Extraction of spectral information from a short-time signal using filter-diagonalization: Recent developments and applications to semiclassical reaction dynamics and nuclear magnetic resonance signals

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Abstract
Filter-diagonalization [M. R. Wall and D. Neuhauser, J. Chem. Phys. 102, 8011 (1995)] is a new method for extracting frequencies and damping constants from a short-time segment of any time-dependent signal, whether of quantum origin or not. The method is efficient and able to handle signals with, e.g., millions of (possibly overlapping) frequencies, since it concentrates on specific spectral ranges. The method was shown to be a powerful tool for extracting eigenstates and normal-modes, and for reducing propagation times, in several recent works by us, by Mandelshtam and Taylor (who recently introduced the box filter) and by other groups. Here we extend the method in several directions: first, we show how it can be used with a filter of any form. Next, we show how the methodology may be extended to treat multi-dimensional signals, of the type that appears, e.g., in 2-D nuclear magnetic resonance(NMR). Finally, we exemplify the performance of the various filters for two types of signals where the time-reduction property is potentially quite important: 1D NMR and a correlation function from a semiclassical propagation (due to Grossmann) analyzed recently with a box filter. Significant reduction in required signal lengths, compared with direct Fourier transform, are found in both cases.