Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the nature of spectral proper orthogonal decomposition and related
  modal decompositions   The spectral proper orthogonal decomposition (SPOD) is a newly introduced
extension of snapshot POD that recently gained attention but also brought up
controversial issues. Within the first proposition, the approach was mainly
presented in a methodological and phenomenological way. The present paper will
detail the relations between SPOD and related POD approaches from an analytical
point of view. To allow for a better grasp of the approach, an alternative
formulation is given that is based on the classic idea from Lumley that was
carried on by George. As will be shown, SPOD is closely related to POD with a
prior segmentation and Fourier transformation in time. Moreover, the SPOD is
shown to be equivalent to snapshot POD combined with time delay embedding.

10
The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
26
The categories of this paper are: bayes-an
2
The categories of this paper are: math
21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
22
The categories of this paper are: chao-dyn
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The categories of this paper are: eess
9
The categories of this paper are: nlin