A procedure based on proper orthogonal decomposition for time-frequency analysis of time series

A procedure for time-frequency analysis of time series is described, which is mainly inspired by singular-spectrum analysis, but it presents some modifications that allow checking the convergence of the results and extracting the detected spectral components through a more efficient technique, especially for real applications. This technique is adaptive, completely data dependent with no a priori assumption and applicable to non-stationary signals. The principal components are extracted from the signals and sorted by their fluctuating energy; moreover, the time variation of their amplitude and frequency is characterized. The technique is first assessed for multi-component computer-generated signals and then applied to experimental velocity signals. The latter are acquired in proximity of the wake generated from a triangular prism placed vertically on a plane, with a vertical edge against the incoming flow. From these experimental signals, three different spectral components, connected to the dynamics of different vorticity structures, are detected, and the time histories of their amplitudes and frequencies are characterized.