A risk analyst attempting to model the tail of a loss distribution using EVT divides...

The risk analyst is using the block maxima approach. The data points that result will then be used to fit a GEV distribution.

Expected shortfall refers to the expected losses beyond a specified threshold. The peaks-over-threshold approach is an alternative approach to the block maxima approach, and involves considering exceedances above a threshold. Fourier transformation is not relevant in this context, and is a non-sensical option.