Harmonic inversion

Main J, Mandelshtam V A, Wunner G and Taylor H S 1998 Harmonic inversion as a general method for periodic orbit quantization Nonlinearity1015... 

Grossmann F, Mandelshtam V A, Taylor H S and Briggs H S 1997 Harmonic inversion of semiclassical short time signals Chem. Phys. Lett. 279 355... 

V. A. Mandelshtam,/. Chem. Phys., 108, 9999 (1998). Harmonic Inversion of Time Cross-... 

Periodic Orbit Quantization by Harmonic Inversion of Gutzwiller s Recurrence Function. 

Harmonic Inversion of Semiclassical Short Time Signals. 

Strategies for Spectral Analysis in Dissipative Systems Filter Diagonalization in the Lanczos Representation and Harmonic Inversion of the Chebychev Order Domain Autocorrelation Function. 

This demonstrates the equivalence between the harmonic inversion and the moment problem [2],... 

There is more to the presented strategy than the equivalence Eq. (308). To illuminate an additional advantage of the presented formalism, we shall analyze its application to the quantification problem (harmonic inversion) with the goal of determining the key spectral parameters uk, dk. To this end, we rewrite the matrix equation (302) as follows ... 

In indirect methods, the resonance parameters are determined from the energy dependence of the absorption spectrum. An important extra step — the non-linear fit of (t E) to a Lorentzian line shape — is required, in addition to the extensive dynamical calculations. The procedure is flawless for isolated resonances, especially if the harmonic inversion algorithms are employed, but the uncertainty of the fit grows as the resonances broaden, start to overlap and melt into the unresolved spectral background. The unimolecular dissociations of most molecules with a deep potential well feature overlapping resonances [133]. It is desirable, therefore, to have robust computational approaches which yield resonance parameters and wave functions without an intermediate fitting procedure, irrespective of whether the resonances are narrow or broad, overlapped or isolated. 

This type of problem, known as quantification, spectral analysis or harmonic inversion, can be solved by the FPT for any theoretically generated/ simulated time signals or experimentally measured data. The obtained solutions gain in their value by the manner in which the accompanying and unavoidable problem of noise is solved. This is done by unequivocal... 

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