  The ideal spectral averaging method depends on one's science goals and the
available information about one's data. Including low-quality data in the
average can decrease the signal-to-noise ratio (SNR), which may necessitate an
optimization method or a consideration of different weighting schemes. Here, we
explore a variety of spectral averaging methods. We investigate the use of
three weighting schemes during averaging: weighting by the signal divided by
the variance ("intensity-noise weighting"), weighting by the inverse of the
variance ("noise weighting"), and uniform weighting. Whereas for
intensity-noise weighting the SNR is maximized when all spectra are averaged,
for noise and uniform weighting we find that averaging the 35-45% of spectra
with the highest SNR results in the highest SNR average spectrum. With this
intensity cutoff, the average spectrum with noise or uniform weighting has ~95%
of the intensity of the spectrum created from intensity-noise weighting. We
apply our spectral averaging methods to GBT Diffuse Ionized Gas (GDIGS)
hydrogen radio recombination line (RRL) data to determine the ionic abundance
ratio, y+, and discuss future applications of the methodology.
