Hilbert Proper Orthogonal Decomposition

The following function is a MATLAB implementation of the Hilbert Proper Orthogonal Decomposition for 2D2C data

HPOD is a MATLAB implementation of the Hilbert Proper Orthogonal Decomposition, a complex-value extension of the standard Proper Orthogonal Decomposition (POD) obtained from the analytic representation of the real-valued dataset prior to its decomposition. The analytic representation is obtained in the form of the analytic signal, computed summing an imaginary component equal to the Hilbert transform of the dataset. The Hilbert transform can be performed in any direction of the dataset, i.e. in time or space. The corresponding modes will correspond to analytic signals in the direction selected. For data including advecting wavepackets, the application in the temporal or spatial direction are demonstrated to be equivalent.

Further details on the decomposition ca be retrieved in the publication:

Raiola, M. and Kriegseis, J. “Hilbert Proper Orthogonal Decomposition: A Tool for Educing Advective Wavepackets from Flow Field Data.” Physical Review Fluids, Mar. 2026, https://doi.org/10.1103/bhlm-qwfh.