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Difference of cross-spectral densities

“…In particular, while the sum of two cross-spectral densities (CSDs) simply accounts for the superposition of two uncorrelated fields, their difference, generally speaking, does not have a clear physical meaning and does not represent another CSD. In fact, its use has caused discussion [7,8]. The problem of finding conditions under which the difference of two CSDs is a CSD itself could be tackled by using the theory of reproducing kernel Hilbert spaces [9].…”