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Dynamic mode decomposition (DMD) is a powerful and increasingly popular toolfor performing spectral analysis of fluid flows. However, it requires data thatsatisfy the Nyquist-Shannon sampling criterion. In many fluid flow experiments,such data are impossible to capture. We propose a new approach that combinesideas from DMD and compressed sensing. Given a vector-valued signal, we takemeasurements randomly in time (at a sub-Nyquist rate) and project the data ontoa low-dimensional subspace. We then use compressed sensing to identify thedominant frequencies in the signal and their corresponding modes. Wedemonstrate this method using two examples, analyzing both an artificiallyconstructed test dataset and particle image velocimetry data collected from theflow past a cylinder. In each case, our method correctly identifies thecharacteristic frequencies and oscillatory modes dominating the signal, provingthe proposed method to be a capable tool for spectral analysis usingsub-Nyquist-rate sampling.

Toward compressed DMD: spectral analysis of fluid flows using sub-Nyquist-rate PIV data