  These are lecture notes for the lecture "Statistical Treatment, Fourier and
Modal Decompositions", given at the VKI Lecture series "Fundamentals and Recent
Advances in Particle Image Velocimetry and Lagrangian Particle Tracking". The
course was held at the von Karman Institute for fluid dynamics from 15 November
to 18 November 2021. This lecture provides a guided tour through the processing
of data acquired via image velocimetry. Far from being an exhaustive account of
the field, which would require an entire course on its own, the scope is to
provide a hands-on tutorial. This begins with basic statistical treatment,
briefly reviews frequency and modal analysis, and conclude with more advanced
research topics such as multiscale modal decompositions and nonlinear
dimensionality reduction. The material covered should hopefully propel
newcomers into the subject while remaining of interest to experienced
practitioners. All the codes related to this lecture are made available on a
github repository.
