## 4 - 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 echo f^{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^{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
S^{sin}(t_{1}, t_{2}), we must introduce
the complex number i, performed in fact with a phase correction.

**(1)** We add a 90°-phase shift to the **sin** file
by selecting the menu items:

#### Process/Phase/Parameters...

The **Phase Correction Parameter** form appears.
In the text field **Zero** of **2nd Dimension**
of **2D Data** area, we type 90. The other fields are zeroed.

**(2)** We apply the i-phase correction by selecting the menu items:

#### Process/Phase/Phase Correct

We obtain exp(i*Pi/2)*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 to
i*S^{sin}(t_{1}, t_{2}) file to build the echo file
f^{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 **echo** filename.

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

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

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

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