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