_{1}, t_{2}) from
i*S^{sin}(t_{1}, t_{2})
obtained previously for the echo signal, we apply
a phase shift of 180° to i*S^{sin}(t_{1}, t_{2}).

**(1)** To this end, we recall the **sin** files by selecting
the menu items:

#### Data/sin

**(2)** We perform twice a 90°-phase correction, that is,
we select twice the menu items:

#### Process/Phase/Phase Correct

We obtain exp(i*Pi/2)*exp(i*Pi/2)*i*S^{sin}(t_{1}, t_{2}),
that is, -i*S^{sin}(t_{1}, t_{2}).

**Figure 1**
Intensity plot of the -i-phase corrected sine file of 2D MQMAS data:

Both axes of the 2D map are labeled in time units.

**(3)** We add the S^{cos}(t_{1}, t_{2})
file with -i*S^{sin}(t_{1}, t_{2}) file to
build the anti-echo file f^{anti-echo}(t_{1}, t_{2})
by selecting the menu items:

#### Data/Add Data...

A window appears, in which we add **sin** to **cos**.
(The two shadowed rectangles are in fact pop-up lists of filenames,
clicking on them allows us to choose files.) We save the resulting
file with **antiecho** filename.

Three 2D files corresponding to the 2D anti-echo MQMAS data appear on the desktop:

- antiecho -> 2D Data - Stacked Plot
- antiecho -> 2D Data - Line Contour Plot
- antiecho -> 2D Data - Intensity Plot

**Figure 2**
Intensity plot of the 2D anti-echo MQMAS data:

Both axes of the 2D map are labeled in time units.

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