  Studies by video microscopy on fluctuating colloids measure the real-space
cross-correlations in particle motion. This set of correlations is then treated
as a matrix, in order to study the spectrum and mode structure. We show that in
general the modes are modified by the truncation of the full real-space
correlations. We perform a theoretical analysis of the truncation, find the
boundary conditions imposed by the truncation, and propose practical windowing
strategies to eliminate artefacts. We study the problem from various
perspectives, to compile a survey for experimentalists.
