  We present a comprehensive study of one method for measuring various
parameters of global modes of oscillation of the Sun. Using velocity data taken
by the Michelson Doppler Imager (MDI), we analyze spherical harmonic degrees l
<= 300. Both current and historical methodologies are explained, and the
various differences between the two are investigated to determine their effects
on global-mode parameters and systematic errors in the analysis. These
differences include a number of geometric corrections made during spherical
harmonic decomposition; updated routines for generating window functions,
detrending timeseries, and filling gaps; and consideration of physical effects
such as mode profile asymmetry, horizontal displacement at the solar surface,
and distortion of eigenfunctions by differential rotation. We apply these
changes one by one to three years of data, and then reanalyze the entire MDI
mission applying all of them, using both the original 72-day long timeseries
and 360-day long timeseries. We find significant changes in mode parameters,
both as a result of the various changes to the processing, as well as between
the 72-day and 360-day analyses. We find reduced residuals of inversions for
internal rotation, but seeming artifacts remain, such as the peak in the
rotation rate near the surface at high latitudes. An annual periodicity in the
f-mode frequencies is also investigated.
