Spectral POD

Aaron Towne et al. have posted a new paper on spectral proper orthogonal decomposition (SPOD) on arXiv.   SPOD refers to space-time POD modes in a statistically stationary process, which can be readily estimated from the eigensystem of the cross-spectral-density matrix (in frequency space).  This form of POD goes back to the early work of John Lumley, Bill George, Joel Delville, Mark Glauser and other researchers, but has been largely overshadowed by 'snapshot' POD modes based on a space-only decomposition.  The paper derives both old and new results about SPOD, and highlights some nice properties of SPOD including a close relation with DMD, Koopman modes, and resolvent analysis.

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