Update PSSS data

PSSS-data.md

@@ -13,9 +13,31 @@ All PSSS data channels are listed in the following sheet:
 | SARFE10-PSSS059:**AVG*** | Data calculated from average (not single shot) spectra |
 
 ## Concepts
-**Width and centre**
+**Width and center**
 
-Spectral width and central energy are calculated by both a Gaussian fit and directly from the spectra.  Depending on the spectral intensity profile, the Gaussian may return a poor representation of the spectra, for example for a spectral with a long tail.
+Spectral width and central energy are calculated by both a Gaussian fit and directly from the spectra.  Depending on the spectral intensity profile, the Gaussian may return a poor representation of the spectra, for example for a spectral with a long tail.  Before both fitting and calculation the spiky single shot spectra are smoothed with a savgol filter:
+
+```
+# smooth the spectrum with savgol filter with 51 window size and 3rd order polynomial
+smoothed_spectrum = scipy.signal.savgol_filter(spectrum, 51, 3)
+```
+
+The standard deviation and center of mass for the spectra are calculated as:
+
+``` 
+smoothed_spectrum_normed = smoothed_spectrum / np.sum(smoothed_spectrum)
+spectrum_com = np.sum(axis * smoothed_spectrum_normed)
+spectrum_std = np.sqrt(np.sum((axis - spectrum_com) ** 2 * smoothed_spectrum_normed))
+```
 
 **Relative energy spread**
-Channels ending in **RES** are a measure of the relative energy spread in units of &#8240.  For FIT data the relative energy spread is calculated as: $$2.355*\sigma\div\mu$$
+
+Channels ending in **RES** are a measure of the relative energy spread in units of ‰.  For **FIT** data the relative energy spread is calculated as:
+
+$`\frac{2.355*\sigma}{\mu}`$
+
+and for directly calculated values (**SPECT**):
+
+$`\frac{2.355*RMS}{\text{Center of mass}}`$
+
+where the factor or 2.355 is included to allow these values to be comparable.