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Biorthogonal decomposition: Difference between revisions
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:<math>Y(i,j) = \sum_k \lambda_k \psi_k(i) \phi_k(j),\,</math> | :<math>Y(i,j) = \sum_k \lambda_k \psi_k(i) \phi_k(j),\,</math> | ||
where ψ<sub>k</sub> is a 'chrono' (a temporal function) and φ<sub>k</sub> a 'topo' (a spatial or detector-dependent function), such that the chronos and topos satisfy the following orthogonality relation | where ψ<sub>k</sub> is a 'chrono' (a temporal function) and φ<sub>k</sub> a 'topo' (a spatial or detector-dependent function)<ref>[[doi:10.1007/BF01048312|N. Aubry, R. Guyonnet and R. Lima, ''Spatiotemporal analysis of complex signals: Theory and applications'', J. Statistical Physics | ||
'''64''', 3-4 (1991) 683]]</ref>, such that the chronos and topos satisfy the following orthogonality relation | |||
:<math>\sum_i{\psi_k(i)\psi_l(i)} = \sum_j{\phi_k(j)\phi_l(j)} = \delta_{kl}.\,</math> | :<math>\sum_i{\psi_k(i)\psi_l(i)} = \sum_j{\phi_k(j)\phi_l(j)} = \delta_{kl}.\,</math> | ||